## University Physics with Modern Physics (14th Edition)

(a) $f_1 = 408~Hz$ (b) The person could hear frequencies up to the 24th harmonic.
(a) We can find the speed of the wave. $v = \sqrt{\frac{F_T}{\mu}}$ $v = \sqrt{\frac{F_T}{(m/L)}}$ $v = \sqrt{\frac{F_T~L}{m}}$ $v = \sqrt{\frac{(800~N)(0.400~m)}{0.00300~kg}}$ $v = 326.6~m/s$ We can find the fundamental frequency, which occurs when n = 1: $f_1 = \frac{v}{2L}$ $f_1 = \frac{326.6~m/s}{(2)(0.400~m)}$ $f_1 = 408~Hz$ (b) We can find the harmonic $n$ which could be heard by a person who can hear frequencies up to 10,000 Hz. $n~f_1 \leq 10,000~Hz$ $n \leq \frac{10,000~Hz}{f_1}$ $n \leq \frac{10,000~Hz}{408~Hz}$ $n \leq 24.5$ The person could hear frequencies up to the 24th harmonic.