Question

A sound wave has a frequency of 620 Hz in air

and a wavelength of 0.5 m.
What is the temperature of the air? As-
sume the velocity of sound at 0°C is 327 m/s.
Answer in units of C.

Answer 1

The temperature of the air is -27°C

Step-by-step explanation:

Given:

Frequency (f)=620 Hz

Wavelength (λ)=0.5 m

To Find:

Temperature of air = ?

Formula to be used:

`T=T_(0) * ( (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* 0.5=310 m/s`

Temperature of the air is given by the expression

`T=T_(0) * ( (v^2)/(v_(0)^2) -1)\\\\=273*((310^2)/(327_(0)^2) -1)\\\\=-27 \°C`

Thus the temperature of the air is -27°C