First slide

Interference

Question

Two waves having equations
$x_{1} = asin (ωt + φ_{1}), x_{2} = asin (ωt + φ_{2})$
If in the resultant wave the frequency and amplitude remain equal to those of superimposing waves. Then phase difference between them is

Moderate

A

$\frac{π}{6}$
B

$\frac{2 π}{3}$
C

$\frac{π}{4}$
D

$\frac{π}{3}$

Solution

Superposition of waves does not alter the frequency of resultant wave and resultant amplitude
$\Rightarrow a^{2} = a^{2} + a^{2} + 2 a^{2} cosφ = 2 a^{2} (1 + cosϕ)$
$\Rightarrow cosφ = - \frac{1}{2} = \cos \frac{2 π}{3} ∴ φ = \frac{2 π}{3}$

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