Sunday, May 27, 2007
Traveling Waves
Traveling waves
Waves that remain in one place are called standing waves—e.g. vibrations on a violin string. Waves that are moving are called traveling waves, also called progressive waves, and have a disturbance that varies both with time t and distance z.
Waves that remain in one place are called standing waves—e.g. vibrations on a violin string. Waves that are moving are called traveling waves, also called progressive waves, and have a disturbance that varies both with time t and distance z.
Propagation Through Strings
Propagation through strings
The speed of a wave traveling along a string (v) is directly proportional to the square root of the tension (T) over the linear density (μ).
The speed of a wave traveling along a string (v) is directly proportional to the square root of the tension (T) over the linear density (μ).
Transmission Medium
Transmission medium
The medium that carries a wave is called a transmission medium. It can be classified into one or more of the following categories:
1. A linear medium if the amplitudes of different waves at any particular point in the medium can be added.
2. A bounded medium if it is finite in extent, otherwise an unbounded medium.
3. A uniform medium if its physical properties are unchanged at different locations in space.
4. An isotropic medium if its physical properties are the same in different directions.
The medium that carries a wave is called a transmission medium. It can be classified into one or more of the following categories:
1. A linear medium if the amplitudes of different waves at any particular point in the medium can be added.
2. A bounded medium if it is finite in extent, otherwise an unbounded medium.
3. A uniform medium if its physical properties are unchanged at different locations in space.
4. An isotropic medium if its physical properties are the same in different directions.
Mathematical Description of Sound
Mathematical description
Waves can be described mathematically using a series of parameters. The amplitude of a wave (commonly notated as A, or another letter) is a measure of the maximum disturbance in the medium during one wave cycle. (the maximum distance from the highest point of the crest to the equilibrium). In the illustration to the right, this is the maximum vertical distance between the baseline and the wave.
The units of the amplitude depend on the type of wave — waves on a string have an amplitude expressed as a distance (meters), sound waves as pressure (pascals) and electromagnetic waves as the amplitude of the electric field (volts/meter). The amplitude may be constant (in which case the wave is a c.w. or continuous wave), or may vary with time and/or position. The form of the variation of amplitude is called the envelope of the wave.
The wavelength (denoted as λ) is the distance between two sequential crests (or troughs). This generally has the unit of meters; it is also commonly measured in nanometers for the optical part of the electromagnetic spectrum.
Waves can be represented by simple harmonic motion.
The period T is the time for one complete cycle for an oscillation of a wave. The frequency f (also frequently denoted as ν) is how many periods per unit time (for example one second) and is measured in hertz. In other words, the frequency and period of a wave are reciprocals of each other.
The angular frequency ω represents the frequency in terms of radians per second.
There are two velocities that are associated with waves. The first is the phase velocity, which gives the rate at which the wave propagates.
The second is the group velocity, which gives the velocity at which variations in the shape of the wave's amplitude propagate through space. This is the rate at which information can be transmitted by the wave. It is given by
Waves can be described mathematically using a series of parameters. The amplitude of a wave (commonly notated as A, or another letter) is a measure of the maximum disturbance in the medium during one wave cycle. (the maximum distance from the highest point of the crest to the equilibrium). In the illustration to the right, this is the maximum vertical distance between the baseline and the wave.
The units of the amplitude depend on the type of wave — waves on a string have an amplitude expressed as a distance (meters), sound waves as pressure (pascals) and electromagnetic waves as the amplitude of the electric field (volts/meter). The amplitude may be constant (in which case the wave is a c.w. or continuous wave), or may vary with time and/or position. The form of the variation of amplitude is called the envelope of the wave.
The wavelength (denoted as λ) is the distance between two sequential crests (or troughs). This generally has the unit of meters; it is also commonly measured in nanometers for the optical part of the electromagnetic spectrum.
Waves can be represented by simple harmonic motion.
The period T is the time for one complete cycle for an oscillation of a wave. The frequency f (also frequently denoted as ν) is how many periods per unit time (for example one second) and is measured in hertz. In other words, the frequency and period of a wave are reciprocals of each other.
The angular frequency ω represents the frequency in terms of radians per second.
There are two velocities that are associated with waves. The first is the phase velocity, which gives the rate at which the wave propagates.
The second is the group velocity, which gives the velocity at which variations in the shape of the wave's amplitude propagate through space. This is the rate at which information can be transmitted by the wave. It is given by
Polarization of Sound
Polarization
A wave is polarized if it can only oscillate in one direction. The polarization of a transverse wave describes the direction of oscillation, in the plane perpendicular to the direction of travel. Longitudinal waves such as sound waves do not exhibit polarization, because for these waves the direction of oscillation is along the direction of travel. A wave can be polarized by using a polarizing filter.
Examples of waves include:
Ocean surface waves, which are perturbations that propagate through water.
Radio waves, microwaves, infrared rays, visible light, ultraviolet rays, x-rays, and gamma rays make up electromagnetic radiation. In this case, propagation is possible without a medium, through vacuum. These electromagnetic waves travel at 299,792,458 m/s in a vacuum.
Sound - a mechanical wave that propagates through air, liquid or solids.
Seismic waves in earthquakes, of which there are three types, called S, P, and L.
Gravitational waves, which are fluctuations in the gravitational field predicted by general Relativity. These waves are nonlinear, and have yet to be observed empirically.Inertial waves, which occur in rotating fluids and are restored by the Coriolis effect
A wave is polarized if it can only oscillate in one direction. The polarization of a transverse wave describes the direction of oscillation, in the plane perpendicular to the direction of travel. Longitudinal waves such as sound waves do not exhibit polarization, because for these waves the direction of oscillation is along the direction of travel. A wave can be polarized by using a polarizing filter.
Examples of waves include:
Ocean surface waves, which are perturbations that propagate through water.
Radio waves, microwaves, infrared rays, visible light, ultraviolet rays, x-rays, and gamma rays make up electromagnetic radiation. In this case, propagation is possible without a medium, through vacuum. These electromagnetic waves travel at 299,792,458 m/s in a vacuum.
Sound - a mechanical wave that propagates through air, liquid or solids.
Seismic waves in earthquakes, of which there are three types, called S, P, and L.
