How Long Does It Take for a Particle on a String to Move Through 1.0 km?

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SUMMARY

The discussion centers on calculating the time required for a particle on a string to move through a distance of 1.0 km, given a wave speed of 450 m/s, a wavelength of 0.18 m, and an amplitude of 2.0 mm. The correct approach involves recognizing that the wave speed is governed by the formula: wave speed = wavelength x frequency. The time taken for the particle's motion is distinct from the wave's propagation, necessitating an understanding of both amplitude and frequency to solve the problem accurately. The final answer is confirmed to be 5.0 x 10 seconds.

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  • Knowledge of the relationship between wave properties and particle motion in a medium.
  • Basic proficiency in solving physics problems involving waves and oscillations.
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Students studying physics, particularly those focusing on wave mechanics, as well as educators and anyone interested in understanding the dynamics of wave motion in strings.

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Homework Statement


A wave is moving through a string at 450 m/s. The wavelength is 0.18 m and the amplitude is 2.0 mm. What is the time required for a particle on the string to move through 1.0 km? (The answer given is 5.0x10 s).


Homework Equations


The only equations I can think of are the ones relating frequency, period, wave speed and wavelength, where wave speed = wave length x frequency. The period is the inverse of frequency.


The Attempt at a Solution


If I divided the 1.0 km by the wave speed, I get 2.22 s. I don't know how else the 1.0 km is related to anything else, and can't figure out how the amplitude has to do with anything. How do you even find the function of the wave? This has been bothering me for almost a week now and I've been looking up every physics text I can find in the library and none of them could offer me a solution. Please help. Thanks.
 
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Don't mix up the motion of the wave itself--governed by that speed = wave length X frequency formula--with the motion of the particles of the string. The wave moves along the string, but which way do the particles of the string move? That's where the amplitude (and the frequency) comes in.
 
Doc Al said:
Don't mix up the motion of the wave itself--governed by that speed = wave length X frequency formula--with the motion of the particles of the string. The wave moves along the string, but which way do the particles of the string move? That's where the amplitude (and the frequency) comes in.

Wow. I finally get it now. Thanks for the brilliant tip. I don't know why I never thought of it that way before.
 

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