question_answer

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 m/s and he hears 10 beats/s. The velocity of sound is 330 m/s. Then, u equals: [JEE Main 12-4-2019 Afternoon]

A)  2.5 m/s                        

B)  15.0 m/s

C)  5.5 m/s                        

D)  10.0 m/s

Correct Answer: A

Solution :

[a]

\[f=660\text{ }Hz,v=330\text{ }m/s\]

\[{{f}_{1}}=f\left( \frac{\text{v}-u}{\text{v}} \right)\]

\[{{f}_{2}}=f\left( \frac{\text{v+}u}{\text{v}} \right)\]

\[{{f}_{2}}-{{f}_{1}}=\frac{f}{\text{v}}[v+u-(v-u)]\]

\[10={{f}_{2}}-{{f}_{1}}=\frac{f}{\text{v}}[2u]\]

\[u=2.5m/s\]