Question

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.)

???s

At what point do the two pulses always cancel?

???m

Answer 1

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.