A device consisting of a combination of elements having mass and compliance whose acoustical reactances cancel at a given frequency. Resonators are often used as a means of eliminating an undesirable frequency component in an acoustical system. In other instances resonators are used to produce an increase in the sound pressure in an acoustic field at a particular frequency.
Resonators are useful most often in the control of low-frequency sound. They are of particular value in reducing the noise from sources having constant frequency excitation.
Resonators have also found considerable application in architectural acoustics. It is often difficult to obtain adequate control of reverberation time at low frequencies in a large studio or auditorium using conventional acoustical materials. A number of designs for these spaces have included the construction of resonators behind walls or in the ceiling to obtain increased low-frequency absorption and thus provide more satisfactory reverberation characteristics.
The Helmholtz resonator (see illustration) is the simplest and most often utilized acoustical resonator. The unit consists of a straight tube of length l and cross-sectional area S, connected to a closed volume V. This combination is directly analogous to the simple series LC electrical circuit. See Acoustic impedance
a vessel that is connected with the external medium through a small orifice or tube called the neck.
A characteristic feature of an acoustic resonator is the ability to execute low-frequency natural oscillations having a wavelength substantially greater than the resonator’s dimensions. The fundamental (natural) frequency f0 of an acoustic resonator with a neck is calculated from the formula f0, where c is the speed of sound in air, S and l are the cross-sectional area and length of the tube, respectively, and V is the volume of the vessel. If an acoustic resonator is placed in a harmonic sound field whose frequency is equal to f0, vibrations are produced in the resonator that have an amplitude many times the amplitude of the sound field. In a nonharmonic sound field, an acoustic resonator responds only to oscillations having a frequency equal to the natural frequency of the resonator. Consequently, a set of resonators having different natural frequencies can be used to analyze sound.
The amplitude of the oscillatory velocity in a resonator’s neck at f0 is high; consequently, when friction exists in the neck, a sound at this frequency is strongly absorbed. This property of an acoustic resonator is used to create acoustic resonance absorbers in architectural acoustics. Acoustic resonators are also used as resonance baffles to reduce the transmission of low-frequency noise along a sound duct. The low input impedance of an acoustic resonator in a sound duct wall at the frequency f0 will sharply alter the conditions for wave propagation at this frequency. Bubbles in a liquid and air cavities in certain other media, such as rubber, are also acoustic resonators, so that the presence of a large number of bubbles in water gives rise to strong sound absorption and interferes with the propagation of sound waves.
The theory of acoustic resonators was developed by H. Helmholtz and Lord Rayleigh.