Question

The equation of a wave along the x-axis is given as: ξ cm = 3.4 sin (1.16 x - 0.85 t)
in which ξ is the displacement. Units on the right hand side are 1/cm for К and 1/s for ω.
Determine the the traveling speed of the wave.

im assuming you get k=1.16 and w=0.85 meaning k=2pi/wavelength so i get wavelength = 541.4 m

and since w=2pi/T T= 7.39

therefore v= 541.4/7.39= 73.3

Im getting it wrong though. Where am i going wrong?

Answer 1

Along the crest of a wave,
1.16 x - 0.85 t = pi/2

The change in x per change is time, at constant phase, is the wave speed.

dx/dt = 0.85/1.16 = 0.733 cm/s

That's a pretty slow wave, but that's what it says.