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Question

A horizontal rope of 1 m length, having a mass 100 g, is fixed at one end and is tied to a light string at the other end. Find the frequency and wavelength of the fifth overtone, if the tension in the string is 40 N.

A
50 Hz,20 cm
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B
55 Hz,36 cm
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C
110 Hz,36 cm
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D
55 Hz,72 cm
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Solution

The correct option is B 55 Hz,36 cm
Given that,
l=1 m
m=100 g or 0.1 kg
T=40 N

Wave speed on a stretched string is

v=Tμ=400.1=20 m/s

Frequency of fifth overtone for string fixed at one end

f5=11v4L=11×204×1=55 Hz

and we know
v=f5λ5
wavelength λ5=vf5=2055=0.3636 m36 cm

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