When two sound waves with a phase difference of $\pi/2$ , and each having amplitude A and frequency $\omega$ , are superimposed on each other, then the maximum amplitude and frequency of resultant wave is
Text Solution
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Let $y_1 = A \sin(\omega t)$
and $y_{2} = A \sin \left( \omega t + \frac{\pi}{2} \right) \ldots$ (i)
Resultant amplitude
$R = A^2 + A^2 + 2A^2 \cos \left(\frac{\pi}{2}\right)$ $\Rightarrow R = \sqrt{2A^2 + 2A^2 \times 0}$ $\Rightarrow R = \sqrt{2A^2}$ $\Rightarrow R = \sqrt{2} A$
However, both will have the same frequency on superimposing.
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