Two waves of the same frequency and same amplitude 'a' are reaching a point simultaneously. What should be the phase difference between the waves so that the amplitude of the resultant wave be :
(i) 2a (ii) `sqrt2a` (iii) a (iv) zero.

Explanation

To solve the problem of determining the phase difference between two waves of the same frequency and amplitude 'a' that results in different amplitudes of the resultant wave, we can use the principle of superposition of waves. The resultant amplitude \( A \) of two waves can be expressed as:

\[ A = \sqrt{A_1^2 + A_2^2 + 2A_1A_2 \cos(\phi)} \]

Where:
- \( A_1 \) and \( A_2 \) are the amplitudes of the two waves (both equal to \( a \) in this case).
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