Question

A crude approximation of voice production is to consider the breathing passages and mouth to be a resonating tube closed at one end.

(a)

What is the fundamental frequency (in Hz) if the tube is 0.265 m long, taking air temperature to be 37.0°C?

Hz

(b)

What would this frequency (in Hz) become if the person replaced the air with helium? Assume the same temperature dependence for helium as air.

Hz

Answer 1

fundamental frequency=speed of sound/(4*length of tube)

Here tube length is constant, ratio of frequencies is ratio of speed of sound in differetn medium

speed of sound is given by sqrt(gamma*R*T/M)

where gamma=adiabatic constant

R=gas constant=8.314

T=temperature in kelvin=37 degre celcius=37+273K=310 K

M=molecular mass

for air,

gamma=1.4

M=0.02895 kg

Then put values in formula..

then speed of sound=sqrt(1.4*8.314*310/0.02895)

=353 m/s

fundamental frequency=353/(4*0.265)=330.02 Hz (Answer)

for helium,

gamma=5/3

M=0.004 kg

so speed of sound=sqrt((5/3)*8.314*310/0.004)

=1036.29 m/s

then fundamnental frequency=1036.29/(4*0.265)=977.63 Hz (Answer)

I hope help you !!