Gravitational waves, which are fluctuations in the gravitational field predicted by general Relativity. These waves are nonlinear, and have yet to be observed empirically.Inertial waves, which occur in rotating fluids and are restored by the Coriolis effect
Characteristic of Sound
Characteristic
Periodic waves are characterized by crests (highs) and troughs (lows), and may usually be categorized as either longitudinal or transverse. Transverse waves are those with vibrations perpendicular to the direction of the propagation of the wave; examples include waves on a string and electromagnetic waves. Longitudinal waves are those with vibrations parallel to the direction of the propagation of the wave; examples include most sound waves.
When an object bobs up and down on a ripple in a pond, it experiences an orbital trajectory because ripples are not simple transverse sinusoidal waves.
Ripples on the surface of a pond are actually a combination of transverse and longitudinal waves; therefore, the points on the surface follow orbital paths.
All waves have common behavior under a number of standard situations.
All waves can experience the following:
Reflection - wave direction change from hitting a reflective surface
Refraction - wave direction change from entering a new medium
Diffraction - wave circular spreading from entering a hole of comparable size to their
wavelengths
Interference - superposition of two waves that come into contact with each other (collide)
Dispersion - wave splitting up by frequency
Rectilinear propagation - wave movement in straight lines
Periodic waves are characterized by crests (highs) and troughs (lows), and may usually be categorized as either longitudinal or transverse. Transverse waves are those with vibrations perpendicular to the direction of the propagation of the wave; examples include waves on a string and electromagnetic waves. Longitudinal waves are those with vibrations parallel to the direction of the propagation of the wave; examples include most sound waves.
When an object bobs up and down on a ripple in a pond, it experiences an orbital trajectory because ripples are not simple transverse sinusoidal waves.
Ripples on the surface of a pond are actually a combination of transverse and longitudinal waves; therefore, the points on the surface follow orbital paths.
All waves have common behavior under a number of standard situations.
All waves can experience the following:
Reflection - wave direction change from hitting a reflective surface
Refraction - wave direction change from entering a new medium
Diffraction - wave circular spreading from entering a hole of comparable size to their
wavelengths
Interference - superposition of two waves that come into contact with each other (collide)
Dispersion - wave splitting up by frequency
Rectilinear propagation - wave movement in straight lines
Introduction/Definition of Wave
Introduction / Definitions
Agreeing on a single, all-encompassing definition for the term wave is non-trivial. A vibration can be defined as a back-and-forth motion around a point of rest (e.g. Campbell & Greated, 1987: 5) or, more generally, as a variation of any physical property of a system around a reference value. However, defining the necessary and sufficient characteristics that qualify a phenomenon to be called a wave is, at least, flexible.
The term is often understood intuitively as the transport of disturbances in space, not associated with motion of the medium occupying this space as a whole. In a wave, the energy of a vibration is moving away from the source in the form of a disturbance within the surrounding medium (Hall, 1980: 8). However, this notion is problematic for a standing wave (e.g. a wave on a string), where energy is being transformed rather than moving, or for electromagnetic / light waves in a vacuum, where the concept of medium does not apply.
For such reasons, wave theory represents a peculiar branch of physics that is concerned with the properties of wave processes independently from their physical origin (Ostrovsky and Potapov, 1999). The peculiarity lies in the fact that this independence from physical origin is accompanied by a heavy reliance on origin when describing any specific instance of a wave process. For example, acoustics is distinguished from optics in that sound waves are related to a mechanical rather than an electromagnetic wave-like transfer / transformation of vibratory energy.
Concepts such as mass, momentum, inertia, or elasticity, become therefore crucial in describing acoustic (as opposed to optic) wave processes. This difference in origin introduces certain wave characteristics particular to the properties of the medium involved (e.g. in the case of air: vortices, radiation pressure, shock waves, etc., in the case of solids: Rayleigh waves, dispersion, etc., and so on).
Other properties, however, although they are usually described in an origin-specific manner, may be generalized to all waves. For example, based on the mechanical origin of acoustic waves there can be a moving disturbance in space-time if and only if the medium involved is neither infinitely stiff nor infinitely pliable. If all the parts making up a medium were rigidly bound, then they would all vibrate as one, with no delay in the transmission of the vibration and therefore no wave motion (or rather infinitely fast wave motion).
On the other hand, if all the parts were independent, then there would not be any transmission of the vibration and again, no wave motion (or rather infinitely slow wave motion). Although the above statements are meaningless in the case of waves that do not require a medium, they reveal a characteristic that is relevant to all waves regardless of origin: within a wave, the phase of a vibration (i.e. its position within the vibration cycle) is different for adjacent points in space because the vibration reaches these points at different times.
Similarly, wave processes revealed from the study of wave phenomena with origins different from that of sound waves can be equally significant to the understanding of sound phenomena. A relevant example is Young’s principle of interference (Young, 1802, in Hunt, 1978: 132). This principle was first introduced in Young’s study of light and, within some specific contexts (e.g. scattering of sound by sound), is still a researched area in the study of sound.
As another example, the phenomenon of dispersion demonstrates that wave modulations behave as regular waves. When modulations propagate in media where the speed of wave propagation depends on frequency, they separate from the complex wave they belonged to and travel independently carrying energy, similarly to the rest of the frequency components of the complex wave. It is true that this separation will never happen in a non-dispersive medium such as air, where all frequencies move with the same speed.
Nonetheless, the important point is that the dispersive case serves to illustrate that modulations in general and amplitude fluctuations in particular behave as waves. Dispersion provides a case where modulations are isolated from the waves that carry them and can therefore be studied easier (assuming that the only characteristic that changes during dispersion is the modulations’ velocity). In addition, systems with dispersion provide better cases for the mathematical analysis of the kinematic properties of waves (i.e. frequency, wavelength, phase and group velocities).
In the case of sound waves, diffraction, absorption, reverberation, and interference are examples of phenomena that have been better understood with the aid of dispersion theory.
To summarize, the term wave implies three general notions: vibrations in time, disturbances in space, and moving disturbances in space-time associated with the transfer/transformation of energy.
