If the frequency of a violin string is to be increased by 20% , what change in tension must be applied?
A) 20%
B) 44%
C) 4.5%
D) 10%

Question

If the frequency of a violin string is to be increased by  20% , what change in tension must be applied?
A)  20% 
B)  44% 
C)  4.5% 
D)  10%

Quizplus · Accepted Answer

The frequency of a string is given by $f = \frac{1}{2L} \sqrt{\frac{T}{\mu}}$, where $f$ is the frequency, $L$ is the length of the string, $T$ is the tension, and $\mu$ is the linear mass density of the string. Since the frequency is to be increased by 20%, and the frequency is proportional to the square root of the tension ($f \propto \sqrt{T}$), to achieve a 20% increase in frequency, the tension must be increased by a factor that, when square rooted, gives 1.20. Solving for the new tension factor: $ \sqrt{T_{new}} = 1.20 \sqrt{T_{old}} $, squaring both sides gives $ T_{new} = 1.44 T_{old} $, which is a 44% increase in tension.

If the Frequency of a Violin String Is to Be