Wave speed as a function of compression?

[PhysicsMike]

Dear physics forum, I am doing an experiment on the vibrational behavior of beams and a question has come up that I can't answer. How does compression affect wave speed?

Brief overview of the experiment:

studying the change in vibrational behavior of a beam that is gradually tapered toward a point (equilateral triangle). Basically I have four beams:
Beam 1: uniform rectangle
Beam 2: tapering begins
Beam 3: more tapering
Beam 4: beam comes to a point at one end.

The beams are clamped at one end, with the other end open. If you take the ground to be the 'x-axis', then the length of the beam is in the 'x-axis', the width in the 'z-axis', and the height in the 'y-axis'. Aka the beam, which is quite flexible (synthetic trim board), does not sag due to gravity.
Their is a sin-wave generator located 100mm from the clamped end. I've found that even when i hang the beam, or stand it up (clamp closest to ground), the node placement does not change. What i have found, is that the wavelength decreases the farther i get from the clamped end, aka the wave speed is decreasing.
basically I've got compression on the bottom and tension on the top of the beam. I know v=sqrt(T/u), but does anyone have any insight into wave speed as a function of compression?

any insight is welcome, thanks

 

[gomunkul51]

Is the beam made out off two parts of which one is under tension and the other under compression? Or what is being compressed by what?Roman.

 

[Khashishi]

If you are talking about sound waves, the speed of sound depends on the bulk modulus. See https://en.wikipedia.org/wiki/Speed_of_sound
I suppose if most materials are compressed, the bulk modulus will increase, so the sound speed should increase.

 

[Khashishi]

If you are talking about sound waves, the speed of sound depends on the bulk modulus. See https://en.wikipedia.org/wiki/Speed_of_sound
I suppose if most materials are compressed, the bulk modulus will increase, so the sound speed should increase.

 

[PJC01]

Dear researcher,

Thank you for sharing your experiment and question with us. The relationship between wave speed and compression can be quite complex and is dependent on various factors such as the material properties of the beam, the shape and dimensions of the beam, and the type of wave being studied. However, there are some general principles that can help us understand this relationship.

Firstly, it is important to note that compression and tension can affect the wave speed in different ways. In compression, the particles of the medium are pushed closer together, while in tension, they are pulled further apart. This can lead to changes in the density and stiffness of the material, which in turn can affect the wave speed.

In a beam that is gradually tapered towards a point, the compression and tension forces are not evenly distributed throughout the beam. As you move away from the clamped end, the compression forces increase while the tension forces decrease. This change in force distribution can cause a change in the stiffness of the beam, which can affect the wave speed.

Another factor to consider is the shape of the beam. As the beam tapers towards a point, the cross-sectional area decreases, which can lead to an increase in stiffness. This can also contribute to a decrease in wave speed as the beam becomes more tapered.

Additionally, the type of wave being studied can also play a role in the relationship between wave speed and compression. For example, longitudinal waves, which involve particles moving parallel to the direction of the wave, are more affected by changes in density and stiffness of the medium. On the other hand, transverse waves, which involve particles moving perpendicular to the direction of the wave, may not be as affected by compression and tension forces.

In summary, the relationship between wave speed and compression is complex and can be affected by various factors such as the material properties, shape, and type of wave being studied. It is important to carefully consider these factors in your experiment and analyze your results to gain a better understanding of how compression affects wave speed in your specific setup. I hope this helps and wish you the best of luck with your experiment.