A string with a mass/length of 0.00200 kg/m is stretched between two points with a tension of 115 N. If the distance between the points is changed by 1.0% (keeping the tension and mass per unit length the same), then what is the percentage change of the frequency?
A) 0.50%
B) 0.75%
C) 1.00%
D) 1.25%
E) 1.50%

Question

Quizplus · Accepted Answer

The frequency of a wave on a string is given by $f = \frac{1}{2L} \sqrt{\frac{T}{\mu}}$, where $L$ is the length of the string, $T$ is the tension in the string, and $\mu$ is the mass per unit length of the string. If the length of the string changes by 1%, the frequency changes as the inverse of the square root of the length. Since the length $L$ is in the denominator and inside a square root, a 1% decrease in $L$ leads to a 1% increase in $f$, because the relationship between frequency and length is inversely proportional and the square root does not change the percentage change.

A String with a Mass/length of 0