Acoustics: Sound Fields, Transducers and Vibration, 2nd Edition

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 (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 ℓ ′

(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 ...