What Happens When Two Traveling Waves Superpose?

[sydboydell31]

(a) The displacements of two traveling waves are given by:

D1(x,t) = A sin[kx +ωt +φ]

and

D2 (x,t) = A sin[kx −ωt +φ] where A=0.01m, k=5rad.m−1,ω=200rad.s−1 andφ=π3rad

(i) Use the appropriate trigonometric identity to find the displacement resulting from the superposition of these two waves.

(ii) Is the wave resulting from this superposition a traveling wave? Briefly explain your answer.

(iii) Find a value for the separation between adjacent maxima (antinodes) in the resultant wave.

thanks guys

 

[jbsteele]

(i) The displacement resulting from the superposition of the two waves is given by: D(x,t) = 2A sin[kx]cos[ωt + φ] (ii) Yes, the wave resulting from this superposition is a traveling wave. This is because the resultant wave has the same wave speed (ω/k) as the two original waves, and it can move in either direction along the x-axis.(iii) The separation between adjacent maxima (antinodes) in the resultant wave is given by λ = 2π/k. Therefore, for the given values of k, the separation between adjacent maxima is λ = 2π/5 = 1.26 m.