Based on these notions, the following origin-specific definition may be adopted for sound waves in air (Vassilakis, 2001): “Sound-waves in air represent a transfer of vibratory energy characterized by: i) rate (frequency), ii) starting position (phase), and iii) magnitude (amplitude) of vibration. In general, amplitude can be expressed equivalently in terms of maximum displacement, velocity, or pressure relative to a reference value.
Sound waves in air are manifested as alternating air-condensations and rarefactions that spread away from the vibrating source with a velocity usually not related to the velocity amplitude of the vibration. They result in pressure/density disturbance patterns in the surrounding medium, which, in general, correspond to the signal that plots the vibration of the source over time.” This definition will serve as an initial operational definition of sound waves in air to which further qualifications may be added as needed.
Agreeing on a single, all-encompassing definition for the term wave is non-trivial. A vibration can be defined as a back-and-forth motion around a point of rest (e.g. Campbell & Greated, 1987: 5) or, more generally, as a variation of any physical property of a system around a reference value. However, defining the necessary and sufficient characteristics that qualify a phenomenon to be called a wave is, at least, flexible.
The term is often understood intuitively as the transport of disturbances in space, not associated with motion of the medium occupying this space as a whole. In a wave, the energy of a vibration is moving away from the source in the form of a disturbance within the surrounding medium (Hall, 1980: 8). However, this notion is problematic for a standing wave (e.g. a wave on a string), where energy is being transformed rather than moving, or for electromagnetic / light waves in a vacuum, where the concept of medium does not apply.
For such reasons, wave theory represents a peculiar branch of physics that is concerned with the properties of wave processes independently from their physical origin (Ostrovsky and Potapov, 1999). The peculiarity lies in the fact that this independence from physical origin is accompanied by a heavy reliance on origin when describing any specific instance of a wave process. For example, acoustics is distinguished from optics in that sound waves are related to a mechanical rather than an electromagnetic wave-like transfer / transformation of vibratory energy.
Concepts such as mass, momentum, inertia, or elasticity, become therefore crucial in describing acoustic (as opposed to optic) wave processes. This difference in origin introduces certain wave characteristics particular to the properties of the medium involved (e.g. in the case of air: vortices, radiation pressure, shock waves, etc., in the case of solids: Rayleigh waves, dispersion, etc., and so on).
Other properties, however, although they are usually described in an origin-specific manner, may be generalized to all waves. For example, based on the mechanical origin of acoustic waves there can be a moving disturbance in space-time if and only if the medium involved is neither infinitely stiff nor infinitely pliable. If all the parts making up a medium were rigidly bound, then they would all vibrate as one, with no delay in the transmission of the vibration and therefore no wave motion (or rather infinitely fast wave motion).
On the other hand, if all the parts were independent, then there would not be any transmission of the vibration and again, no wave motion (or rather infinitely slow wave motion). Although the above statements are meaningless in the case of waves that do not require a medium, they reveal a characteristic that is relevant to all waves regardless of origin: within a wave, the phase of a vibration (i.e. its position within the vibration cycle) is different for adjacent points in space because the vibration reaches these points at different times.
Similarly, wave processes revealed from the study of wave phenomena with origins different from that of sound waves can be equally significant to the understanding of sound phenomena. A relevant example is Young’s principle of interference (Young, 1802, in Hunt, 1978: 132). This principle was first introduced in Young’s study of light and, within some specific contexts (e.g. scattering of sound by sound), is still a researched area in the study of sound.
As another example, the phenomenon of dispersion demonstrates that wave modulations behave as regular waves. When modulations propagate in media where the speed of wave propagation depends on frequency, they separate from the complex wave they belonged to and travel independently carrying energy, similarly to the rest of the frequency components of the complex wave. It is true that this separation will never happen in a non-dispersive medium such as air, where all frequencies move with the same speed.
Nonetheless, the important point is that the dispersive case serves to illustrate that modulations in general and amplitude fluctuations in particular behave as waves. Dispersion provides a case where modulations are isolated from the waves that carry them and can therefore be studied easier (assuming that the only characteristic that changes during dispersion is the modulations’ velocity). In addition, systems with dispersion provide better cases for the mathematical analysis of the kinematic properties of waves (i.e. frequency, wavelength, phase and group velocities).
In the case of sound waves, diffraction, absorption, reverberation, and interference are examples of phenomena that have been better understood with the aid of dispersion theory.
To summarize, the term wave implies three general notions: vibrations in time, disturbances in space, and moving disturbances in space-time associated with the transfer/transformation of energy.
Based on these notions, the following origin-specific definition may be adopted for sound waves in air (Vassilakis, 2001): “Sound-waves in air represent a transfer of vibratory energy characterized by: i) rate (frequency), ii) starting position (phase), and iii) magnitude (amplitude) of vibration. In general, amplitude can be expressed equivalently in terms of maximum displacement, velocity, or pressure relative to a reference value.
Sound waves in air are manifested as alternating air-condensations and rarefactions that spread away from the vibrating source with a velocity usually not related to the velocity amplitude of the vibration. They result in pressure/density disturbance patterns in the surrounding medium, which, in general, correspond to the signal that plots the vibration of the source over time.” This definition will serve as an initial operational definition of sound waves in air to which further qualifications may be added as needed.
What is wave ?
WAVE
A wave is a disturbance that propagates through space or spacetime, often transferring energy. While a mechanical wave exists in a medium (which on deformation is capable of producing elastic restoring forces), waves of electromagnetic radiation (and probably gravitational radiation) can travel through vacuum, that is, without a medium. Waves travel and transfer energy from one point to another, often with little or no permanent displacement of the particles of the medium (i.e. little or no associated mass transport); instead there are oscillations around almost fixed positions.
A wave is a disturbance that propagates through space or spacetime, often transferring energy. While a mechanical wave exists in a medium (which on deformation is capable of producing elastic restoring forces), waves of electromagnetic radiation (and probably gravitational radiation) can travel through vacuum, that is, without a medium. Waves travel and transfer energy from one point to another, often with little or no permanent displacement of the particles of the medium (i.e. little or no associated mass transport); instead there are oscillations around almost fixed positions.
