Quarter Wave Tube

A resonator used most commonly on air intake systems to reduce resonance. Works over a narrow frequency range, i.e. used to attenuate a specific frequency.

The quarter wave tube is open at the end that connects with the air inlet pipe and closed at the other end.

The frequency at which the quarter wave tube attenuates is controlled by the length of the quarter wave tube.

The maximum attenuation is achieved when the cross-section of the quarter wave tube matches that of the main duct.

The quarter wave tube, as per the title, a quarter of a wavelength long. The total distance that the acoustic wave travels is half a wavelength. Therefore, in the time taken for the acoustic wave to travel down the quarter wave tube and back to the main duct the acoustic wave in the main duct has moved along half a wavelength. The following diagram shows the operation of the quarter wave tube.

The fundamental resonant frequency of a quarter wave tube, fr
where
c = speed of sound [ms-1]
Lb = length of sidebranch [m]

The transmission loss, TL
where
f = excitation frequency [Hz]
S = cross-sectional area of main duct [m2]
Sb = cross-sectional area of sidebranch [m2]


dB

Frequency (Hz)

Reference

Michael C. LoPresto, "Measuring End Correction for a Quarter-Wave Tube", The Physics Teacher, September 2005, Volume 43, Issue 6, pp. 380

See also: Acoustic Filter Elements, Expansion Chamber, Helmholtz Resonator, Resonator, Side Branch Orifice.

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Subjects: Audio Mechanical Engineering Noise & Vibration