Question 171: Waves

Question

Two sources of sound S1 and S2 produce sound waves of same frequency 660 Hz. A listener is moving from
source S1 towards S2 with a constant speed u m/s and he hears 10 beats/s. The velocity of sound is 330 m/s.
Then, u equals :

Accepted Answer

As observer goes away from source S
1
so apparent frequency,
$${f_1} = \left( {{{v - u} \over v}} ight)f$$
here $$v$$ = speed of sound, $$u$$ = speed of observer
As observer goes towards source S
2
so apparent frequency,
$${f_2} = \left( {{{v + u} \over v}} ight)f$$
Beat frequency = $${f_2} - {f_1}$$ = 10
$$ \Rightarrow $$ $$\left( {{{v + u} \over v}} ight)f$$ - $$\left( {{{v - u} \over v}} ight)f$$ = 10
$$ \Rightarrow $$ $$f\left( {{{v - u - v + u} \over v}} ight)$$ = 10
$$ \Rightarrow $$ $$f\left( {{{2u} \over v}} ight)$$ = 10
$$ \Rightarrow $$ $$u = {{10v} \over {2f}}$$ = $${{10 	imes 330} \over {2 	imes 660}}$$ = 2.5 m/s

Answer

10.0 m/s

Answer

5.5 m/s

Answer

15.0 m/s

Answer

2.5 m/s

Waves

Two sources of sound S1 and S2 produce sound waves of same frequency 660 Hz. A listener is moving from source S1 towards S2 with a constant speed u m/s and he hears 10 beats/s. The velocity of sound is 330 m/s. Then, u equals :

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