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Two waves of equal frequency f and velocity v travel in opposi

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Two waves of equal frequency f and velocity v travel in opposite directions along the same path. The waves have amplitudes A and 3A. Then:

the amplitude of the resulting wave varies with position between maxima of amplitude 4 A and minima of zero amplitude

the distance between a maxima and adjacent minima of amplitude is v/2 f

maximum amplitude is 4 A and minimum amplitude is 2 A

the position of a maxima or minima of amplitude does not change with time

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Two waves of equal frequency f and velocity v travel in opposite directions along the same path. The waves have amplitudes A and 3A. Then:

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Text solutionVerified

y = y_{1} + y_{2}

= A s in (ω t - k x) + 3 A s in (ω t + k x)

= A s in ω t cos k x - A cos ω t s ink x + 3 A s in ω t cos k x + 3 A cos ω t s ink x

= 4 A s in ω t cos k x + 2 A cos ω t s ink x

= 2 A s in ω t cos k x + 2 A s in (ω t + k x)

It is combination of a stationary and travelling wavw.
Maximum amplitude = 4 A
Minimum amplitude = 2 A
Distance between points having amplitude 4 A and 2 A will be

= λ /4 = v /4 f

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Question Text	Two waves of equal frequency f and velocity v travel in opposite directions along the same path. The waves have amplitudes A and 3A. Then:
Answer Type	Text solution:1
Upvotes	151

Two waves of equal frequency f and velocity v travel in opposite directions along the same path. The waves have amplitudes A and 3A. Then:

Text solutionVerified

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