Stiffness (constant) of string/wire relationship to Amplitude/Energy output

[blahblah.]

Homework Statement

So I'm doing a string/wire telephone experiment where I'm using a signal generator to vibrate a wire at a certain input frequency. I am then taking results down for the Amplitude output. I'm not quite sure on the relationship between Stiffness constant K and Amplitude.
I've worked out the stiffness constant for 3 wires Nichrome, Copper and Constantan, and just want to show the relationship between the stiffness from Hooke's law and the amplitude.

Homework Equations

F = KΔX
Stored energy W = (1/2)KX²
Amplitude ∞ Energy²

The Attempt at a Solution

I'm not sure if it's as simple as just finding the area under the Hooke's law graphs for each metal wire (up until it's no longer elastic/the non-liner part). As the stored energy in the stiffer wires would be greater, this energy is transferred into Kinetic energy for the wires which will vibrate faster and therefore give a greater amplitude.

Would really appreciate some help, my calculations are all over the place!

 

[anathema]

Hello,

Thank you for sharing your experiment and questions. It sounds like a very interesting experiment! First of all, let's clarify the relationship between the stiffness constant, K, and amplitude. The stiffness constant, as you mentioned, is related to Hooke's law and is a measure of how much force is needed to deform an object. The amplitude, on the other hand, is a measure of the maximum displacement of the vibrating wire. So, in general, the higher the stiffness constant, the more force is needed to deform the wire and thus the smaller the amplitude. This can be seen in the equation F = KΔX, where a higher K would result in a smaller ΔX for a given force, and thus a smaller amplitude.

Now, regarding your question on how to show the relationship between stiffness and amplitude for different wire materials, you are correct in thinking that the area under the Hooke's law graph can give us an idea of the stored energy and thus the amplitude. However, this may not be the most accurate way to compare the stiffness and amplitude for different materials. This is because the stiffness constant, K, is also affected by other factors such as the length and cross-sectional area of the wire. So, simply comparing the areas under the Hooke's law graphs may not give a fair comparison.

One way to show the relationship between stiffness and amplitude for different materials would be to plot a graph of stiffness constant (K) vs amplitude for each wire material. This would allow you to directly compare the stiffness and amplitude for each material. Additionally, you can also plot a graph of stiffness constant vs maximum displacement (ΔX) for each material, as this would also give you an idea of how the stiffness affects the maximum displacement of the wire.

I hope this helps and good luck with your experiment!