A 60.00 cm guitar string under a tension of 46.000 N has a mass per unit length of 0.11000 g/ cm.
(a) What is the speed of the wave? (b) What is the fundamental wavelength for this string? (c) What is the fundamental frequency for this string? (d)What is the highest resonant frequency that can be heard by a person capable of hearing frequencies up to 20,000 Hz?
Mass per unit length m(o) =0.011 kg/m T=46 N
Speed in the stretched string is v = sqrt(T/m(o)) =sqrt(46/0.011)= 64.7 m/s
λ=2L=1.2 m
f=v/ λ=64.7/1.2=53.9 Hz
Resonant frequency F(n)=n•v/2L=n(64.7/1.2)=53.9•n=20000
n=20000/53.9 =370 => f(n)= n•v/2L=370•64.7/1.2=19949 HZ