First slide

Superposition of waves

Question

Two waves having equations
$x_{1} = asin (ω t + φ_{1}), x_{2} = asin (ω t + φ_{2})$
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
$\Rightarrow a^{2} = a^{2} + a^{2} + 2 a^{2} cosφ = 2 a^{2} (1 + cosφ)$
$\Rightarrow cosφ = - 1 / 2 = \cos 2 π / 3 ∴ φ = 2 π / 3$

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