# Acoustic Filter

## acoustic filter

[ə′küs·tik ′fil·tər]
(computer science)

## Filter, Acoustic

a device for isolating a certain frequency band from a complex sound. It is the acoustical analogue of an electric filter. The simplest acoustic filter is the Helmholtz resonator (seeRESONATOR, ACOUSTIC).

The theory of acoustic filters was developed by means of the electromechanical analogy method on the basis of the theory of electric filters. The classification and terminology already established for electric filters were applied to acoustic filters. An acoustic filter that passes all frequencies from zero up to some specified frequency is called a low-pass filter. A high-pass filter, on the other hand, passes all frequencies above a specified value and no frequencies below it. An acoustic filter that passes a more or less narrow frequency range between two specified frequencies is called a band-pass filter.

A low-pass acoustic filter (Figure 1,a) consists of a set of identical cavities connected by narrow tubes (the electrical analogue is shown in Figure 1,b). To a first approximation it can be assumed that all the kinetic energy of the system is concentrated in the air

Figure 1. Schematic of a low-pass acoustic filter (a) and its electrical analogue (b)

moving in the tubes and that the potential energy is associated with the elastic deformation of the air in the cavities. The upper limit of the passband of this acoustic filter is the cutoff frequency , where S is the cross-sectional area of the tube, l is the length of the tube, V is the volume of the cavity, and c is the speed of sound in air.

A high-pass acoustic filter (Figure 2,a) consists of a narrow tube with holes drilled in it at equal intervals (the electrical analogue is shown in Figure 2,b). In this system the kinetic energy is concentrated in the air moving near the holes, and the potential energy is associated with the air in the tube. Under the action of the low-frequency components of the field the air in the holes vibrates intensely; as a result, there exists for these components a

Figure 2. Schematic of a high-pass acoustic filter (a) and its electrical analogue (b)

“short circuit” in the system. At high frequencies the air in the holes is unable to vibrate, so that the high-frequency components pass freely through the tube. By combining a low-pass filter and a high-pass filter, it is possible to construct a band-pass filter, whose passband is determined by the dimensions of the holes and resonators.

Acoustic filters are widely used in engineering to reduce the noise created by the flow of exhaust gases in jet engines and internal combustion engines. The automobile muffler, for example, is an acoustic filter. Architectural acoustics employs acoustic filters to decrease the transmission of noise through ventilating ducts and pipes; along with the use of filters, the ducts or pipes are often lined with sound-absorbing materials.

The acoustic filter’s basic property of separating out a frequency band from a complex sound is exhibited by plane-parallel plates. Known as an interference acoustic filter, such plates are used to selectively pass sound waves that are propagating in a specific direction. For example, a plate having a thickness equal to an integral number of half waves at a given frequency will pass the sound-field component that has this frequency and is propagating in a direction normal to the plate.

### REFERENCES

Rzhevkin, S. N. Kurs lektsii po teorii zvuka. Moscow, 1960.
Tartakovskii, B. D. “Ul’trazvukovye interferentsionnye fil’try s izmeniaemymi chastotami propuskaniia.” Akusticheskii zhurnal, 1957, vol. 3, no. 2, pp. 183–91.
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