Two wave pulses travel on a string toward each other. The wave pulses can be described as y1 = 5/(((kx − ωt)^2) 2) and y2 = −5/(((kx + ωt − 6)2 )+2)' , where k = 1 rad/m and ω = 8 rad/s. At what instant do the two cancel everywhere? (Assume x is in meters and t is in seconds.)
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At what point do the two pulses always cancel?
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Take the superposition of the two displacements
the required condition is, y1 + y2 = 0
=>
=>
taking square root on both sides,
this gives
substitute the value 8 rad/s to get, t = 0.375 s
So, at t = 0.375 s, the waves cancel out.
Now, for the two waves to get cancelled,
Substitute for = 8 rad/s, t = 0.375 s and k = 1 rad/s to get x
=> x - 8(0.375) = 0
=> x = 3 m.
this is the point where the pulse always get cancelled.
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