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Question

Adjoining figure shows the snapshot of two waves A and B at any time t. The equation for A is y=Asin(kxωtϕ), and for B it is y = A sin (kxωt). It is clearly shown in the figure that wave A is ahead of B by a distance ϕk.

The motion of a single point in time, i.e., y versus t for two waves is best represented by

A
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B
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C
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D
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Solution

The correct option is B
The equation for wave A can be rewritten as
y=A sin[kxωtϕ]
=A sin[k(xϕkωt)]
A sin[kω(t+ϕk)]
While equation of wave B is y=A sin(kxωt).
Comparing above equations, we can easily conclude that A is at a distance ahead of ϕk from B or wave
A is ahead of B by a time difference of ϕω. So, (b) is the correct option.

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