NEET Physics Question - Waves - Principle of Superposition, Interference and Beats

Assertion (A): If two waves of same amplitude produce a resultant wave of same amplitude, then the phase difference between them will be \(120^\circ\).

Reason (R): The resultant amplitude of two waves is equal to sum of amplitude of two waves.

Both (A) & (R) are true and the (R) is the correct explanation of the (A)

Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

(A) is true but (R) is false

Both (A) and (R) are false

Solution:

For two waves of amplitude \(A\) and phase difference \(phi\), the resultant amplitude is \(A_r = 2A \cos(\frac{\phi}{2})\). Given \(A_r = A\), so \(A = 2A \cos(\frac{\phi}{2})\), which means \(cos(\frac{\phi}{2}) = \frac{1}{2}\). Thus \(\frac{\phi}{2} = 60^\circ\), so \(\phi = 120^\circ\). Hence (A) is true. The resultant amplitude is the sum only if \(\phi = 0\). So (R) is false.

Rankers Physics

Assertion and Reason

Solution:

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