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Q.

The equation of a simple harmonic wave is given by y=3sin⁡π2(50t−x)  where x and y are in meters and t is in seconds. The ratio of maximum particle velocity to the wave velocity is

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a

32π

b

c

23π

d

answer is A.

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Detailed Solution

y=3sin⁡π2(50t−x)  Particle velocity =∂y∂t=3π2×50cos⁡π2(50t−x)  Maximum particle velocity =75πm/s  Wave velocity v=ωk=501=50m/s& Required ratio =75π50=32π
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The equation of a simple harmonic wave is given by y=3sin⁡π2(50t−x)  where x and y are in meters and t is in seconds. The ratio of maximum particle velocity to the wave velocity is