Equipment for Dealing with Sound
Equipment for dealing with sound
Equipment for generating or using sound includes musical instruments, hearing aids, sonar systems and sound reproduction and broadcasting equipment. Many of these use electro-acoustic transducers such as microphones and loudspeakers
Equipment for generating or using sound includes musical instruments, hearing aids, sonar systems and sound reproduction and broadcasting equipment. Many of these use electro-acoustic transducers such as microphones and loudspeakers
Sound Pressure Level
Sound pressure level
As the human ear can detect sounds with a very wide range of amplitudes, sound pressure is often measured as a level on a logarithmic decibel scale.
Since the human ear does not have a flat spectral response, sound pressure levels are often frequency weighted so that the measured level will match perceived levels more closely. The International Electrotechnical Commission (IEC) has defined several weighting schemes.
A-weighting attempts to match the response of the human ear to noise and A-weighted sound pressure levels are labeled dBA. C-weighting is used to measure peak levels.
Examples of sound pressure and sound pressure levelsSource of sound sound pressure sound pressure level pascal dB re 20 µPa threshold of pain 100 134 hearing damage during short-term effect 20 approx. 120 jet engine, 100 m distant 6–200 110–140 jack hammer, 1 m distant / discotheque 2 approx. 100 hearing damage during long-term effect 0.6 approx. 90 major road, 10 m distant 0.2–0.6 80–90 passenger car, 10 m distant 0.02–0.2 60–80 TV set at home level, 1 m distant 0.02 ca. 60 normal talking, 1 m distant 0.002–0.02 40–60 very calm room 0.0002–0.0006 20–30 leaves noise, calm breathing 0.00006 10 auditory threshold at 2 kHz 0.00002
As the human ear can detect sounds with a very wide range of amplitudes, sound pressure is often measured as a level on a logarithmic decibel scale.
Since the human ear does not have a flat spectral response, sound pressure levels are often frequency weighted so that the measured level will match perceived levels more closely. The International Electrotechnical Commission (IEC) has defined several weighting schemes.
A-weighting attempts to match the response of the human ear to noise and A-weighted sound pressure levels are labeled dBA. C-weighting is used to measure peak levels.
Examples of sound pressure and sound pressure levelsSource of sound sound pressure sound pressure level pascal dB re 20 µPa threshold of pain 100 134 hearing damage during short-term effect 20 approx. 120 jet engine, 100 m distant 6–200 110–140 jack hammer, 1 m distant / discotheque 2 approx. 100 hearing damage during long-term effect 0.6 approx. 90 major road, 10 m distant 0.2–0.6 80–90 passenger car, 10 m distant 0.02–0.2 60–80 TV set at home level, 1 m distant 0.02 ca. 60 normal talking, 1 m distant 0.002–0.02 40–60 very calm room 0.0002–0.0006 20–30 leaves noise, calm breathing 0.00006 10 auditory threshold at 2 kHz 0.00002
Sound Pressure
Sound pressure
Sound pressure is the pressure deviation from the local ambient pressure caused by a sound wave. Sound pressure can be measured using a microphone in air and a hydrophone in water. The SI unit for sound pressure is the pascal (symbol: Pa). The instantaneous sound pressure is the deviation from the local ambient pressure caused by a sound wave at a given location and given instant in time.
The effective sound pressure is the root mean square of the instantaneous sound pressure averaged over a given interval of time. In a soundwave, the complementary variable to sound pressure is the acoustic particle velocity. For small amplitudes, sound pressure and particle velocity are linearly related and their ratio is the acoustic impedance. The acoustic impedance depends on both the characteristics of the wave and the medium. The local instantaneous sound intensity is the product of the sound pressure and the acoustic particle velocity and is, therefore, a vector quantity in time.
The loudest sound ever historically reported was the 1883 volcanic eruption of Krakatoa whereby sound levels reached levels of 180 dBSPL 100 miles (160 km) away.
Sound pressure is the pressure deviation from the local ambient pressure caused by a sound wave. Sound pressure can be measured using a microphone in air and a hydrophone in water. The SI unit for sound pressure is the pascal (symbol: Pa). The instantaneous sound pressure is the deviation from the local ambient pressure caused by a sound wave at a given location and given instant in time.
The effective sound pressure is the root mean square of the instantaneous sound pressure averaged over a given interval of time. In a soundwave, the complementary variable to sound pressure is the acoustic particle velocity. For small amplitudes, sound pressure and particle velocity are linearly related and their ratio is the acoustic impedance. The acoustic impedance depends on both the characteristics of the wave and the medium. The local instantaneous sound intensity is the product of the sound pressure and the acoustic particle velocity and is, therefore, a vector quantity in time.
The loudest sound ever historically reported was the 1883 volcanic eruption of Krakatoa whereby sound levels reached levels of 180 dBSPL 100 miles (160 km) away.
Speed of Sound
Speed of sound
The speed at which sound travels depends on the medium through which the waves are passing, and is often quoted as a fundamental property of the material. In general, the speed of sound is proportional to the square root of the ratio of the elastic modulus (stiffness) of the medium and its density. Those physical properties and the speed of sound change with ambient conditions. For example, the speed of sound in air and other gases depends on temperature.
In air, the speed of sound is approximately 344 m/s, in water 1500 m/s and in a bar of steel 5000 m/s. The speed of sound is also slightly sensitive (to second order) to the sound amplitude, resulting in nonlinear propagation effects, such as the weak production of harmonics and the mixing of tones. (see parametric array).
The speed at which sound travels depends on the medium through which the waves are passing, and is often quoted as a fundamental property of the material. In general, the speed of sound is proportional to the square root of the ratio of the elastic modulus (stiffness) of the medium and its density. Those physical properties and the speed of sound change with ambient conditions. For example, the speed of sound in air and other gases depends on temperature.
In air, the speed of sound is approximately 344 m/s, in water 1500 m/s and in a bar of steel 5000 m/s. The speed of sound is also slightly sensitive (to second order) to the sound amplitude, resulting in nonlinear propagation effects, such as the weak production of harmonics and the mixing of tones. (see parametric array).
Perception of Sound
Perception of sound
Sound is perceived through the sense of hearing. Humans and many animals use their ears to hear sound, but loud sounds and low-frequency sounds can be perceived by other parts of the body through the sense of touch as vibrations. Sounds are used in several ways, notably for communication through speech and music. They can also be used to acquire information about properties of the surrounding environment such as spatial characteristics and presence of other animals or objects. For example, bats use echolocation, ships and submarines use sonar and humans can determine spatial information by the way in which they perceive sounds.
