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Question

Three one dimensional mechanical waves in an elastic medium is given as and
y1=3Asin(ωtkx)
y2=Asin(ωtkx+π)
y3=2Asin(ωt+kx)
are superimposed with each other. The maximum displacement amplitude of the medium particle would be

A
4A
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B
3A
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C
2A
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D
A
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Solution

The correct option is A 4A
It is very clear from the question that the waves 1 and 2 will always interfere destructively since, they are completely out of phase with respect to each other.

Therefore, the resultant wave will always have an amplitude of 3A - A = 2A

Now, this wave has to interact with the third wave, constructively to produce a wave that has the maximum amplitude.

This would only be possible if the resultant wave has an amplitude of 2A + 2A = 4A

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