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

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Homework Help Overview

The discussion revolves around calculating the maximum speed of a point on a progressive wave generated by simple harmonic motion on a rope. The parameters include an amplitude of 90 mm, a wavelength of 1.2 m, and a wave speed of 3.6 m/s.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to understand the formula for maximum speed in the context of wave motion and questions the origin of the 2π factor, suggesting a link to simple harmonic motion. Other participants inquire about the general equation of a wave and discuss related equations.

Discussion Status

Participants are exploring various equations related to wave motion and simple harmonic motion. Some guidance has been offered regarding the general equations, but there is no explicit consensus on the derivation of the formula or its components.

Contextual Notes

There is a mention of a physics data sheet that includes a similar equation, indicating potential constraints in the information available to the original poster. The discussion also reflects uncertainty about the equations and their applications in the context of the problem.

nirvana1990
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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.
 
Physics news on Phys.org
What is the general equation of a wave?
 
equation

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

v=f lambda?
 
nirvana1990 said:
v=f lambda?

Have you see this equation before:

x = Acos(kx - wt)
 
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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