A guitar string with a tension of $150 \mathrm{~N}$ is played together with a tuning fork whose frequency is $256 \mathrm{~Hz}$, and beats of $2 \mathrm{~Hz}$ are heard. Assuming the guitar string is higher in frequency than the tuning fork, to what new tension should the guitar string be adjusted for the string and tuning fork to have the same frequency?
A) $151 \mathrm{~N}$
B) $148 \mathrm{~N}$
C) $152 \mathrm{~N}$
D) $149 \mathrm{~N}$
E) The length of the string must be given in order to solve this problem.

Question

Quizplus · Accepted Answer

The beat frequency is 2 Hz, so the guitar string's frequency is 258 Hz. The frequency of a string is proportional to the square root of the tension. To decrease the frequency to 256 Hz, the tension should be decreased. Using the formula $ f \propto \sqrt{T} $, solve for the new tension: $ \frac{256}{258} = \sqrt{\frac{T_{\text{new}}}{150}} $. Solving gives $ T_{\text{new}} \approx 148 \mathrm{~N} $.

A Guitar String with a Tension Of 150 N150 \mathrm{~N}150 N Is Played Together with a Tuning Fork Whose Frequency Is

A Guitar String with a Tension Of $150 \mathrm{~N}$ Is Played Together with a Tuning Fork Whose Frequency Is