Question

A sound wave propagates in air at 27°C with frequency 4.00 kHz. It passes through a region where the temperature gradually changes and then moves through air at 0°C. Give numerical answers to the following questions to the extent possible and state your reasoning about what happens to the wave physically.

(a) What happens to the speed of the wave?
(b) What happens to its frequency?
(c) What happens to its wavelength?

Answer 1

given,

temperature of wave propagates = 27°C

frequency of the sound wave = 4 kHz

speed of the sound wave depends upon the temperature according to the following equation

a)
`v = 331 * \sqrt{1 + (T_c)/(273^0C)}`

at 27°C

`v = 331 * \sqrt{1 + (27)/(273^0C)}`

v = 347 m/s

at 0°C

`v = 331 * \sqrt{1 + (0)/(273^0C)}`

v = 331 m/s

velocity of the wave is decreased by 16 m/s or

velocity is decreased by 4.6 %

b) frequency of the wave will remain unchanged.

c) wavelength of the wave will also decrease by 4.6 %

`\lambda = (v)/(f)`

`\lambda = (347)/(4000)`

`\lambda =86.7mm`

`\lambda = (v)/(f)`

`\lambda = (331)/(4000)`

`\lambda =82.7mm`