A simplified version of our voice production system consists of considering the

Question

A simplified version of our voice production system consists of considering the breathing passage and the mouth to be a tube closed at one end.

(a) Determine the frequency of the fundamental (to the nearest Hertz) if the simulation tube is 0.197 m long and the air temperature to be 35.0°C. The speed of sound in air at 0°C is 331 m/s.

(b) Assuming that the temperature dependence for helium is the same as for air, determine the frequency of the fundamental (to the nearest Hertz) if the air is replaced by helium. The speed of sound in helium at 0°C is 965 m/s.

Explanation / Answer

given,

length of tube = 0.197 m

speed of sound in air at 0°C = 331 m/s

speed of sound in air at degree celcius 331.3 + (0.6 × )

speed of sound in air at 35 degree celcius 331.3 + (0.6 × 35)

speed of sound in air at 35 degree celcius 352.3 m/s

For the first harmonic, the wavelength is four times the length

so,

wavelength = 4 * length

wavelength = 4 * 0.197

wavelength = 0.788 m

speed = frequency * wavelength

352.3 = frequency * 0.788

frequency = 352.3 / 0.788

fundamental frequency = 447.08 Hz

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