A string with a linear density of 0.035 kg/m and a mass of 0.014 kg is clamped at both ends.Under what tension in the string will it have a fundamental frequency of 110 Hz?
A)270 N
B)310 N
C)450 N
D)580 N
E)690 N

Question

Quizplus · Accepted Answer

The fundamental frequency (f) of 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 linear density of the string. Given $\mu = 0.035 \, \text{kg/m}$ and the mass of the string $m = 0.014 \, \text{kg}$, we can find the length $L$ of the string as $L = \frac{m}{\mu} = \frac{0.014}{0.035} = 0.4 \, \text{m}$. Substituting the given fundamental frequency $f = 110 \, \text{Hz}$ and solving for $T$, we get $T = \mu (2Lf)^2 = 0.035 \times (2 \times 0.4 \times 110)^2 = 270 \, \text{N}$.

A String with a Linear Density of 0