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Question

A wave is travelling along positive x direction with speed 4 m/s. Further, equation of the wave pulse at t=0 is y(x,0)=54+(3x+6)2. The equation of the same pulse after t s will be

A
54+9(x+12t+2)2
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B
54+9(x4t+2)2
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C
54+9(x+4t+2)2
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D
54+(3x+12t+6)2
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Solution

The correct option is B 54+9(x4t+2)2
Given, at t=0
y(x,0)=54+(3x+6)2
Re-writing the above equation, we get
y(x,0)=54+9(x+2)2 .......(1)

If the speed of the pulse is v, then the pulse will travel to the right by a distance vt in time t.
Assuming the shape of the pulse does not change with time, the transverse position of the particles for all positions and times, measured in a stationary frame with the origin at O can be written as
y(x,t)=y(xvt,0)

Therefore, replacing x with xvt in the equation (1), we get
y(x,t)=54+9(xvt+2)2
Given that , speed of the wave v=4 m/s
y(x,t)=54+9(x4t+2)2

Thus, option (b) is the correct answer.

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