Question

John ties a 15-m-long, 5 kg rope to a wall and stretches it out horizontally, placing it under a tension of 2000 N, which gives the rope a wave speed of 77.5 m/s. He then creates a wave in the rope by oscillating one end.

a) What is the frequency of the third harmonic for this rope?

b) What is the fundamental frequency of this rope?

c) What is the frequency of the third harmonic for this rope?

Answer 1

The frequency of a wave is given in terms of its wavelength and speed of propagation as

$f=\frac{v}{\lambda}$

The fundamental frequency corresponds to half wavelength fitting on the length of the rope. So at fundamental frequency the wavelength of the wave is twice of the length of the rope

f =

Substituting values

77.5 m/s J 2X (15 m)

f = 2.58 H2

The frequency of this rope is 2.58Hz.

The third harmonic of this rope is three times it's fundamental frequency.

f3 = 3f = 3 x 2.58 Hz = 7.74 Hz

The frequency of the third harmonic of this rope is 7.74 Hz.