Acoustic resonance

Acoustic resonance is a phenomenon in which an acoustic system amplifies sound waves whose frequency matches one of its own natural frequencies of vibration (its resonance frequencies).12 Acoustic resonance is a phenomenon in which an acoustic system amplifies sound waves whose frequency matches one of its own natural frequencies of vibration (its resonance frequencies). The term 'acoustic resonance' is sometimes used to narrow mechanical resonance to the frequency range of human hearing, but since acoustics is defined in general terms concerning vibrational waves in matter, acoustic resonance can occur at frequencies outside the range of human hearing. An acoustically resonant object usually has more than one resonance frequency, especially at harmonics of the strongest resonance. It will easily vibrate at those frequencies, and vibrate less strongly at other frequencies. It will 'pick out' its resonance frequency from a complex excitation, such as an impulse or a wideband noise excitation. In effect, it is filtering out all frequencies other than its resonance. Acoustic resonance is an important consideration for instrument builders, as most acoustic instruments use resonators, such as the strings and body of a violin, the length of tube in a flute, and the shape of a drum membrane. Acoustic resonance is also important for hearing. For example, resonance of a stiff structural element, called the basilar membrane within the cochlea of the inner ear allows hair cells on the membrane to detect sound. (For mammals the membrane has tapering resonances across its length so that high frequencies are concentrated on one end and low frequencies on the other.) Like mechanical resonance, acoustic resonance can result in catastrophic failure of the vibrator. The classic example of this is breaking a wine glass with sound at the precise resonant frequency of the glass. In musical instruments, strings under tension, as in lutes, harps, guitars, pianos, violins and so forth, have resonant frequencies directly related to the mass, length, and tension of the string. The wavelength that will create the first resonance on the string is equal to twice the length of the string. Higher resonances correspond to wavelengths that are integer divisions of the fundamental wavelength. The corresponding frequencies are related to the speed v of a wave traveling down the string by the equation where L is the length of the string (for a string fixed at both ends) and n = 1, 2, 3...(Harmonic in an open end pipe (that is, both ends of the pipe are open)). The speed of a wave through a string or wire is related to its tension T and the mass per unit length ρ: