Pitch of sound: Elasticity vs Tension of string

[ap_cycles]

Hi there,

I saw this question in a book. Basically, we are asked to comment on the effects of Tension of a guitar chord and the Elasticity of the chord itself on the frequency of the sound the guitar produces.

I understand Elasticity will have a positive effect on the speed of sound, and the natural frequency of the chord itself, but will it have any effect on the frequency of sound produced when the guitar chord is struck?

I fully understand that the bigger the applied tension, the higher pitch the sound will be. But elasticity stumps me...quick frankly.

Can fellow forummers help me pls? I am a high school Science teacher...

 

[Eynstone]

Tension is proportional to the elasticity.

 

[Stonebridge]

I'm not sure I fully understand the question, but there are 2 ways of looking at this.
The frequency of the sound the string produces will depend on a) its length, b) tension and c) linear density (mass per unit length)
Once you have a string on the instrument, you can't change c) so that for practical purposes, the note you get depends only on a) and b)
You adjust b) to tune up and then it's only a) that matters.
The elasticity, on the other hand, (Youngs Modulus) depends on the material you use. Steel wires have a higher value than, say, copper. (Though copper isn't normally used!)
Once you have the wire on the guitar and tuned up, the elasticity of the wire itself doesn't determine the frequency of the note. It does, on the other hand, determine how much you have to turn the tuning key to get the right tension. (Effectively, the extension needed to create the right tension. This is what post 2 above is alluding to.).
Wires made from different materials (and therefore having a different elasticity) will give the sound produced a different timbre, but that would be difficult to quantify.
Hope this helps.

 

[ap_cycles]

Thanks Stonebridge for the reply.I see the problem is more of being logically coherent...

 

[PJC01]

I can provide some insight into the relationship between the pitch of sound and the elasticity and tension of a string. First, it's important to understand that the pitch of a sound is determined by its frequency, which is the number of vibrations or cycles per second. In the case of a guitar string, the frequency is determined by the tension and elasticity of the string.

When a guitar string is struck, it vibrates at a certain frequency, which is determined by the tension of the string. The higher the tension, the higher the frequency and therefore the higher the pitch of the sound produced. This is because the tension of the string affects the speed at which the string vibrates and the distance it can travel during each vibration.

Now, let's consider the role of elasticity. Elasticity refers to the ability of a material to stretch and return to its original shape. In the case of a guitar string, the elasticity of the material allows it to vibrate at its natural frequency, which is determined by its length and thickness. This natural frequency is also known as the fundamental frequency. When a guitar string is struck, it not only vibrates at its fundamental frequency but also at multiple higher frequencies, known as harmonics. These harmonics contribute to the overall sound produced by the guitar string.

So, to answer the question, the elasticity of a guitar string does not directly affect the pitch of the sound produced. However, it does play a role in allowing the string to vibrate at its natural frequency, which contributes to the overall sound and can be adjusted by changing the tension of the string. As a high school science teacher, it's important to understand these concepts and how they relate to sound and music. I hope this helps clarify the relationship between pitch, tension, and elasticity in the context of a guitar string.