A guitar string has a linear density of 8.30 × 10^-⁴ kg/m and a length of 0.660 m.The tension in the string is 56.7 N.When the fundamental frequency of the string is sounded with a 196.0-Hz tuning fork,what beat frequency is heard? A)6 Hz B)4 Hz C)12 Hz D)8 Hz E)2 Hz

Question

Quizplus · Accepted Answer

The fundamental frequency of the 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 linear density of the string. Substituting the given values: $f = \frac{1}{2 \times 0.660} \sqrt{\frac{56.7}{8.30 \times 10^{-4}}}$, calculating this gives $f \approx 194 \, \text{Hz}$. The beat frequency is the absolute difference between the frequencies of the tuning fork and the string, which is $|196 - 194| = 2 \, \text{Hz}$. Therefore, there was an error in the initial selection; the correct answer is E, not D.

A Guitar String Has a Linear Density of 8