Q.

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

Moderate

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

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

maximum amplitude is 4A and minimum amplitude is 2A

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

answer is 3,4.

(Detailed Solution Below)

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Detailed Solution

y=y1+y2=A sin (ωt−kx)+3A sin (ωt+kx)=A sin ωt cos kx−A cos ωt sin kx+3A sin ωt cos kx+3A cos ωt sin kx=4A sin ωt cos kx+2A cos ωt sin kx=2A sin ωt cos kx+2A sin (ωt+kx)It is combination of a stationary and travelling wave.Maximum amplitude = 4 A.Minimum amplitude = 2 ADistance between points having amplitude 4A and 2A will be =λ/4=v/4f

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