Max. speed of particle on wave

In summary, the conversation discusses the generation and properties of progressive waves on a rope, including the calculation of the maximum speed of a point on the rope. The conversation also touches on the general equation of a wave and its relation to simple harmonic motion. The formula used to calculate the maximum speed is derived and compared to a similar equation found on a physics data sheet.
  • #1
nirvana1990
46
0

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.
 
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  • #2
What is the general equation of a wave?
 
  • #3
equation

learningphysics said:
What is the general equation of a wave?

v=f lambda?
 
  • #4
nirvana1990 said:
v=f lambda?

Have you see this equation before:

x = Acos(kx - wt)
 
  • #5
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
 

1. What is the maximum speed of a particle on a wave?

The maximum speed of a particle on a wave depends on the type of wave and the medium it is traveling through. In a transverse wave, the maximum speed is equal to the speed of the wave itself. In a longitudinal wave, the maximum speed is determined by the amplitude of the wave and the properties of the medium.

2. How does the maximum speed of a particle on a wave relate to the frequency and wavelength?

The maximum speed of a particle on a wave is directly proportional to the frequency and wavelength of the wave. This means that as the frequency or wavelength increases, the maximum speed of the particle also increases.

3. Is there a limit to the maximum speed of a particle on a wave?

Yes, there is a limit to the maximum speed of a particle on a wave. This limit is determined by the speed of light, which is the fastest speed possible in the universe. In most cases, the speed of a particle on a wave will be significantly slower than the speed of light.

4. How does the medium affect the maximum speed of a particle on a wave?

The properties of the medium, such as density and elasticity, can affect the maximum speed of a particle on a wave. In a denser or more elastic medium, the maximum speed of the particle will be higher compared to a less dense or less elastic medium.

5. Can the maximum speed of a particle on a wave be greater than the speed of the wave itself?

No, the maximum speed of a particle on a wave cannot be greater than the speed of the wave itself. This is because the particle is carried by the wave, so it cannot travel faster than the wave itself. However, the maximum speed of the particle can be equal to the speed of the wave in certain cases, such as in a transverse wave.

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