Two sources of sounds S_{1} and S_{2} produce sound waves of the 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:

  • Option 1)

    5.5 m/s

  • Option 2)

    15.0 m/s

  • Option 3)

    2.5 m/s

  • Option 4)

    10.0 m/s

 

Answers (1)

f_{1}= apparent frequency received from S_{1}=\frac{C-u}{C}  f_{0}

f_{2}= apparent frequency received from S_{2}=\frac{C+u}{C} f_{0}

beat frequency = f_{2}-f_{1}=\left [ \frac{C+u}{C}-\frac{C-u}{C} \right ] f_{0} 

=\frac{2u}{C}f_{0}=10

\frac{2u\times 660}{330}=10

      u=\frac{10}{4}=2.5 m/s


Option 1)

5.5 m/s

Option 2)

15.0 m/s

Option 3)

2.5 m/s

Option 4)

10.0 m/s

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