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?
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.
In order to determine the traveling speed of the wave, we need to use the equation:
v = λ/T
where v is the wave velocity, λ is the wavelength, and T is the period of the wave.
You correctly calculated the wavelength (λ) as 541.4 m by using the equation λ = 2π/k, where k is given as 1.16 (which is the wave number).
However, you made a mistake while calculating the period (T). The equation you used, w = 2π/T, is correct, where w is the angular frequency given as 0.85 (which is ω).
Using the correct equation, we can rearrange it to solve for T:
T = 2π / w
Plugging in the value for w (0.85), we can calculate T:
T = 2π / 0.85 = 7.37 s (approximately)
Now, let's calculate the wave velocity (v) using the formula v = λ / T:
v = 541.4 m / 7.37 s ≈ 73.6 m/s
So, the correct traveling speed of the wave is approximately 73.6 m/s.