Question

Can two waves of the same frequency and amplitude travelling in the same direction give rise to a stationary wave after superposition?

Accepted Answer

Superposition of two waves travelling in the same direction give rise to another travelling wave (not a standing wave).

Let the two superposing waves be

$y_{1} = A \sin (ω t - k x)$
$y_{2} = A \sin (ω t - k x + ϕ)$

where $ϕ$ is the phase difference between the two waves. From principle of superposition the resultant wave function is
$= y_{1} + y_{2} = A \sin (ω t - k x) + A \sin (ω t - k x + ϕ)$

$= 2 Acos \frac{ϕ}{2} \sin (ω t - k x + \frac{ϕ}{2})$

This is the expression for a travelling wave with amplitude $2 Acos ϕ / 2 .$ Hence superposition of two waves travelling in the same direction give rise to another travelling wave with different amplitude, which depends on the phase difference between the two waves.

B M Sharma Solutions for Chapter: Superposition and Standing Waves, Exercise 1: ILLUSTRATIONS

B M Sharma Physics Solutions for Exercise - B M Sharma Solutions for Chapter: Superposition and Standing Waves, Exercise 1: ILLUSTRATIONS

Questions from B M Sharma Solutions for Chapter: Superposition and Standing Waves, Exercise 1: ILLUSTRATIONS with Hints & Solutions

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