How is the Maximum Speed of a Point on a Progressive Wave Calculated?

[nirvana1990]

Homework Statement

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.

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.

 

[learningphysics]

What is the general equation of a wave?

 

[nirvana1990]

equation

What is the general equation of a wave?

v=f lambda?

 

[learningphysics]

v=f lambda?

Have you see this equation before:

x = Acos(kx - wt)

 

[nirvana1990]

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