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

(a) and (c) Third harmonic frequency will be 7.75 Hz

(b) Fundamental frequency will be 2.5833 Hz

Explanation :

Mass of the rope m = 5 kg

(b) We have given length of the rope l = 15 m

Wave speed v = 77.5 m /sec

We know that frequency is given by
`f=(v)/(\lambda )`

Here
`\lambda =2l`

So
`f=(v)/(2l)=(77.5)/(2* 15)=2.5833Hz`

(a) and (c) Frequency of the third harmonic of the rope will be = 3× fundamental frequency = 3×2.5833 = 7.75 Hz