Amplitude of a wave represented by displacement equation y = frac{1}{{√ a }},sin ,omega t pm

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14.Waves and Sound

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The amplitude of a wave represented by displacement equation $y = \frac{1}{{\sqrt a }}\,\sin \,\omega t \pm \frac{1}{{\sqrt b }}\,\cos \,\omega t$ will be

A

$\frac{{a + b}}{{ab}}$

B

$\frac{{\sqrt a + \sqrt b }}{{ab}}$

C

$\frac{{\sqrt a \pm \sqrt b }}{{ab}}$

D

$\sqrt {\frac{{a + b}}{{ab}}} $

Solution

$\mathrm{y}=\frac{1}{\sqrt{\mathrm{a}}} \sin \omega \mathrm{t} \pm \frac{1}{\sqrt{\mathrm{b}}} \sin \left(\omega \mathrm{t}+\frac{\pi}{2}\right)$

Here phase difference $=\frac{\pi}{2}$

Resultant amp. $=\sqrt{\left(\frac{1}{\sqrt{a}}\right)^{2}+\left(\frac{1}{\sqrt{b}}\right)^{2}}=\sqrt{\frac{1}{a}+\frac{1}{b}}$

$=\sqrt{\frac{a+b}{a b}}$

Standard 11

Physics

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