A 25-g string is stretched with a tension of 43 N between two fixed points 12 m apart.What is the frequency of the second harmonic?
A)6.0 Hz
B)12 Hz
C)18 Hz
D)24 Hz
E)36 Hz

Question

Quizplus · Accepted Answer

The frequency of the second harmonic (n=2) in a stretched string can be calculated using the formula $f_n = \frac{n}{2L} \sqrt{\frac{T}{\mu}}$, where $f_n$ is the frequency of the nth harmonic, $L$ is the length of the string, $T$ is the tension in the string, and $\mu$ is the mass per unit length of the string. Given that the string is 25 g (0.025 kg) and 12 m long, the mass per unit length $\mu = \frac{0.025}{12}$ kg/m. Substituting the given values and $n=2$, we find $f_2 = \frac{2}{2 \times 12} \sqrt{\frac{43}{0.025/12}}$, which simplifies to 12 Hz.

A 25-G String Is Stretched with a Tension of 43