Answer to Question #105522 in Physics for Lily

Question

A sound wave has a frequency of 738 Hz in air
and a wavelength of 0.5 m.
What is the temperature of the air? Assume the velocity of sound at 0◦C is 333 m/s.
Answer in units of ◦C.

Answer 1

$$v(T)=f\lambda=(738)(0.5)=369\frac{m}{s}$$

$$T=T_0\left(\left(\frac{v(T)}{v_0}\right)^2-1\right)$$

$$T=273\left(\left(\frac{369}{333}\right)^2-1\right)=62.2\degree C$$