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Principle of Superposition

Two waves of ...

Question

Two waves of amplitude $A_{1}$ and $A_{2}$ respectively and equal frequency travels towards the same point. The amplitude of the resultant wave is

A

A_{1} + A_{2}

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B

A_{1} - A_{2}

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C

between

A_{1} + A_{2}

and

A_{1} - A_{2}

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D

Can not say

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Solution

The correct option is C between $A_{1} + A_{2}$ and $A_{1} - A_{2}$
If the two waves are in constructive phase, then the resultant amplitude will be equal to
$A = A_{1} + A_{2}$ (maximum)
If they are in destructive phase, then
$A = A_{1} - A_{2}$
Therefore the resultant amplitude will be always between $A_{1} + A_{2}$ & $A_{1} - A_{2}$
Hence option (C) is correct.
The resultant will depend on their phase difference.

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