Longitudinal waves on a string

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• zongo123
In summary, a string can transmit sound without tension, but longitudinal waves are more likely to be heard because they propagate faster.
zongo123
Good day to everyone,

I kindly ask for your help. My question is: "Does a string have to be under tension, to transmit longitudinal waves? Why is it so?" I have trouble finding relevant scientific articles regarding the question and for reasearching "longitudinal waves on a string". If anyone knows a good source for studying this, please point at that direction.

Thank you! Have a nice day :)

Hello @zongo123 ,
!
Your question is definitely valid. But I think you could come up with some arguments alll by yourself. Take a piece of rope, fix one end and experiment.

For waves to propagate, whether longitutinal or transverse, there has to be some kind of restoring force. It's hard to imagine a restoring force in the absence of any tension whatsoever.

Do you agree ?

##\ ##

zongo123 said:
Does a string have to be under tension, to transmit longitudinal waves?
Technically a material can transmit sound even without pretension. But this might not be what is meant by "longitudinal waves in a string". For example, in a string made of fibers the sound speed within the fiber material can be different than the longitudinal wave speed in the whole compound, where fibers change shape and move relative to each other.

sophiecentaur
What do you think is the difference between a sound wave and a longitudinal wave? And how can the sound speed within the material differ from that of a longitudinal wave? I would say they are the same thing.

Arjan82 said:
And how can the sound speed within the material differ from that of a longitudinal wave?
The question is about a "string" which is not a material. It is an object that can contain parts of various geometries and materials.

Consider the difference between the longitudinal wave propagating along the axis of a spring vs. the sound propagating in wire the spring is made of.

nasu
I have been told that when playing a stringed instrument such as a guitar, players can cause longitudinal waves to propagate along a string when they slide their fingers along the string. You hear this as a note with a higher pitch because longitudinal waves propagate faster than transverse waves in a guitar spring.

sophiecentaur
The speed of longitudinal waves would certainly be a lot higher than transverse waves on a string so resonances would be a lot higher. The fact that the squeaks can be so loud would suggest that there could be resonances involved. (Those squeaks are only (afair) set up on the wound strings.)

Edit [ I suggest that the 'surface wave mode' could also exist (Thick and thin cross sections) - slower than straight compression wave but faster than transverse]

Last edited:
The Yamaha G12 midi guitar relies on longitudinal waves to measure distance from bridge to the fret the string is pressed against. Any transverse waves are ignored.

sophiecentaur

1. What are longitudinal waves on a string?

Longitudinal waves on a string are a type of mechanical wave that travels along the length of a string or other elastic medium. They are characterized by particles of the medium vibrating parallel to the direction of wave propagation.

2. How do longitudinal waves on a string differ from transverse waves?

Unlike transverse waves, which have particles that vibrate perpendicular to the direction of wave propagation, longitudinal waves have particles that vibrate parallel to the direction of wave propagation. This results in a compression and rarefaction of the medium, rather than a displacement.

3. What factors affect the speed of longitudinal waves on a string?

The speed of longitudinal waves on a string is affected by the tension, density, and thickness of the string. Generally, higher tension and lower density will result in a faster wave speed, while a thicker string will have a slower wave speed.

4. How are longitudinal waves on a string measured and represented?

Longitudinal waves on a string are typically measured and represented using a graph of displacement versus time. The amplitude of the wave represents the maximum displacement of the string, while the wavelength is the distance between two consecutive points of maximum displacement.

5. What are some real-world applications of longitudinal waves on a string?

Longitudinal waves on a string have many practical applications, such as in musical instruments (e.g. guitar strings), seismic exploration, and medical imaging (e.g. ultrasound). They are also used in non-destructive testing to detect flaws or defects in materials.

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