Question

A guitar produces sound at specific frequencies generated by standing waves that are created by the plucking of the string under tension.

Calculate the frequency of the first harmonic (in Hz) of the sound generated from plucking a string with a mass per unit length of 6 g/m, under tension of 133 N and a length between supports of 0.7 m.

Answer 1

Solution:

First find the wave speed in the string,

v = T/

= [133/6*10^-3]^1/2

= 148.9 m/s.

Consider a string in a guitar is a string with fixed at both sides,

The wavelength for fundamental frequency is = 2L = 2*0.7 = 1.4 m.

The fundamental frequency is,

f = v/ = 148.9/1.4

= 106.35 Hz.

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