A sound wave has a frequency of 684 Hz in air and a wavelength of 0.53 m. What is the temperature of the air? Assume the velocity of sound at 0◦C is 327 m/s. Answer in units of ◦C.

The temperature of air is 335.52 K or 62.52° C

Explanation:

First, we calculate the speed of sound wave at the temperature 'T'. We know that:

v = f λ

where,

v = speed of sound at temperature T

f = frequency of sound at Temperature T = 684 Hz

λ = wavelength of sound at temperature T = 0.53 m

Therefore,

v = (684 Hz) (0.53 m)

v = 362.52 m/s

Now, the speed of sound at any temperature, T, is given by the formula:

V = Vo√ (T/273)

T = (273) (V² / Vo²)

where,

Vo = speed of sound at 0° C = 327 m/s

Therefore,

T = (273) (362.52/327) ²

T = 335.52 K = 62.52° C