Factors affecting speed of travelling waves along a cable

[pez.hayes]

I have a question concerning the speed of propagation of a traveling wave along a cable. If I have a cable and I move one end in a direction perpendicular to that of the length of the cable, it will generate a wave/pulse which will propagate along the cable with some speed. I imagine this speed depends on a number of properties of the cable: tension, elasticity, stiffness, density and also perhaps the viscosity of the fluid that the cable is resting in.

I can't, however, seem to find a formula to describe the speed of wave propagation based on these factors - has this been determined and can anyone point me in the right direction?

To give you some context, the cable I am concerned with is a cable in a biological sample. I've observed the propagation of waves of velocity along the cable and was hoping that extracting their speed could give me some insight into the properties of the biological tissue.

Thanks for any help!

 

[sophiecentaur]

'Waves on Strings" is what you should look up.
Here's one link.

 

[pez.hayes]

Thanks - that definitely gives more search results than waves on cables - so I find that velocity = sqrt(tension/linear density) but this doesn't take into account stiffness & plasticity of the string or the viscosity of the surrounding medium. I'm wondering if this is because with a typical tethered string in air all of these values are negligible and they approximate them to zero. Alternatively perhaps these values don't play a role in the velocity of propagation, only in the level of damping...

Can anyone help me out further on that?

 

[sophiecentaur]

This is quite a lot harder and not the 'ideal case'. The modulus of the medium would definitely contribute to the velocity and it would be hard to find the relationships involved.

Is there any particular reason why you want to use a cable in this way for your measurement? I would have thought that there would be easier alternative approaches which would involve a simpler basic arrangement with fewer variables - what about observing a standing compression wave in a container with the sample in it. That could give you the speed of propagation which. along with the would then give the modulus. Attenuation would give you the losses.
A rigid cylinder with an actuator one end and various loads the other end would do the job, in some circs. But of course, it's the specifics of your system that need to drive your choice.

 

[PJC01]

The speed of travelling waves along a cable is determined by several factors, including tension, elasticity, stiffness, density, and the surrounding medium's viscosity. These factors can affect the cable's ability to transmit the wave and the speed at which it travels.

Tension in the cable refers to the amount of force applied to it, and it can affect the speed of propagation by altering the cable's shape and stiffness. A higher tension can result in a stiffer cable, which can lead to faster wave propagation.

Elasticity is another important factor as it determines how easily the cable can be deformed and how quickly it can return to its original shape. A more elastic cable can transmit waves faster than a less elastic one.

Stiffness, or the resistance of a material to deformation, also plays a role in wave propagation. A stiffer cable will have a higher speed of wave propagation compared to a less stiff one.

Density, or the mass per unit volume of the cable, can also impact wave speed. A higher density cable will have a slower wave speed compared to a lower density one.

The surrounding medium's viscosity, or its resistance to flow, can also affect wave propagation. A more viscous medium can slow down the wave's speed as it moves through it.

To determine the exact formula for calculating the speed of wave propagation along a cable, you will need to consider the specific properties of the cable, such as its material, size, and shape, as well as the surrounding medium. Additionally, the type of wave being transmitted, such as a transverse or longitudinal wave, can also impact the speed.

In your case, studying the speed of waves in a biological sample can provide valuable insights into the tissue's properties, such as its elasticity and stiffness. I suggest consulting with a biologist or a materials scientist for further guidance on extracting this information from your observations.