Question

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 2a.​

Answer 1

Explanation:

Resultant amplitude of two waves of amplitude A1 and A2 having phase angle theta is given by formula

R= √(A1^2 + A2^2 + 2× A1×A2×cos(theta)

Given A1 =A2 and resultant = 2×A

2×A = √(A^2 + A^2 + 2× A×A× cos(theta)

2A = √(2×A^2 + 2×A^2×cos(theta)

2A = √2A^2(1 + cos(theta)

Squaring both sides

4A^2 = 2A^2(1 + cos(theta)

2 = 1 + cos (theta)

Cos(theta) = 1

Theta = 0

Means two waves should superimpose such that phase difference must be zero.

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