Question

a crude approximation of voice production is to consider the breathing passages and mouth to be a resonating tube closed at one end. what is the fundamental frequency ????1 if the tube is 0.240 m long, by taking air temperature to be 37.0∘c? ????1

Answer 1

The fundamental frequency of the tube is 0.240 m long, by taking air temperature to be $37^o$C is 367.42 Hz.

A standing wave is basically a superposition of two waves propagating opposite to each other having equal amplitude. This is the propagation in a tube.

The fundamental frequency in the tube is given by

$f=\frac{v_T}{4L}$

where, $v_T=v\sqrt{\frac{T}{273} }$

Since, T=37+273 K = 310 K

v = 331 m/s

$\therefore v_T=331\sqrt{\frac{310}{273} } = 352.72 \ m/s$

Using this, we get:

$f=\frac{352.72}{4(0.240)} \\f=367.42 \ Hz$

Hence, the fundamental frequency is 367.42 Hz.

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