Waves on a string and frequency

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SUMMARY

The discussion centers on the oscillation frequency of mass elements in a string modeled as a system of N masses. It establishes that each mass element oscillates at the same frequency in an ideal string without friction. The participants seek mathematical proof for this phenomenon and inquire whether it applies to realistic strings as well. The conversation references the wave equation as a foundational concept in understanding these oscillations.

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Physgeek64
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So I was reading our lecture notes about generalising the motion of a string by considering it as a system of N masses, and one of the arguments was that no matter where you are on the string, each mass element will oscillate with the same frequency. This makes intuitive sense for an ideal string with no friction, but is there a way to mathematically prove this/ does it only apply to ideal strings, or can it be extended to realistic strings?

Many thanks :)
 
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Svein said:
https://en.wikipedia.org/wiki/Wave_equation

I appreciate the reply, and I've had a scan through, but unless I've missed something I don't think it quite answers my question. It talks about eigenmodes, but not really about why this occurs.

Thank you though :)
 

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