In the production of beats by two waves of same amplitude and nearly same frequency, the maximum intensity to each of the constituent waves is

Same

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2

times

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4

times

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8

times

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Solution

The correct option is C $4$ times
Let the two wave superimposing to produce beats be-
$y_{1} = A s i n (k x + w t)$
$y_{2} = A s i n (k x + [w + Δ w] t)$
$∴$ The beat equation $y = y_{1} + y_{2} = 2 A s i n (k x) c o s (w t)$
Thus the amplitude of the beat produced $A^{'} = 2 A$
Intensity $I \propto A^{2}$
$∴$ $\frac{I^{'}}{I} = \frac{(A^{'})^{2}}{A^{2}} = \frac{(2 A)^{2}}{A^{2}} = 4$
$⟹$ $I^{'} = 4 I$
Hence the intensity becomes $4$ times that of constituent waves.

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