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Question

A steel wire of mass 4.0 g and length 80 cm is fixed at the two ends. The tension in the wire is 50 N. Find the frequency and wavelength of the fourth harmonic of the fundamental.

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Solution

m=(480)g/cm

=0.005 kg/m

T=50N

L=80cm=0.8m

v=(Tm)

=(500.005)=100 m/s

Fundamental frequency,

f=12L(Tm)

={12×0.8×(500.005)}

=100(2×0.8)

=10016=62.5 Hz

First harmonic = 62.5 Hz

f4= frequency of forth harmonic

=4f0=f3=62.5×4

=250Hz

v=f4λ4

(vf)=100250

=0.4m=40cm


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