A wave y = a,sin ,left( {omega t - kx} right) on a string meets with another wave producing a node a

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14.Waves and Sound

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A wave $y = a\,\sin \,\left( {\omega t - kx} \right)$ on a string meets with another wave producing a node at $x = 0$. Then the equation of the unknown wave is

A

$y = a\,\sin \,\left( {\omega t + kx} \right)$

B

$y = - a\,\sin \,\left( {\omega t + kx} \right)$

C

$y = a\,\sin \,\left( {\omega t - kx} \right)$

D

$y = - a\,\sin \,\left( {\omega t - kx} \right)$

Solution

$y = a\,\sin \,\left( {\omega t – kx} \right) – a\,\sin \,\left( {\omega t + kx} \right)$

$y = – 2a\,\cos \,\omega t\,\sin \,kx$

at $x = 0 \Rightarrow y = 0$ (node)

Standard 11

Physics

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