Question

A sound wave has a frequency of 620 Hz in air

Answer 1

The temperature of the air is -27°C

Explanation:

Given:

Frequency (f)=620 Hz

Wavelength (λ)=0.5 m

To Find:

Temperature of air = ?

Formula to be used:

$T=T_{0} \times ( \frac{v^2}{v_{0}^2} -1)$

Solution:

$velocity\ of\ sound\ at\ 0\°C v_{0} =327 m/s$

velocity at the current temperature v=fλ

$v=620\times 0.5=310 m/s$

Temperature of the air is given by the expression

$T=T_{0} \times ( \frac{v^2}{v_{0}^2} -1)\\\\=273\times(\frac{310^2}{327_{0}^2} -1)\\\\=-27 \°C$

Thus the temperature of the air is -27°C