Mass per Unit Length of Violin Strings

[e(ho0n3]

[SOLVED] Mass per Unit Length of Violin Strings

Homework Statement

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?

Homework Equations

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

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, f_n = 1.5^{n - 1}f₁ = v_n/(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?

 

[e(ho0n3]

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