Two stationary sources each emit waves of wavelength -An observer moves from one source to another with velocity u- Then the number of beats heard by him-

Let the two sources A, B emit sound of frequency v_o =vλ When observer moves B → A ,It receives compressed waves from A , whose frequency i ...

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Standard XII

Physics

Listener and Source Moving

Two stationar...

Question

Two stationary sources each emit waves of wavelength $λ$ .An observer moves from one source to another with velocity u. Then the number of beats heard by him?

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Solution

Let the two sources $A, B$ emit sound of frequency $v_{o} = \frac{v}{λ}$
When observer moves $B \to A$ ,
It receives compressed waves from $A$ , whose frequency is :
$v_{A} = v_{o} (\frac{u + v}{u})$ [From Doppler'n Effect ]
It receives elongated waves from $B,$ given by
$v_{B} = v_{o} (\frac{u - v}{u})$
Thus, frequency of beats observed by him :
$v_{b e a t} = | v_{A} - v_{B} | = v_{o} (\frac{u + v - u + v}{u})$
$\Rightarrow v_{b e a t} = \frac{2 v^{2}}{u λ} (a s v_{o} = \frac{v}{λ})$

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Two stationary sources each emit waves of wavelength λ.An observer moves from one source to another with velocity u. Then the number of beats heard by him?

Two stationary sources each emit waves of wavelength $λ$ .An observer moves from one source to another with velocity u. Then the number of beats heard by him?