Observe end find a pattern Tie one end of a rope (or one end of a long, tightly

Question

Observe end find a pattern Tie one end of a rope (or one end of a long, tightly wound spring) securely to a post. Hold the other end in your hand and vibrate it up and down at different frequencies. At most frequencies, the rope responds little to your efforts. However, at special frequencies, big amplitude vibrations occur (the figure that follows shows four of these vibrations). If you videotape the process and view the video frame by frame, you will find that the period of the second vibration is half the period of the first, the period of the third is one-third of the period of the first, and so forth. Write expression for the frequency of the other standing-wave vibrations; there are many more possible than are shown in the figure.

Explanation / Answer

a) fn = n*v/(2*L)

n --> no of loops (n = 1,2,3,4,5,6....)

L ---> length of the string.

b) wavelength, lamda = 2*L/n (m = 1,2,3,4,5,....)

so,

lamda = 2*L, L, 2*L/3 , L/2 , .....

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