# Q & A: Dropping balls on guitar strings

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Most recent answer: 03/21/2014
Q:
Hi! I was in deep thought one day and just wondered this. If I take some balls (maybe steel?) of different weights and drop them (at the same hight) on a string (which are propped up like guitar strings are), will each of the different balls have different frequencies? If it does, why is it like that? This question was just something I was curious about.
- Anonymous
A:

Hello ....

It depends whether or not the ball sticks to the string.   If not, then the string doesn't care what hit it and it will oscillate at its own natural frequency.   It the ball sticks to the string then the oscillation frequency will depend on the mass of the ball. The heavier the mass the lower the frequency of oscillation.

LeeH

(published on 03/06/2014)

## Follow-Up #1: Balls striking strings

Q:
Hi its me again. This is in response to the "dropping balls on guitar stings". I sent this question twice already and i waited for one week each time i entered this question in. But to my surprise i didnt get an answer. Anyways, back to the question... If the balls didnt stick to the string and instead, made a sound. Would the different weights of the balls make a different sound frequency when it hits the string. Hopefully i will get a response this time. :(
- Anonymous
A:

Hi

If the balls stick and their mass is much larger than the mass of the string then you will get eigenmodes.  For N equally spaced balls on the string there are N eigenmodes.   The frequency or frequencies of oscillation will have a factor of √(T/ma)  where T is the tension, m is the mass of one ball and a is the separation of the balls.If you want the gory details take a look at

If the mass or masses do not stick then the string will oscillate at several of its natural frequencies, fN = Nv/2L where v = √(T/ρ) and ρ is the mass per unit length.

I don't know the answer if the mass of the ball and the mass of the string are comparable.   Why don't you do a little experiment by sticking a small mass to a stretched string and measuring its frequency.  You could do this on a guitar.  let us know your results.

LeeH

(published on 03/21/2014)