Question

A sound wave has a frequency of 645 Hz in air

Answer 1

Answer:

$-14.2^{\circ}C$

Explanation:

First of all, we can find the speed of the sound wave, which is given by:

$v=f \lambda$

where

f = 645 Hz is the frequency

$\lambda=0.5 m$ is the wavelength

Substituting,

$v=(645 Hz)(0.5 m)=322.5 m/s$

Now we can find the temperature of the air by using the following relationship:

$v = 331 m/s + 0.6 T$

where T is the temperature in Celsius degrees. Since we know v = 322.5 m/s, we can re-arrange the formula to find the temperature:

$T=\frac{v-331 m/s}{0.6}=\frac{322.5 m/s-331 m/s}{0.6}=-14.2^{\circ}C$