Answer :
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:
[tex]T=T_{0} \times ( \frac{v^2}{v_{0}^2} -1)[/tex]
Solution:
[tex]velocity\ of\ sound\ at\ 0\°C v_{0} =327 m/s\\[/tex]
velocity at the current temperature v=fλ
[tex]v=620\times 0.5=310 m/s[/tex]
Temperature of the air is given by the expression
[tex]T=T_{0} \times ( \frac{v^2}{v_{0}^2} -1)\\\\=273\times(\frac{310^2}{327_{0}^2} -1)\\\\=-27 \°C[/tex]
Thus the temperature of the air is -27°C