First slide

Superposition of waves

Question

Two sound waves (expressed in CGS units) given by $y_{1} = 0 .3 \sin \frac{2 π}{λ} (vt - x)$ and $y_{2} = 0 .4 \sin \frac{2 π}{λ} (vt - x + θ)$ interfere. The resultant amplitude at a place where phase difference is $π / 2$ will be

Moderate

A

0.7 cm
B

0.1 cm
C

0.5 cm
D

$\frac{1}{10} \sqrt{7} cm$

Solution

Resultant amplitude = $\sqrt{a_{1}^{2} + a_{2}^{2} + 2 a_{1} a_{2} cosφ}$
$= \sqrt{0 {.3}^{2} + 0 {.4}^{2} + 2 \times 0 .3 \times 0 .4 \times \cos \frac{π}{2}} = 0 .5 cm$

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