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Three one-dimensional mechanical waves i...

Three one-dimensional mechanical waves in an elastic medium is given as
`y_1 = 3A sin (omegat - kx), y_2 = A sin (omegat - kx + pi) and y_3 = 2A sin (omegat + kx)`
are superimposed with each other. The maximum displacement amplitude of the medium particle would be

A

4A

B

3A

C

2A

D

A

Text Solution

Verified by Experts

The correct Answer is:
A
`y=y_(1)+y_(2)+y_(3)`
`=3Asin(omegat-kx)+Asin(omegat-kx+pi)+2Asin(omegat+kx)`
`=[Asin(omegat-kx)-Asin(omegat-kx)]+[2Asin(omegat-kx)+2Asin(omegat+kx)]`
`=2Asin(omegat-kx)+2Asin(omegat+kx)=4Asinomegatcoskx y_(max)=4A`.
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