(adsbygoogle = window.adsbygoogle || []).push({}); [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

[tex]f = v/(2L)[/tex]

[tex]v = \sqrt{T / \mu }[/tex]

3. The attempt at a solution

Suppose the lowest string is tuned at the fundamental frequency f_{1}= v_{1}/(2L), where v_{1}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}f_{1}= v_{n}/(2L). So,

[tex]1.5^{n - 1}v_1 = v_n[/tex]

Now, since [itex]v_i = \sqrt{T/\mu_i}[/itex], then

[tex]\mu_n = \frac{\mu_1}{1.5^{2(n-1)}}[/tex]

Is that right?

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# Homework Help: Mass per Unit Length of Violin Strings

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