At time t=0, equation of a wave pulse is y(x,0)=53+(x−4)2 and at t=2s, equation of the same wave pulse is y(x,2)=53+(x+8)2. Here, y is in mm, x is in m and t is in sec. The wave speed is
A
5m/s
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B
6m/s
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C
6mm/s
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D
3mm/s
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Solution
The correct option is B6m/s Given, at t=0, y(x,0)=53+(x−4)2.....(1) Also, at t=2s, y(x,2)=53+(x+8)2.....(2)
Assuming the wave pulse is travelling towards right, we can replace x with x−vt, where v is wave speed in m/s and t is time (in seconds). Therefore from (1), we get y(x,t)=53+((x−vt)−4)2.....(3)
Comparing (2) with (3) we get, −vt−4=8⇒−v=12t At t=2s, v=−6m/s Thus, wave speed |v|=6m/s