Answer to Question #82886 in Mechanics | Relativity for Surej

Question

A 100cm long rod is clamped at its centre and stroked. At what other points might
be clamped in order to amid the same tone, (a) in the 1st overtone (b) in the 2nd
overtone? Draw each case with detail.

Answer 1

The fundamental frequency is f. The first overtone is the second harmonic and will be at a frequency 2·f, thus the wavelength will be

λ=2 L/2=L=100 cm.

The same tone will be if the frequencies’ ratio will be 1/√(6&2), thus to emit the same tone the rod might be clamped at the points of

x=λ/6=100/6=16.67 cm.

To amid the same tone in the second overtone the frequency must be 3·f, thus the wavelength of the third harmonic is

λ=2 L/3=2 100/3=66.67 cm.

x=λ/(20/3)=66.67/(20/3)=10 cm.