Gujarati
Hindi
14.Waves and Sound
normal

Two waves represented by

$y_1 = 10\,sin\,(2000\,\pi t + 2x)$

and ${y_2} = 10{\mkern 1mu} \,sin\,{\mkern 1mu} \left( {2000{\mkern 1mu} \pi t + 2x + \frac{\pi }{2}} \right)$ are superposed at any point at a particular instant. The resultant amplitude is ..... $unit$

A

$10$

B

$20$

C

$14.1$

D

$0$

Solution

The resultant amplitude $A$ of two waves of amplitudes ${a_1}$ and ${a_2}$ at $a$ phase difference $\phi$ is

$\left(a_{1}^{2}+a_{2}^{2}+2 a_{1} a_{2} \cos \phi\right)^{1 / 2}$

Substituting

$[{a_1} = 10,{a_2} = 10$ and ${\rm{ }}\phi  = {90^\circ },$ we get $A = 14.1]$

Standard 11
Physics

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