A guitar string with a mass of 12 g is 80 cm long and attached to the guitar at two points separated by 65 cm.What is the frequency of its fundamental note when it is placed under a tension of 170 N?
A)74 Hz
B)82 Hz
C)93 Hz
D)150 Hz
E)160 Hz

Question

Quizplus · Accepted Answer

The fundamental frequency of a string is given by the formula $ f = \frac{1}{2L} \sqrt{\frac{T}{\mu}} $, where $ L $ is the length of the vibrating part of the string (65 cm = 0.65 m), $ T $ is the tension (170 N), and $ \mu $ is the linear mass density (mass/length = 0.012 kg/0.8 m = 0.015 kg/m). Plugging in these values gives $ f \approx 82 $ Hz.

A Guitar String with a Mass of 12 G Is