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Question

Two small objects are 15 m apart on the water surface of a lake. Each object pops up and down with a period of 4.5 second due to wave motion on water surface.
When one object is at its highest point, the another one is at its lowest point. Consider that objects are always within a single cycle of wave, the speed of wave is
(Assume transverse surface waves)

A
2.5 m/s
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B
103 m/s
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C
12 m/s
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D
203 m/s
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Solution

The correct option is D 203 m/s
Assuming transverse displacement of objects.
Both the objects are having a phase difference of π, because while one is at its maximum (highest) point the other one is at lowest position.

Seperation between particles = λ2
15=λ2 or λ=30 m
and Time period, T=4.5 sec
v=fλ=λT
v=304.5=203 m/s (wave speed)

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