Two piano strings are simultaneously played-their mass and length are identical, but the tensions differ. If the first string resonates with a fundamental frequency of 330 Hz, and its tension is 1.2% greater than that of the second string, what is the fundamental frequency of the second string?
A) 328 Hz
B) 326 Hz
C) 336 Hz
D) 334 Hz

Question

Quizplus · Accepted Answer

The fundamental frequency of a string is proportional to the square root of the tension. If the tension in the first string is 1.2% greater, then the frequency of the second string will be lower. The relationship between frequency and tension is given by $f \propto \sqrt{T}$, so if the tension in the first string is 1.012 times the tension in the second, the frequency ratio is $\sqrt{1.012}$. Thus, the frequency of the second string is $330 / \sqrt{1.012}$ ≈ 328 Hz.

Two Piano Strings Are Simultaneously Played-Their Mass and Length Are