How do i solve A sound wave has a frequency of 658 Hz in air

and a wavelength of 0.46 m.

What is the temperature of the air? Assume the velocity of sound at 0◦C is 331 m/s.

Answer in units of ◦C

-47 °C

Explanation:

Speed of sound in air at sea level is:

v = 331 m/s + 0.6 m/s/°C T

where T is the temperature in Celsius.

The speed of sound is also the frequency times the wavelength:

v = fλ

Therefore:

fλ = 331 m/s + 0.6 m/s/°C T

(658 Hz) (0.46 m) = 331 m/s + 0.6 m/s/°C T

302.68 m/s = 331 m/s + 0.6 m/s/°C T

-28.32 m/s = 0.6 m/s/°C T

T = - 47.2 °C

Rounding to two significant figures, the temperature is - 47 °C.