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The stationary wave y = 2a sinkx cosomeg...

The stationary wave y = 2a sinkx cos`omega`t in a stretched string is the result of superposition of `y_(1)=a sin(kx-omegat)` and

A

`y_(2)=acos(kx+omegat)`

B

`y_(2)=asin(kx+omegat)`

C

`y_(2)=acos(kx-omegat)`

D

`y_(2)=asin(kx-omegat)`

Text Solution

Verified by Experts

The correct Answer is:
B
`y_(1)=asin(kx-omegat)`
`y_(2)=asin(kx+omegat)`
According to the principle of superposition, the resultant wave is
`y=y_(1)+y_(2)=asin(kx-omegat)+asin(kx+omegat)`
Using trigonometric identity
`sin(A+B)+sin(A-B)=2sinAcosB`
we get, y=2asinkxcos`omega`t
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