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Question:

A standing wave is formed by the superposition of two waves travelling in opposite directions. The transverse displacement is given by y(x,t)=0.5sin(5π/4x)cos(200πt). What is the speed of the travelling wave moving in the positive x direction?

180m/s

160m/s

120m/s

90m/s

Solution:

y(x,t) = 0.5sin(5π/4x)cos(200πt)
y1 =Asin(kx+ωt)
y2=Asin(-ωt+kx)
y1+y2=A [ sin(kx)cos(ωt)+cos(kx)sin(ωt) + sin(kx)cos(ωt)-cos(kx)sin(ωt)]
y1+y2=2Asin(kx)cos(ωt)
v=ω/k =200π/(5π/4) =160m/s