Humans can generally hear sounds with frequencies between 20 Hz and 20 kHz (the audio range) although this range varies significantly with age, occupational hearing damage, and gender; the majority of people can no longer hear 20,000 Hz by the time they are teenagers, and progressively lose the ability to hear higher frequencies as they get older. Most human speech communication takes place between 200 and 8,000 Hz and the human ear is most sensitive to frequencies around 1000-3,500 Hz. Sound above the hearing range is known as ultrasound, and that below the hearing range as infrasound.
The amplitude of a sound wave is specified in terms of its pressure. The human ear can detect sounds with a very wide range of amplitudes and so a logarithmic decibel amplitude scale is used. The quietest sounds that humans can hear have an amplitude of approximately 20 µPa (micropascals) or a sound pressure level (SPL) of 0 dB re 20 µPa (often incorrectly abbreviated as 0 dB SPL). Prolonged exposure to a sound pressure level exceeding 85 dB can permanently damage the ear, resulting in tinnitus and hearing impairment. Sound levels in excess of 130 dB are more than the human ear can safely withstand and can result in serious pain and permanent damage. At very high amplitudes, sound waves exhibit nonlinear effects, including shock.
The way in which sound travels or propagates is difficult to imagine, as sound appears to humans as invisible. Imagine a long tube exposed to air whereby sound travels longitudinally through it. The air acts like a Slinky spring in this tube. As sound is generated at one end, the wave will begin to travel down through the air in the tube, (watching an earth worm move by pulsating its long body on the top of the ground helps to visualize this same phenomenon). The length of pulse cycle will determine the sound wave length. Low bass sounds will have large pulse lengths, in the order of 10-50 feet long, where high treble sounds will have pulse lengths as small as 1/2 an inch.
such as microphones and loudspeakers
Sound is perceived through the sense of hearing. Humans and many animals use their ears to hear sound, but loud sounds and low-frequency sounds can be perceived by other parts of the body through the sense of touch as vibrations. Sounds are used in several ways, notably for communication through speech and music. They can also be used to acquire information about properties of the surrounding environment such as spatial characteristics and presence of other animals or objects. For example, bats use echolocation, ships and submarines use sonar and humans can determine spatial information by the way in which they perceive sounds.
Humans can generally hear sounds with frequencies between 20 Hz and 20 kHz (the audio range) although this range varies significantly with age, occupational hearing damage, and gender; the majority of people can no longer hear 20,000 Hz by the time they are teenagers, and progressively lose the ability to hear higher frequencies as they get older. Most human speech communication takes place between 200 and 8,000 Hz and the human ear is most sensitive to frequencies around 1000-3,500 Hz. Sound above the hearing range is known as ultrasound, and that below the hearing range as infrasound.
The amplitude of a sound wave is specified in terms of its pressure. The human ear can detect sounds with a very wide range of amplitudes and so a logarithmic decibel amplitude scale is used. The quietest sounds that humans can hear have an amplitude of approximately 20 µPa (micropascals) or a sound pressure level (SPL) of 0 dB re 20 µPa (often incorrectly abbreviated as 0 dB SPL). Prolonged exposure to a sound pressure level exceeding 85 dB can permanently damage the ear, resulting in tinnitus and hearing impairment. Sound levels in excess of 130 dB are more than the human ear can safely withstand and can result in serious pain and permanent damage. At very high amplitudes, sound waves exhibit nonlinear effects, including shock.
The way in which sound travels or propagates is difficult to imagine, as sound appears to humans as invisible. Imagine a long tube exposed to air whereby sound travels longitudinally through it. The air acts like a Slinky spring in this tube. As sound is generated at one end, the wave will begin to travel down through the air in the tube, (watching an earth worm move by pulsating its long body on the top of the ground helps to visualize this same phenomenon). The length of pulse cycle will determine the sound wave length. Low bass sounds will have large pulse lengths, in the order of 10-50 feet long, where high treble sounds will have pulse lengths as small as 1/2 an inch.
such as microphones and loudspeakers
perception of Sound
Perception of sound
Sound is perceived through the sense of hearing. Humans and many animals use their ears to hear sound, but loud sounds and low-frequency sounds can be perceived by other parts of the body through the sense of touch as vibrations. Sounds are used in several ways, notably for communication through speech and music. They can also be used to acquire information about properties of the surrounding environment such as spatial characteristics and presence of other animals or objects. For example, bats use echolocation, ships and submarines use sonar and humans can determine spatial information by the way in which they perceive sounds.
Humans can generally hear sounds with frequencies between 20 Hz and 20 kHz (the audio range) although this range varies significantly with age, occupational hearing damage, and gender; the majority of people can no longer hear 20,000 Hz by the time they are teenagers, and progressively lose the ability to hear higher frequencies as they get older. Most human speech communication takes place between 200 and 8,000 Hz and the human ear is most sensitive to frequencies around 1000-3,500 Hz. Sound above the hearing range is known as ultrasound, and that below the hearing range as infrasound.
The amplitude of a sound wave is specified in terms of its pressure. The human ear can detect sounds with a very wide range of amplitudes and so a logarithmic decibel amplitude scale is used. The quietest sounds that humans can hear have an amplitude of approximately 20 µPa (micropascals) or a sound pressure level (SPL) of 0 dB re 20 µPa (often incorrectly abbreviated as 0 dB SPL). Prolonged exposure to a sound pressure level exceeding 85 dB can permanently damage the ear, resulting in tinnitus and hearing impairment. Sound levels in excess of 130 dB are more than the human ear can safely withstand and can result in serious pain and permanent damage. At very high amplitudes, sound waves exhibit nonlinear effects, including shock.
The way in which sound travels or propagates is difficult to imagine, as sound appears to humans as invisible. Imagine a long tube exposed to air whereby sound travels longitudinally through it. The air acts like a Slinky spring in this tube. As sound is generated at one end, the wave will begin to travel down through the air in the tube, (watching an earth worm move by pulsating its long body on the top of the ground helps to visualize this same phenomenon). The length of pulse cycle will determine the sound wave length. Low bass sounds will have large pulse lengths, in the order of 10-50 feet long, where high treble sounds will have pulse lengths as small as 1/2 an inch.
