Why Does a Longer or Thicker String Produce a Lower Note?

[1MileCrash]

Why does a longer, or thicker string produce a lower note when plucked? What is it about the larger spring that causes a lesser energy output?

My common intuition says that a larger spring is harder to move and therefore will vibrate with lesser frequency, but I am not satisfied with that reason.

 

[JaredJames]

A longer / thicker string vibrates at a lower frequency and so produces a lower note.

What do you mean "that causes a lesser energy output"? A spring can only output, at most, the same energy used to compress it. The larger the spring (larger in the 'thicker wire' sense), the more energy to compress it and so the more energy it outputs.

 

[1MileCrash]

A longer / thicker string vibrates at a lower frequency and so produces a lower note.

Yes. My question is, why does a thicker string vibrate at a lower frequency?

I am also under the impression that a wave with a higher frequency carries more energy.

 

[JaredJames]

I am also under the impression that a wave with a higher frequency carries more energy.

I'll start here for you, the energy of a wave is related to its amplitude, not frequency.

A good place for you to read up on the subject:

http://www.physicsclassroom.com/class/waves/u10l2c.cfm

The amount of energy carried by a wave is related to the amplitude of the wave. A high energy wave is characterized by a high amplitude; a low energy wave is characterized by a low amplitude.

Putting a lot of energy into a transverse pulse will not affect the wavelength, the frequency or the speed of the pulse. The energy imparted to a pulse will only affect the amplitude of that pulse.

 

[1MileCrash]

I see, so waves of equal amplitude but with wildy varying frequency are transporting the same amount of energy per time period?

 

[Andy Resnick]

Why does a longer, or thicker string produce a lower note when plucked? What is it about the larger spring that causes a lesser energy output?

My common intuition says that a larger spring is harder to move and therefore will vibrate with lesser frequency, but I am not satisfied with that reason.

The frequency f produced by a stretched string is given by:

f =\frac{1}{\lambda} \sqrt{\frac{T}{\rho}}

where \lambda is the wavelength (and is fixed by the geometry of the instrument),T the tension in the string, and \rho is the mass density (mass/length). A thicker string has a higher mass density.

So it's possible to tension a thicker string to have the same pitch as a thinner string, but that introduces other issues- stress on the attachment points, for example.

 

[JaredJames]

I see, so waves of equal amplitude but with wildy varying frequency are transporting the same amount of energy per time period?

Correct.

 

[1MileCrash]

Thanks guys. Andy, i can't see the equation on the mobile theme but i will be sure to check it out.

What characteristics of a wave ARE effected by frequency? Or is frequency more of an effect than a cause?

 

[schip666!]

One slight enhancement...

Originally Posted by 1MileCrash View Post

I am also under the impression that a wave with a higher frequency carries more energy.

Originally Posted by jarednjames View Post
I'll start here for you, the energy of a wave is related to its amplitude, not frequency.

The energy of a _mechanical_ wave is related to amplitude. You may have been thinking of electromagnetic waves where the energy is proportional to the frequency. But that's a different fettle of kish.

 

[893289004]

why is it that the shorter the string the higher the note?
why is a tighter string make a higher note?

 

[JaredJames]

why is it that the shorter the string the higher the note?
why is a tighter string make a higher note?

This has been answered by Andy Resnick in post number 6.