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# 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.

"... acoustics 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 medium." Origins in Acoustics. F.V. Hunt. Yale University Press, 1978

The main sub-disciplines of acoustics are

• Aeroacoustics is the study of aerodynamic sound, generated when a fluid flow interacts with a solid surface, steady or moving. It has particular application to aeronautics, examples being the study of sound made by jets and the physics of shock waves (sonic booms).
• Architectural acoustics is the study of how sound and buildings interact including the behavior of sound in concert halls and auditoriums but also in office buildings, factories and homes.
• Biomedical acoustics is the study of the use of sound in medicine, for example the use of ultrasound for diagnostic and therapeutic purposes.
• Physiological acoustics is the study of the mechanical, electrical and biochemical function of hearing in living organisms.
• Physical acoustics is the 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 is the study of how speech is produced, the analysis of speech signals and the properties of speech transmission, storage, recognition and enhancement.
• Vibration acoustics Structural Acoustics and Vibration is the study of how sound and mechanical structures interact and includes the transmission of sound through walls and the radiation of sound from vehicle panels.
• Underwater acoustics is the study of the propagation of sound in the oceans.

A sound wave is characterized by its speed, its wavelength and its amplitude. The speed of sound depends on the medium through which the sound travels and also depends on temperature and not on the air pressure. The speed of sound is about 340 m/s in air and 1500 m/s in water. The wavelength is the distance from one wave peak to the next. The wavelength, λ of a sound wave is related to the speed of sound c and its frequency f by

$\lambda = \frac{c}{f}$.
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## Sound pressure levelSPL

The amplitude of a sound wave is most commonly characterized by its sound pressure. In a normal working environment, a very wide range of pressures can occur and it is therefore a convention that sound pressure is measured on a logarithmic scale using the decibel. If p is the rms sound pressure amplitude then the sound pressure level (SPL) is defined as 20 times the logarithm of the ratio of the pressure to some reference pressure.

Sound pressure level SPL is calculated in decibels as

$L_p =20\, \log_{10}\left(\frac{p_1}{p_0}\right)=10\, \log_{10}\left(\frac{p_1^2}{p_0^2}\right)dBSPL$

The reference sound pressure is by convention the threshold of hearing:

$p_0 = 2 \cdot 10^{-5} Pa$
= 20 µPa in air and 1 µPa in water. (Pa = pascal = N / m²; N = newton)

When speaking of sound levels, one must be sure to differentiate between sound pressure levels and sound power levels. Sound pressure levels are recorded by microphones and other devices. This is a measurement of the amount of pressure in the air being sensed at a given location. It follows that its value can be determined through direct experimentation. In comparison, sound power levels are a measurement of the actual energy being put into use by a given device to create noise. Because of environmental factors, and other influences, the amount of energy a device devotes to creating sound may not be equal to the actual level of the sound as it's perceived. It can be useful to express sound pressure in this way when dealing with hearing, as the perceived loudness of a sound correlates roughly logarithmically to its sound pressure. Both microphones and eardrums respond to the sound pressure level. They cannot convert the sound intensity. Sound power measurements cannot be directly measured, and must be inferred through other data.

## Measurement methods

There are two popular ways for scientists to perform acoustical measurements. They include a "direct method", and a "comparison method". The direct method computes sound power levels by computing an equation of environmental factors (such as room temperature, humidity, reverberation time, etc.) and sound pressure levels. A more precise implementation of this method can be found in the ISO3745 acoustics standard. The comparison method however, is conducted by measuring sound pressure levels from a reference sound source which emits a known, constant, sound power level, and then comparing that level with the sound pressure level of the object being recorded. Each way is equally valid and accurate.

## Reverberation and anechoic rooms

Experiments such as the two methods mentioned above are sometimes performed in reverberation rooms, or in some cases, anechoic rooms. The design of a reverberation room is to create long lasting echoes of sound waves. This helps create a highly averaged and omnidirectional sound level throughout the entire chamber. A typical example of rooms with characteristics similar to reverberation rooms are concrete tunnels, caves, etc. Anechoic rooms, such as hemi-anechoic rooms, or fully anechoic rooms are created to simulate what is called a free field. A free field is the representation of a theoretical infinite space , in which no sound wave reflections, or echoes, take place. In rooms such as these, the only sounds which exist are being emitted directly from the source, and are not reflected from another part of the chamber. Anechoic rooms have the characteristic of being muted and muffled.

## Helmholtz Resonator

A helmholtz resonator is a container with an open hole or neck. It is sometimes used as a passive noise control device.

• f = resonant frequency
• s = speed of sound in air
• r = radius of neck
• a = area of neck
• l = length of neck
• L' = effective length of neck
L' = l+1.7r (outer end flanged)
L' = l+1.4r (outer end unflanged)
• v = volume
$f = (s/2 \pi)(\sqrt{a/(L' \cdot v)})$

The helmholtz resonator is an example of the lumped component model of acoustic systems which is useful when the wavelength of interest is significantly larger than the physical dimensions of the system.

## Rectangular Boxes

• f = frequency of standing wave of a rectangular box
• s = speed of sound in air
• x,y,z = dimensions of box
• Nx,Ny,Nz = any integers
$f = (s/2)(\sqrt{(Nx/x)^2+(Ny/y)^2+(Nz/z)^2})$

## More

More specialized areas of acoustics include, but are not limited to, tonal analysis , sound quality assessments , and noise control .

Subfields and related fields of acoustics: