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Max. speed of particle on wave

by nirvana1990
Tags: particle, speed, wave
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nirvana1990
#1
Sep15-07, 03:36 PM
P: 46
1. The problem statement, all variables and given/known data

Progressive waves are generated on a rope by vibrating vertically the end, P, in simple
harmonic motion of amplitude 90 mm. The wavelength of the waves
is 1.2 m and they travel along the rope at a speed of 3.6ms–1. Assume that the wave motion is not damped.

Calculate the maximum speed of point P.



3. The attempt at a solution

The actual solution is V=2(pi)xfxA
Since f=v/wavelength= 3.0 Hz and A=90x10^-3m the answer is 1.70 m/s

I don't understand why this formula is used and where the 2pi has come from. Is it to do with simple harmonic motion? I would be very grateful if someone could help with a derivation of the formula.
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learningphysics
#2
Sep15-07, 03:51 PM
HW Helper
P: 4,124
What is the general equation of a wave?
nirvana1990
#3
Sep15-07, 03:56 PM
P: 46
Quote Quote by learningphysics View Post
What is the general equation of a wave?
v=f lambda???

learningphysics
#4
Sep15-07, 04:11 PM
HW Helper
P: 4,124
Max. speed of particle on wave

Quote Quote by nirvana1990 View Post
v=f lambda???
Have you see this equation before:

x = Acos(kx - wt)
nirvana1990
#5
Sep15-07, 04:20 PM
P: 46
oh gosh no I haven't! erm on my physics data sheet there's a similar equation: x=Acos2Pift. hmmm I'll see what comes up when I google the equation you just gave me! Thanks


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