Solved: Two identical taut strings under the same tension

Chapter 16, Problem 16.57

(choose chapter or problem)

Two identical taut strings under the same tension F produce a note of the same fundamental frequency \(f_0\). The tension in one of them is now increased by a very small amount \(\Delta F\).

(a) If they are played together in their fundamental, show that the frequency of the beat produced is \(f_{\text {beat }}=f_{0}(\Delta F / 2 F)\).

(b) Two identical violin strings, when in tune and stretched with the same tension, have a fundamental frequency of 440.0 Hz. One of the strings is retuned by increasing its tension. When this is done, 1.5 beats per second are heard when both strings are plucked simultaneously at their centers. By what percentage was the string tension changed?