Answer to Question #103004 in Physics for Nyx

Question

A sound wave has a frequency of 658 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 335 m/s.
Answer in units of ◦C.

Answer 1

$$v=\lambda f=(0.53)(658)=348.7\frac{m}{s}$$

$$\frac{T}{T_0}=\frac{v^2}{v_0^2}-1$$

$$\frac{T}{273}=\frac{348.7^2}{335^2}-1$$

$$T=22.8\degree C$$