s of the same frequency demonstrating
acoustic resonance. Striking one fork induces vibrational motion in the other through the production of air‑pressure oscillations. Sound travels as a mechanical wave through a medium (e.g.
water,
crystals,
air). Sound waves are generated by a sound source, such as a vibrating
diaphragm of a loudspeaker. As the sound source vibrates the surrounding medium, mechanical disturbances propagate away from the source at the local
speed of sound, thus resulting in a sound wave. At a fixed distance from the source, the
pressure,
velocity, and displacement of the medium's particles vary in
time. At an instant in time, the pressure, velocity, and displacement vary spatially. The particles of the medium do not travel with the sound wave; instead, the disturbance and its
mechanical energy propagate through the medium. Though intuitively expectable for solids, this also applies for liquids and gases. The matter that supports the transmission of a sound is named the
transmission medium. Media may be any
form of matter, whether solids, liquids, gases or
plasmas. However, sound cannot propagate through a
vacuum because there is no medium to support mechanical disturbances. The propagation of sound in a medium is influenced primarily by: • A complicated relationship between the
density and pressure of the medium. This relationship, also affected by temperature, determines the speed of sound within the medium. • Motion of the medium itself. If the medium is moving, this movement may increase or decrease the absolute speed of the sound wave depending on the direction of the movement. For example, sound moving through wind will have its speed of propagation increased by the speed of the wind if the sound and wind are moving in the same direction. If the sound and wind are moving in opposite directions, the speed of the sound wave will be decreased by the speed of the wind. • The viscosity of the medium. Medium
viscosity determines the rate at which sound is attenuated. For many media, such as air or water, attenuation due to viscosity is negligible. Theoretical work indicates that sound waves carry an extremely small effective gravitational mass. This mass arises from
nonlinear corrections to the
stress–energy of the wave, and implies that sound waves both respond to gravity and generate a very weak gravitational field of their own. For ordinary equations of state, the effective mass is negative, meaning that sound waves in such media act as if they carry a tiny negative gravitational mass. The effect is extremely small because it appears only at nonlinear order in the equations governing wave motion.
Waves Sound waves exhibit behaviours such as reflection,
transmission,
refraction,
diffraction,
absorption, and
attenuation. When sound is moving through a non‑homogeneous medium , it may be
refracted (either
dispersed or focused). Sound is transmitted through fluids (e.g. gases, plasmas, and liquids) as
longitudinal waves, also called
compression waves. Through solids, however, sound can be transmitted as both longitudinal waves and
transverse waves. Longitudinal sound waves are waves of alternating
pressure deviations from the
equilibrium pressure, causing local regions of
compression and
rarefaction, while
transverse waves (in solids) are waves of alternating
shear stress perpendicular to the direction of propagation. Unlike longitudinal sound waves, transverse sound waves have the property of
polarisation. Spherical pressure waves.gif|Circular, longitudinal waves propagating from a source and causing particle vibration. Onde compression impulsion 1d 30 petit.gif|A longitudinal plane wave, the horizontally distorted region moving across the grid. Onde cisaillement impulsion 1d 30 petit.gif|A transverse plane wave, the vertically distorted region moving across the grid. Sound waves may be viewed using parabolic mirrors and objects that produce sound. The energy carried by a
periodic sound wave alternates between the potential energy of the extra
compression (in the case of longitudinal waves) or lateral displacement
strain (in the case of transverse waves) of the matter, and the kinetic energy of the particles' displacement velocity in the medium. Although sound transmission involves many physical processes, the
signal received at a point (such as a microphone or the ear) can be fully described as a time‑varying pressure. This pressure‑versus‑time waveform provides a complete representation of any sound or audio signal detected at that location. Sound
waves are often simplified as
sinusoidal plane waves, which are characterized by these generic properties: •
Frequency, or its inverse, period. •
Wavelength, or its inverse,
wavenumber. •
Amplitude,
sound pressure or
Intensity •
Speed of sound •
Direction Sometimes speed and direction are combined as a
velocity vector; wave number and direction are combined as a
wave vector. To analyse audio, a complicated
waveform—such as the one shown on the right—can be represented as a
linear combination of sinusoidal components of different frequencies,
amplitudes, and
phases. The Elements of Sound jpg.jpg|Pressure‑versus‑time waveform of a 20‑millisecond clarinet tone. Sine waves different frequencies.svg|Sinusoidal waveforms with wavelengths increasing upwards, representing pure frequency components used in
Fourier analysis.
Speed approaching the speed of sound. The white halo is formed by condensed water droplets thought to result from a drop in air pressure around the aircraft (see
Prandtl–Glauert singularity). The speed of sound depends on the medium the waves pass through, and is a fundamental property of the material. The first significant effort towards measurement of the speed of sound was made by
Isaac Newton. He believed the speed of sound in a particular substance was equal to the square root of the pressure acting on it divided by its density: : c = \sqrt{\frac{p}{\rho}}. This was later disproven and the French mathematician
Laplace corrected the formula by deducing that the phenomenon of sound travelling is not isothermal, as believed by Newton, but
adiabatic. He added another factor to the equation—
gamma—and multiplied \sqrt{\gamma} by \sqrt{p/\rho}, thus coming up with the equation c = \sqrt{\gamma \cdot p/\rho}. Since K = \gamma \cdot p, the final equation came up to be c = \sqrt{K/\rho}, which is also known as the Newton–Laplace equation. In this equation,
K is the elastic bulk modulus,
c is the velocity of sound, and \rho is the density. Thus, the speed of sound is proportional to the
square root of the
ratio of the
bulk modulus of the medium to its density. Those physical properties and the speed of sound change with ambient conditions. For example, the speed of sound in gases depends on temperature. In air at sea level, the speed of sound is approximately using the formula . The speed of sound is also slightly sensitive, being subject to a second-order
anharmonic effect, to the sound amplitude, which means there are non-linear propagation effects, such as the production of harmonics and mixed tones not present in the original sound (see
parametric array). If
relativistic effects are important, the speed of sound is calculated from the
relativistic Euler equations. In fresh water the speed of sound is approximately . In steel, the speed of sound is about . Sound moves the fastest in solid atomic hydrogen at about .
Sound pressure level Sound pressure is the difference, in a given medium, between average local pressure and the pressure in the sound wave. A square of this difference (i.e., a square of the deviation from the equilibrium pressure) is usually averaged over time and/or space, and a square root of this average provides a
root mean square (RMS) value. For example, 1
Pa RMS sound pressure (94 dBSPL) in atmospheric air implies that the actual pressure in the sound wave oscillates between (1 atm -\sqrt{2} Pa) and (1 atm +\sqrt{2} Pa), that is between 101323.6 and 101326.4 Pa. As the human ear can detect sounds with a 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 : L_\mathrm{p}=10\, \log_{10}\left(\frac{{p}^2}{{p_\mathrm{ref}}^2}\right) =20\, \log_{10}\left(\frac{p}{p_\mathrm{ref}}\right)\mbox{ dB}\, :where
p is the
root-mean-square sound pressure and p_\mathrm{ref} is a
reference sound pressure. Commonly used reference sound pressures, defined in the standard
ANSI S1.1-1994, are 20
μPa in air and 1
μPa in water. Without a specified reference sound pressure, a value expressed in decibels cannot represent a sound pressure level. Since the human ear does not have a flat
spectral response, sound pressures are often
frequency weighted so that the measured level matches 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. ==Perception==