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  4. Two sound sources emitting sound each of wavelength λ are fixed at points A and B. A listener moves with velocity u from A to B. The number of beats heard by him per second is

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Q. Two sound sources emitting sound each of wavelength $\lambda$ are fixed at points $A$ and $B. A$ listener moves with velocity u from $A$ to $B$. The number of beats heard by him per second is

JIPMERJIPMER 2014Waves

Solution:

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The observed frequency from $A$,
$\upsilon_A = \frac{\upsilon(\upsilon_s - u)}{\upsilon_s}$
where $\upsilon_s$ is the velocity of sound The observed frequency from $B$,
$\upsilon_B = \frac{\upsilon(\upsilon_s - u)}{\upsilon_s}$
$\therefore $ Number of beats per second
$ = \upsilon_B - \upsilon_A = 2 \frac{\upsilon}{\upsilon_s} u = \frac{2u}{\lambda}$