Physics - Sound Wave Question with Solution | TestHub

Let the frequency of the sirens be $f=330$ Hz and the speed of sound be $v=330$ m/s.

The observer moves away from the first siren with speed $v_o=2$ m/s. The apparent frequency heard from the first siren is:

$f_1=f\left(\frac{v-v_o}{v}\right)$

The observer moves towards the second siren with speed $v_o=2$ m/s. The apparent frequency heard from the second siren is:

$f_2=f\left(\frac{v+v_o}{v}\right)$

The beat frequency heard by the observer is the difference between the two apparent frequencies:

$f_{beat}=f_2-f_1=f\left(\frac{v+v_o}{v}\right)-f\left(\frac{v-v_o}{v}\right)=f\left(\frac{2v_o}{v}\right)$

Substituting the given values:

$f_{beat}=330\left(\frac{2\times 2}{330}\right)=4$ Hz.

Answer: $4$ Hz