The displacement equations of two interfering waves are given by respectively. The amplitude of the resultant wave is ________ cm. [2023]

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Solution

Q.
The displacement equations of two interfering waves are given by

$y_{1} = 10 \sin (ω t + \frac{π}{3}) cm$

$y_{2} = 5 [\sin (ω t) + \sqrt{3} \cos (ω t)] cm$ respectively.

The amplitude of the resultant wave is ________ cm. [2023]

Ans.
(20)

$y_{2} = 5 (\sin ω t + \sqrt{3} \cos ω t)$

$= 10 \sin (ω t + \frac{π}{3})$

$Thus the phase difference between the waves is 0$

$So A = A_{1} + A_{2} = 20 cm$

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