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14.Waves and Sound
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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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