Question

A guitar string is 90 cm long and has a mass of 3.4 g . The distance from the bridge to the support post is L=62cm, and the string is under a tension of 540 N . What are the frequencies of the fundamental and first two overtones? (Enter your answers in ascending order separated by commas).

Answer 1

length of string l = 90 cm = 0.9 m

mass of string m = 3.4 g = 3.4*10^-3 kg

linear mass density u = m/l = (3.4*10^-3)/0.9 = 3.78*01^-3 kg /m

speed of transverse wave in string v = sqrt(F/u) = sqrt(540/(3.78*10^-3)) = 378 m/s

length of the string under vibration L = 62 cm = 0.62 m

fundamental frequency fo = v/(2L)

fundamental frequency fo = 378/(2*0.62) = 304.8 Hz

first overtone f1 = 2*fo = 609.6 Hz

first overtone f2 = 3*fo = 914.4 Hz

304.8 Hz , 609.6 Hz , 914.4 Hz