A standing wave is formed by the superposition of two waves travelling in opposite directions. The transverse
displacement is given by: yx,t=0.5sin
-x)cos 200mt) What is the speed of the travelling wave moving in
the positive x direction? (x and t are in meter and second respectively)
1) 160 m/s
2) 90 m/s
3) 180 m/s
4) 120 m/s
Answers
answer : option (1) 160 m/s
it is given that a standing wave is formed by the superposition of two waves travelling in opposite directions.
the displacement wave is given by, y(x, t) = 0.5sin(5π/4 x)cos(200πt/
we have to find the speed of the travelling wave.
we know, if two waves y₁ = Asin(ωt + kx) and y₂ = Asin(ωt - kx)
then supposition of these two waves , y = y₁+ y₂
= Asin(ωt + kx) + Asin(ωt - kx)
= 2Asin(ωt)cos(kx)
we also know, speed of travelling wave is given as v = ω/k
given equation is y = 0.5sin(5π/4 x)cos(200π t)
here ω = 200π , k = 5π/4
so, speed of travelling wave, v = (200π)/(5π/4)
Answer:
the displacement wave is given by, y(x, t) = 0.5sin(5π/4 x)cos(200πt/
we have to find the speed of the travelling wave.
we know, if two waves y₁ = Asin(ωt + kx) and y₂ = Asin(ωt - kx)
then supposition of these two waves , y = y₁+ y₂
= Asin(ωt + kx) + Asin(ωt - kx)
= 2Asin(ωt)cos(kx)
we also know, speed of travelling wave is given as v = ω/k
given equation is y = 0.5sin(5π/4 x)cos(200π t)
here ω = 200π , k = 5π/4
so, speed of travelling wave, v = (200π)/(5π/4)