Two guitar strings, S1 and S2, are made of the same material and are stretched under identical tension so that waves travel along them at the same speed. String S1 is 0.65m long and vibrates at 300Hz in its fourth harmonic. String S2 is to be used to play the same 300Hz note but will be tuned to a different harmonic of its own.
(1) Derive an expression that relates the frequency f, harmonic number n, string length L, and common wave speed v for either string.
(2) Using your expression from part (a), determine the length L2 that S2 must have to sound 300Hz in its third harmonic.
(3) Suppose S1 is next excited at its sixth harmonic. Determine whether S2, without retensioning, could simultaneously resonate at one of its own harmonics to produce the same frequency. Justify your answer quantitatively.