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Acoustics: Sound Fields, Transducers and Vibration, 2nd Edition by Tim Mellow, Leo Beranek

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4.3. Acoustic compliances

In Eq. (2.72) we showed that a length of tube, rigidly closed on one end (x   =   0), with a radius in meters greater than 0 . 05 / f image (so that the sidewall friction can be neglected) and less than 10/f (so lateral standing waves are not present) has an input acoustic impedance at the open end equal to
Z A = j ρ 0 c π a 2 cot k
image (4.9)
where Z A   =   Z s /(πa 2), ρ 0 is density of the gas in kg/m3, c is speed of sound in m/s, a is radius of tube in m, k is wave ...

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