A guitar string has a tension of 95 N and is 75 cm long. If its mass is 0.27 g, what is the frequency of the first resonance above the fundamental?
A) 685 Hz
B) 69 Hz
C) 217 Hz
D) 470 kHz

Question

Quizplus · Accepted Answer

The frequency of the first resonance above the fundamental (first harmonic or second mode of vibration) for a string is given by the formula $f = \frac{n}{2L} \sqrt{\frac{T}{\mu}}$, where $n$ is the mode number (n=2 for the first overtone), $L$ is the length of the string, $T$ is the tension in the string, and $\mu$ is the linear mass density of the string ($\mu = \frac{m}{L}$, with $m$ being the mass of the string). Given: $T = 95\,N$, $L = 75\,cm = 0.75\,m$, $m = 0.27\,g = 0.27 \times 10^{-3}\,kg$, the linear mass density $\mu = \frac{0.27 \times 10^{-3}}{0.75}$, and $n=2$. Plugging these values into the formula gives the frequency of the first overtone, which is approximately 685 Hz.

A Guitar String Has a Tension of 95 N and Is