First slide

Characterstics of wave

Question

If two waves of same frequency and same amplitude respectively, on superposition produce a resultant disturbance of the same amplitude, the waves differ in phase by

Moderate

A

$π$
B

$2 π / 3$
C

$π / 3$
D

3 $π$

Solution

Resultant amplitude fl is given by
$= {[a_{1}^{2} + a_{2}^{2} + 2 a_{1} a_{2} \cos θ]}^{1 / 2} = {[a^{2} + a^{2} + 2 a^{2} \cos θ]}^{1 / 2} But R = a ∴ a = {[2 a^{2} (1 + \cos θ)]}^{1 / 2} = {[4 a^{2} \cos^{2} θ / 2]}^{1 / 2} a = 2 acos θ / 2 or \cos (θ / 2) = 1 / 2 or \frac{θ}{2} = \frac{π}{3} or θ = \frac{2 π}{3}$

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