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Question

A 2.00 m-long rope, having a mass of 80 g, is fixed at one end and is tied to a light string at the other end. The tension in the string is 256 N. Find the frequencies of the fundamental and the first two overtones.


A

20 Hz, 40 Hz, 80 Hz

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B

10 Hz, 20 Hz, 30 Hz

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C

10 Hz, 30 Hz, 50 Hz

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D

None of these

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Solution

The correct option is C

10 Hz, 30 Hz, 50 Hz


Since one end is tied to a light string on the other side. At this point an antinode will be formed and a node will be formed at the fixed end.

given m = 80g = 0.08 kg

L = 2m

μ = mL = 0.082 = 0.04 kgm

tension,T = 256

v = Tμ = 2560.04 = 160.2 = 80 ms1

fundamental frequency is given by v4L

f0 = 804 × 2 = 10 Hz

The first overtone is the 3rd harmonic and is given by 30 Hz.

The second overtone is the 5th harmonic and is given by 50 Hz


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