# Mass per Unit Length of Violin Strings

1. Apr 25, 2007

### e(ho0n3

[SOLVED] Mass per Unit Length of Violin Strings

1. The problem statement, all variables and given/known data
Each string on a violin is tuned to a frequency 1.5 times that of its neighbor. If all the strings are to be placed under the same tension, what must be the mass per unit length of each string relative to that of the lowest string?

2. Relevant equations
$$f = v/(2L)$$
$$v = \sqrt{T / \mu }$$

3. The attempt at a solution
Suppose the lowest string is tuned at the fundamental frequency f1 = v1/(2L), where v1 is the velocity of the standing wave on the lowest string and L being the length of the string. For n > 1, fn = 1.5n - 1f1 = vn/(2L). So,

$$1.5^{n - 1}v_1 = v_n$$

Now, since $v_i = \sqrt{T/\mu_i}$, then

$$\mu_n = \frac{\mu_1}{1.5^{2(n-1)}}$$

Is that right?

Last edited: Apr 25, 2007
2. Apr 25, 2007

### e(ho0n3

I have checked the answer with the book. It coincides. Thanks anyways.