Speed of sound
The speed at which sound travels depends on the medium through which the waves are passing, and is often quoted as a fundamental property of the material. In general, the speed of sound is proportional to the square root of the ratio of the elastic modulus (stiffness) of the medium and its density. Those physical properties and the speed of sound change with ambient conditions. For example, the speed of sound in air and other gases depends on temperature. In air, the speed of sound is approximately 344 m/s, in water 1500 m/s and in a bar of steel 5000 m/s. The speed of sound is also slightly sensitive (to second order) to the sound amplitude, resulting in nonlinear propagation effects, such as the weak production of harmonics and the mixing of tones. (see parametric array).
Sound pressure
Sound pressure is the pressure deviation from the local ambient pressure caused by a sound wave. Sound pressure can be measured using a microphone in air and a hydrophone in water. The SI unit for sound pressure is the pascal (symbol: Pa). The instantaneous sound pressure is the deviation from the local ambient pressure caused by a sound wave at a given location and given instant in time. The effective sound pressure is the root mean square of the instantaneous sound pressure averaged over a given interval of time. In a soundwave, the complementary variable to sound pressure is the acoustic particle velocity. For small amplitudes, sound pressure and particle velocity are linearly related and their ratio is the acoustic impedance. The acoustic impedance depends on both the characteristics of the wave and the medium. The local instantaneous sound intensity is the product of the sound pressure and the acoustic particle velocity and is, therefore, a vector quantity in time.
The loudest sound ever historically reported was the 1883 volcanic eruption of Krakatoa whereby sound levels reached levels of 180 dBSPL 100 miles (160 km) away.
Sound pressure level
As the human ear can detect sounds with a very wide range of amplitudes, sound pressure is often measured as a level on a logarithmic decibel scale.
The sound pressure level (SPL) or Lp is defined as
where p is the root-mean-square sound pressure and p0 is a reference sound pressure. (When using sound pressure levels, it may be important to quote the reference sound pressure used.) Commonly used reference sound pressures, defined in the standard ANSI S1.1-1994, are 20 µPa in air and 1 µPa in water.
Since the human ear does not have a flat spectral response, sound pressure levels are often frequency weighted so that the measured level will match perceived levels more closely. The International Electrotechnical Commission (IEC) has defined several weighting schemes. A-weighting attempts to match the response of the human ear to noise and A-weighted sound pressure levels are labeled dBA. C-weighting is used to measure peak levels.
Examples of sound pressure and sound pressure levels
Source of sound sound pressure sound pressure level pascal dB re 20 µPa threshold of pain 100 134 hearing damage during short-term effect 20 approx. 120 jet engine, 100 m distant 6–200 110–140 jack hammer, 1 m distant / discotheque 2 approx. 100 hearing damage during long-term effect 0.6 approx. 90 major road, 10 m distant 0.2–0.6 80–90 passenger car, 10 m distant 0.02–0.2 60–80 TV set at home level, 1 m distant 0.02 ca. 60 normal talking, 1 m distant 0.002–0.02 40–60 very calm room 0.0002–0.0006 20–30 leaves noise, calm breathing 0.00006 10 auditory threshold at 2 kHz 0.00002
Equipment for dealing with sound
Equipment for generating or using sound includes musical instruments, hearing aids, sonar systems and sound reproduction and broadcasting equipment. Many of these use electro-acoustic transducers such as microphones and loudspeakers
Sound is perceived through the sense of hearing. Humans and many animals use their ears to hear sound, but loud sounds and low-frequency sounds can be perceived by other parts of the body through the sense of touch as vibrations. Sounds are used in several ways, notably for communication through speech and music. They can also be used to acquire information about properties of the surrounding environment such as spatial characteristics and presence of other animals or objects. For example, bats use echolocation, ships and submarines use sonar and humans can determine spatial information by the way in which they perceive sounds.
Humans can generally hear sounds with frequencies between 20 Hz and 20 kHz (the audio range) although this range varies significantly with age, occupational hearing damage, and gender; the majority of people can no longer hear 20,000 Hz by the time they are teenagers, and progressively lose the ability to hear higher frequencies as they get older. Most human speech communication takes place between 200 and 8,000 Hz and the human ear is most sensitive to frequencies around 1000-3,500 Hz. Sound above the hearing range is known as ultrasound, and that below the hearing range as infrasound.
The amplitude of a sound wave is specified in terms of its pressure. The human ear can detect sounds with a very wide range of amplitudes and so a logarithmic decibel amplitude scale is used. The quietest sounds that humans can hear have an amplitude of approximately 20 µPa (micropascals) or a sound pressure level (SPL) of 0 dB re 20 µPa (often incorrectly abbreviated as 0 dB SPL). Prolonged exposure to a sound pressure level exceeding 85 dB can permanently damage the ear, resulting in tinnitus and hearing impairment. Sound levels in excess of 130 dB are more than the human ear can safely withstand and can result in serious pain and permanent damage. At very high amplitudes, sound waves exhibit nonlinear effects, including shock.
The way in which sound travels or propagates is difficult to imagine, as sound appears to humans as invisible. Imagine a long tube exposed to air whereby sound travels longitudinally through it. The air acts like a Slinky spring in this tube. As sound is generated at one end, the wave will begin to travel down through the air in the tube, (watching an earth worm move by pulsating its long body on the top of the ground helps to visualize this same phenomenon). The length of pulse cycle will determine the sound wave length. Low bass sounds will have large pulse lengths, in the order of 10-50 feet long, where high treble sounds will have pulse lengths as small as 1/2 an inch.
Speed of sound
The speed at which sound travels depends on the medium through which the waves are passing, and is often quoted as a fundamental property of the material. In general, the speed of sound is proportional to the square root of the ratio of the elastic modulus (stiffness) of the medium and its density. Those physical properties and the speed of sound change with ambient conditions. For example, the speed of sound in air and other gases depends on temperature. In air, the speed of sound is approximately 344 m/s, in water 1500 m/s and in a bar of steel 5000 m/s. The speed of sound is also slightly sensitive (to second order) to the sound amplitude, resulting in nonlinear propagation effects, such as the weak production of harmonics and the mixing of tones. (see parametric array).
