Waves on a string and frequency

In summary, the conversation discusses generalizing the motion of a string by considering it as a system of N masses. It is noted that each mass element will oscillate with the same frequency, regardless of its position on the string. The question is raised about whether this holds true for both ideal strings and realistic strings. The reply mentions eigenmodes, but does not fully address the question.
  • #1
Physgeek64
247
11
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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  • #3
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 :)
 

Related to Waves on a string and frequency

What is a wave on a string?

A wave on a string is a type of mechanical wave that travels through a medium, such as a string or rope. It is characterized by the transfer of energy from one particle to the next, without the actual movement of the medium itself.

How does frequency affect a wave on a string?

Frequency is the number of complete cycles or oscillations that a wave completes in one second. In a wave on a string, the frequency determines the pitch or perceived sound of the wave. A higher frequency will result in a higher pitch, while a lower frequency will result in a lower pitch.

What is the relationship between wavelength and frequency in a wave on a string?

Wavelength and frequency are inversely proportional in a wave on a string. This means that as the frequency increases, the wavelength decreases, and vice versa. This relationship is described by the equation: wavelength = speed of the wave / frequency.

How does tension in the string affect the frequency of a wave?

The tension in the string directly affects the frequency of a wave on a string. As the tension increases, the frequency also increases, resulting in a higher pitch. This is because a higher tension allows for the wave to travel faster through the string, resulting in more oscillations per second.

What is the difference between a standing wave and a traveling wave on a string?

A standing wave is a wave on a string that appears to be still, while a traveling wave moves through the string. This is due to the interference of two waves traveling in opposite directions, resulting in certain points of the string remaining stationary. In contrast, a traveling wave will continue to move through the string without any points remaining still.

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