Question

Two sources of sound $S_{1}$ and $S_{2}$ produce sound waves of same frequency $660 \, Hz.$ A listener is moving from source $S_{1}$ towards $S_{2}$ with a constant speed $u_{0} \, ms^{- 1}$ and he hears $10 \, beat\,s^{- 1}$ . The velocity of sound is $330 \, ms^{- 1}.$ Then, $u_{0}$ equals:

• A. $10.0 \, ms^{- 1}$
• B. $2.5 \, ms^{- 1}$
• C. $5.5 \, ms^{- 1}$
• D. $15.0 \, ms^{- 1}$

Answer 1

Answer: (B)

Frequency observed from $S_{1}:\, f_{1}=660\left(\frac{330 - u_{0}}{330 - 0}\right)$
Frequency observed from $S_{2}:\, f_{2}=660\left(\frac{330 + u_{0}}{330 - 0}\right)$
As $f_{2}-f_{1}=10$
$660\left[\frac{330 + u_{0}}{330 - 0} - \frac{330 - u_{0}}{330 - 0}\right]=10$
$2\left(2 u_{0}\right)=10$
$u_{0}=2.5 \, ms^{- 1}$