Science Buddies: "Ask an Expert"

What is the difference in frequency of guitar strings that are the same size, tension, etc, but are composed of different materials?

Moondog - When you say 'same size' of the guitar wires I assume you are refering to the diameter and length of the material. The materials may be very different, and the 'mass' of the string material will greatly change the vibrating or 'resonant' frequency. The greater the mass (even though the diameter, length and tension are the same) the lower the frequency. Many guitar strings may use the same diameter steel wire cores for several frequencies, but to achieve a lower, or more bass frequency, wrap additional wire around the core wire. The tension and length may be the same, but the increased mass that the additional winding adds produces a very low vibrating frequency.

Rick

Hi moondog, if you are interested in the mathematics of this problem, you might like to see this equation for the fundamental frequency of an ideal taut string:

f = √(TL/m)/2L
where

* f is the frequency in Hertz (Hz)
* T is the string tension in Newtons (N)
* L is the length of the string in meters (m)
* m is the mass of the string in kilograms (kg)
* √(TL/m) is the square root of T times L divided by m

http://www.school-for-champions.com/sci ... uation.htm

From that equation, you can see that the frequency decreases as the mass increases.

Another version of the math (slightly more advanced) is here:
http://openlearn.open.ac.uk/mod/resourc ... ?id=289483

Good luck!
Chris

Hi moondog,

It seems like you're asking that if everything was constant EXCEPT the mechanical properties of the material, what the difference in frequency would be

As far as I know, there is no simple (or even complex?) equation that can quantify that. Is there any way that you can change your project that involves the manipulation of variables that are more easily quantified, such as mass, length, natural frequency, etc.?

-Dan

Dan, excuse me but

As far as I know, there is no simple (or even complex?) equation that can quantify that.

is clearly contradicted by a first order approximation given by Chris above in

f = √(TL/m)/2L

which means the mass per unit length of the string will be the primary differentiating factor. This is something that can be predicted by using an accurate scale to weight the strings.

Unfortunately, the diameters of strings for musical instruments made from different materials are often different so doing your experiment with them would be difficult. On the other hand, copper, aluminum, and steel wire can be obtained that is the same guage if you want to do this kind of an experiment.

There are some second order effects that deal with bending moments of materials but these effects are much much smaller than the ones in the equation Chris gave you.