A string on a guitar is stretched between two points 30.0 cm apart with a tension of 100 N. The mass/length of the string is 0.00300 kg/m. The frequency of the mode of vibration with the lowest frequency is
A) 304 Hz.
B) 350 Hz.
C) 376 Hz.
D) 415 Hz.
E) 433 Hz.

Question

Quizplus · Accepted Answer

The frequency of the mode of vibration with the lowest frequency (fundamental frequency) for a string can be calculated using the formula $f = \frac{1}{2L} \sqrt{\frac{T}{\mu}}$, 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. Substituting the given values: $L = 0.30$ m, $T = 100$ N, and $\mu = 0.00300$ kg/m, we get $f = \frac{1}{2 \times 0.30} \sqrt{\frac{100}{0.00300}}$, which calculates to approximately 304 Hz.

A String on a Guitar Is Stretched Between Two Points