Sound pressure
Sound pressure is the pressure deviation from the local ambient pressure caused by a sound wave. Sound pressure can be measured using a microphone in air and a hydrophone in water. The SI unit for sound pressure is the pascal (symbol: Pa). The instantaneous sound pressure is the deviation from the local ambient pressure caused by a sound wave at a given location and given instant in time. The effective sound pressure is the root mean square of the instantaneous sound pressure averaged over a given interval of time. In a soundwave, the complementary variable to sound pressure is the acoustic particle velocity. For small amplitudes, sound pressure and particle velocity are linearly related and their ratio is the acoustic impedance. The acoustic impedance depends on both the characteristics of the wave and the medium. The local instantaneous sound intensity is the product of the sound pressure and the acoustic particle velocity and is, therefore, a vector quantity in time.
The loudest sound ever historically reported was the 1883 volcanic eruption of Krakatoa whereby sound levels reached levels of 180 dBSPL 100 miles (160 km) away.
Sound pressure level
As the human ear can detect sounds with a very wide range of amplitudes, sound pressure is often measured as a level on a logarithmic decibel scale.
The sound pressure level (SPL) or Lp is defined as
where p is the root-mean-square sound pressure and p0 is a reference sound pressure. (When using sound pressure levels, it may be important to quote the reference sound pressure used.) Commonly used reference sound pressures, defined in the standard ANSI S1.1-1994, are 20 µPa in air and 1 µPa in water.
Since the human ear does not have a flat spectral response, sound pressure levels are often frequency weighted so that the measured level will match perceived levels more closely. The International Electrotechnical Commission (IEC) has defined several weighting schemes. A-weighting attempts to match the response of the human ear to noise and A-weighted sound pressure levels are labeled dBA. C-weighting is used to measure peak levels.
Examples of sound pressure and sound pressure levels
Source of sound sound pressure sound pressure level pascal dB re 20 µPa threshold of pain 100 134 hearing damage during short-term effect 20 approx. 120 jet engine, 100 m distant 6–200 110–140 jack hammer, 1 m distant / discotheque 2 approx. 100 hearing damage during long-term effect 0.6 approx. 90 major road, 10 m distant 0.2–0.6 80–90 passenger car, 10 m distant 0.02–0.2 60–80 TV set at home level, 1 m distant 0.02 ca. 60 normal talking, 1 m distant 0.002–0.02 40–60 very calm room 0.0002–0.0006 20–30 leaves noise, calm breathing 0.00006 10 auditory threshold at 2 kHz 0.00002
Equipment for dealing with sound
Equipment for generating or using sound includes musical instruments, hearing aids, sonar systems and sound reproduction and broadcasting equipment. Many of these use electro-acoustic transducers such as microphones and loudspeakers
What Is Sound ?
Sound
Sound is a disturbance of mechanical energy that propagates through matter as a wave. Sound is characterized by the properties of waves, which are frequency, wavelength, period, amplitude, and speed.
Humans perceive sound by the sense of hearing. By sound, we commonly mean the vibrations that travel through air and can be heard by humans. However, scientists and engineers use a wider definition of sound that includes low and high frequency vibrations in air that cannot be heard by humans, and vibrations that travel through all forms of matter, gases, liquids, solids, and plasmas.
The matter that supports the sound is called the medium. Sound propagates as waves of alternating pressure, causing local regions of compression and rarefaction. Particles in the medium are displaced by the wave and oscillate. The scientific study of sound is called acoustics.
Noise is often used to refer to an unwanted sound. In science and engineering, noise is an undesirable component that obscures a wanted signal.
Sound is a disturbance of mechanical energy that propagates through matter as a wave. Sound is characterized by the properties of waves, which are frequency, wavelength, period, amplitude, and speed.
Humans perceive sound by the sense of hearing. By sound, we commonly mean the vibrations that travel through air and can be heard by humans. However, scientists and engineers use a wider definition of sound that includes low and high frequency vibrations in air that cannot be heard by humans, and vibrations that travel through all forms of matter, gases, liquids, solids, and plasmas.
The matter that supports the sound is called the medium. Sound propagates as waves of alternating pressure, causing local regions of compression and rarefaction. Particles in the medium are displaced by the wave and oscillate. The scientific study of sound is called acoustics.
Noise is often used to refer to an unwanted sound. In science and engineering, noise is an undesirable component that obscures a wanted signal.
Divisions of Acoustic
Divisions of acoustics
The following are the main sub-disciplines of acoustics:
Acoustical measurements and instrumentation
Acoustic signal processing
Aeroacoustics: study of aerodynamic sound, generated when a fluid flow interacts with a solid surface or with another flow. It has particular application to aeronautics, examples being the study of sound made by flying jets and the physics of shock waves (sonic booms).
Architectural acoustics: study of sound waves distribution in variously shaped enclosed or partly enclosed spaces with effects of sound waves on objects of different shapes which are in their way. Mostly concentrated on how sound and buildings interact, including the behavior of sound in concert halls and auditoriums but also in office buildings, factories and homes.
Bioacoustics: study of the use of sound by animals such as whales, dolphins, bats etc.
Biomedical acoustics: study of the use of sound in medicine, for example the use of ultrasound for diagnostic and therapeutic purposes.
Environmental noise: study of the sound propagation in the human environment, noise health effects and noise mitigation analysis.
Psychoacoustics: study of subjective reaction of living beings to sound, hearing, perception, and localization.
Physiological acoustics: study of the mechanical, electrical and biochemical function of hearing in living organisms.
Physical acoustics: study of the detailed interaction of sound with materials and fluids and includes, for example, sonoluminescence (the emission of light by bubbles in a liquid excited by sound) and thermoacoustics (the interaction of sound and heat).
Speech communication: study of how speech is produced, the analysis of speech signals and the properties of speech transmission, storage, recognition and enhancement.
Structural acoustics and vibration: study of how sound and mechanical structures interact; for example, the transmission of sound through walls and the radiation of sound from vehicle panels.
Transduction: study of how sound is generated and measured by loudspeakers, microphones, sonar projectors, hydrophones, ultrasonic transducers and sensors.
