Acoustic wave
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Acoustic waves are a type of energy propagation through a medium by means of
Wave properties
Acoustic wave is a mechanical wave that transmits energy through the movements of atoms and molecules. Acoustic wave transmits through liquids in longitudinal manner (movement of particles are parallel to the direction of propagation of the wave); in contrast to electromagnetic wave that transmits in transverse manner (movement of particles at a right angle to the direction of propagation of the wave). However, in solids, acoustic wave transmits in both longitudinal and transverse manners due to presence of shear moduli in such a state of matter.[1]
Acoustic wave equation
The acoustic wave equation describes the propagation of sound waves. The acoustic wave equation for sound pressure in one dimension is given by
- is sound pressure in Pa
- is position in the direction of propagation of the wave, in m
- is speed of sound in m/s
- is time in s
The wave equation for particle velocity has the same shape and is given by
- is particle velocity in m/s
For lossy media, more intricate models need to be applied in order to take into account frequency-dependent attenuation and phase speed. Such models include acoustic wave equations that incorporate fractional derivative terms, see also the acoustic attenuation article.
- is angular frequency in rad/s
- is time in s
- is wave numberin rad·m−1
- is a coefficient without unit
For the wave becomes a travelling wave moving rightwards, for the wave becomes a travelling wave moving leftwards. A standing wave can be obtained by .
Phase
In a travelling wave pressure and particle velocity are in phase, which means the phase angle between the two quantities is zero.
This can be easily proven using the ideal gas law
Consider a volume . As an acoustic wave propagates through the volume, adiabatic compression and decompression occurs. For adiabatic change the following relation between volume of a parcel of fluid and pressure holds
As a sound wave propagates through a volume, the horizontal displacement of a particle occurs along the wave propagation direction.
- is cross-sectional area in m2
From this equation it can be seen that when pressure is at its maximum, particle displacement from average position reaches zero. As mentioned before, the oscillating pressure for a rightward traveling wave can be given by
During adiabatic change, temperature changes with pressure as well following
Propagation speed
The propagation speed, or acoustic velocity, of acoustic waves is a function of the medium of propagation. In general, the acoustic velocity c is given by the Newton-Laplace equation:
- C is a coefficient of stiffness, the bulk modulus (or the modulus of bulk elasticity for gas mediums),
- is the density in kg/m3
Thus the acoustic velocity increases with the stiffness (the resistance of an elastic body to deformation by an applied force) of the material, and decreases with the density. For general equations of state, if classical mechanics is used, the acoustic velocity is given by
Phenomena
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Acoustic waves are elastic waves that exhibit phenomena like
Interference
Standing wave
A standing wave is a special kind of wave that can occur in a resonator. In a resonator superposition of the incident and reflective wave occurs, causing a standing wave. Pressure and particle velocity are 90 degrees out of phase in a standing wave.
Consider a tube with two closed ends acting as a resonator. The resonator has
At the ends particle velocity becomes zero since there can be no particle displacement. Pressure however doubles at the ends because of interference of the incident wave with the reflective wave. As pressure is maximum at the ends while velocity is zero, there is a 90 degrees phase difference between them.
Reflection
An acoustic travelling wave can be reflected by a solid surface. If a travelling wave is reflected, the reflected wave can interfere with the incident wave causing a standing wave in the near field. As a consequence, the local pressure in the near field is doubled, and the particle velocity becomes zero.
Attenuation causes the reflected wave to decrease in power as distance from the reflective material increases. As the power of the reflective wave decreases compared to the power of the incident wave, interference also decreases. And as interference decreases, so does the phase difference between sound pressure and particle velocity. At a large enough distance from the reflective material, there is no interference left anymore. At this distance one can speak of the
The amount of reflection is given by the reflection coefficient which is the ratio of the reflected intensity over the incident intensity
Absorption
Acoustic waves can be absorbed. The amount of absorption is given by the absorption coefficient which is given by
- is the absorption coefficientwithout a unit
- is the reflection coefficient without a unit
Often acoustic absorption of materials is given in decibels instead.
Layered media
When an acoustic wave propagates through a non-homogeneous medium, it will undergo diffraction at the impurities it encounters or at the interfaces between
The acoustic absorption, reflection and transmission in multilayer materials can be calculated with the transfer-matrix method.[3]
See also
- Acoustics
- Acoustic attenuation
- Acoustic metamaterial
- Auditory imagery
- Audio signal processing
- Beat
- Biot–Tolstoy–Medwin_diffraction_model
- Diffraction
- Doppler effect
- Echo
- Entropy-vorticity wave
- Gravity wave
- Music
- Musical note
- Musical tone
- Phonon
- Physics of music
- Pitch
- Psychoacoustics
- Resonance
- Refraction
- Reflection
- Reverberation
- Signal tone
- Sound
- Sound localization
- Soundproofing
- Stereo imaging
- Structural acoustics
- Timbre
- Ultrasound
- Wave equation
- One-way wave equation
- List of unexplained sounds
References
- )
- ^ Gorishnyy, Taras, Martin Maldovan, Chaitanya Ullal, and Edwin Thomas. "Sound ideas." Physics World 18, no. 12 (2005): 24.
- ISBN 978-3-11-030266-0.