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
$\text{0}\text{.}05/\sqrt{f}$
(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

${Z}_{A}=\frac{-j{\rho}_{\text{0}}c}{\pi {a}^{2}}\mathrm{cot}k{\ell}^{\prime}$

(4.9)

where Z
_{
A
}
=
Z
_{
s
}/(πa
^{2}), ρ
_{0} is density of the gas in kg/m^{3}, c is speed of sound in m/s, a is radius of tube in m, k is wave ...

Start Free Trial

No credit card required