Ultrasonics: study of high frequency sound, beyond the range of human hearing.
Musical acoustics: study of the physics of musical instruments.
Underwater acoustics: study of the propagation of sound in water.
Nonlinear Acoustics: study of large amplitude sound waves that propagate according to the Westervelt-Lighthill equation (in fluids) and analogous theories in other types of media (see parametric array).
The following are the main sub-disciplines of acoustics:
Acoustical measurements and instrumentation
Acoustic signal processing
Aeroacoustics: study of aerodynamic sound, generated when a fluid flow interacts with a solid surface or with another flow. It has particular application to aeronautics, examples being the study of sound made by flying jets and the physics of shock waves (sonic booms).
Architectural acoustics: study of sound waves distribution in variously shaped enclosed or partly enclosed spaces with effects of sound waves on objects of different shapes which are in their way. Mostly concentrated on how sound and buildings interact, including the behavior of sound in concert halls and auditoriums but also in office buildings, factories and homes.
Bioacoustics: study of the use of sound by animals such as whales, dolphins, bats etc.
Biomedical acoustics: study of the use of sound in medicine, for example the use of ultrasound for diagnostic and therapeutic purposes.
Environmental noise: study of the sound propagation in the human environment, noise health effects and noise mitigation analysis.
Psychoacoustics: study of subjective reaction of living beings to sound, hearing, perception, and localization.
Physiological acoustics: study of the mechanical, electrical and biochemical function of hearing in living organisms.
Physical acoustics: study of the detailed interaction of sound with materials and fluids and includes, for example, sonoluminescence (the emission of light by bubbles in a liquid excited by sound) and thermoacoustics (the interaction of sound and heat).
Speech communication: study of how speech is produced, the analysis of speech signals and the properties of speech transmission, storage, recognition and enhancement.
Structural acoustics and vibration: study of how sound and mechanical structures interact; for example, the transmission of sound through walls and the radiation of sound from vehicle panels.
Transduction: study of how sound is generated and measured by loudspeakers, microphones, sonar projectors, hydrophones, ultrasonic transducers and sensors.
Ultrasonics: study of high frequency sound, beyond the range of human hearing.
Musical acoustics: study of the physics of musical instruments.
Underwater acoustics: study of the propagation of sound in water.
Nonlinear Acoustics: study of large amplitude sound waves that propagate according to the Westervelt-Lighthill equation (in fluids) and analogous theories in other types of media (see parametric array).
Acoustic
Acoustics
Acoustics is a branch of physics and is the study of sound (mechanical waves in gases, liquids, and solids). A scientist who works in the field of acoustics is an acoustician. The application of acoustics in technology is called acoustical engineering. There is often much overlap and interaction between the interests of acousticians and acoustical engineers.
The word acoustic is derived from the ancient Greek word ακουστός, meaning able to be heard. (Woodhouse, 1910, 392)
...[A]coustics is characterized by its reliance on combinations of physical principles drawn from other sources; and that the primary task of modern physical acoustics is to effect a fusion of the principles normally adhering to other sciences into a coherent basis for understanding, measuring, controlling, and using the whole gamut of vibrational phenomena in any material.
Origins in Acoustics. F.V. Hunt. Yale University Press, 1978
Acoustics is the science concerned with the production, control, transmission, reception, and effects of sound. Its origins began with the study of mechanical vibrations and the radiation of these vibrations through mechanical waves, and still continues today. Research was done to look into the many aspects of the fundamental physical processes involved in waves and sound and into possible applications of these processes in modern life. The study of sound waves also lead to physical principles that can be applied to the study of all waves.
The study of acoustics has been fundamental to many developments in the arts. Some of these, especially in the area of musical scales and instruments, were only explained theoretically by scientists after long years of long experimentation by artists. For example, much of what is now known about architectural acoustics was actually learned by trial and error over centuries of experience and was only recently formalized into a science.
Other applications of acoustic technology are in the study of geologic, atmospheric, and underwater phenomena. Psychoacoustics, the study of the physical effects of sound on biological systems, has been of interest since Pythagoras first heard the sounds of vibrating strings and of hammers hitting anvils in the 6th century BC, but the application of modern ultrasonic technology has only recently provided some of the most exciting developments in medicine. The ear itself is another biological instrument dedicated to receiving certain wave vibrations and interpreting them as sound.
Acoustics is a branch of physics and is the study of sound (mechanical waves in gases, liquids, and solids). A scientist who works in the field of acoustics is an acoustician. The application of acoustics in technology is called acoustical engineering. There is often much overlap and interaction between the interests of acousticians and acoustical engineers.
The word acoustic is derived from the ancient Greek word ακουστός, meaning able to be heard. (Woodhouse, 1910, 392)
...[A]coustics is characterized by its reliance on combinations of physical principles drawn from other sources; and that the primary task of modern physical acoustics is to effect a fusion of the principles normally adhering to other sciences into a coherent basis for understanding, measuring, controlling, and using the whole gamut of vibrational phenomena in any material.
Origins in Acoustics. F.V. Hunt. Yale University Press, 1978
Acoustics is the science concerned with the production, control, transmission, reception, and effects of sound. Its origins began with the study of mechanical vibrations and the radiation of these vibrations through mechanical waves, and still continues today. Research was done to look into the many aspects of the fundamental physical processes involved in waves and sound and into possible applications of these processes in modern life. The study of sound waves also lead to physical principles that can be applied to the study of all waves.
The study of acoustics has been fundamental to many developments in the arts. Some of these, especially in the area of musical scales and instruments, were only explained theoretically by scientists after long years of long experimentation by artists. For example, much of what is now known about architectural acoustics was actually learned by trial and error over centuries of experience and was only recently formalized into a science.
Other applications of acoustic technology are in the study of geologic, atmospheric, and underwater phenomena. Psychoacoustics, the study of the physical effects of sound on biological systems, has been of interest since Pythagoras first heard the sounds of vibrating strings and of hammers hitting anvils in the 6th century BC, but the application of modern ultrasonic technology has only recently provided some of the most exciting developments in medicine. The ear itself is another biological instrument dedicated to receiving certain wave vibrations and interpreting them as sound.
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