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.
Sunday, May 27, 2007
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
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