# 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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