Question

A rod 120 cm long is clamped at the center and is stroked in such a way as to give its 1rst overtone. Make a drawing showing the location of the nodes and antinodes, and determine at what other points the rod might be clamped and still emit the same tone.

Answer 1

Answer on Question #82564 - Physics - Mechanics - Relativity

A rod 120 cm long is clamped at the center and is stroked in such a way as to give its 1rst overtone. Make a drawing showing the location of the nodes and antinodes, and determine at what other points the rod might be clamped and still emit the same tone.

Solution

The oscillations of the left and right halves of the rod make its first overtone. Node is a point at the centre, antinodes are the points in peaks of the wave:

Its wavelength:

$$\lambda = 2 \cdot \frac {1}{2} L.$$

The same tone will be if the frequencies' ratio will be $\frac{1}{\sqrt[6]{2}}$, thus to emit the same tone the rod might be clamped at the points of

$$\lambda_{t} = \frac {\lambda}{6} = 20 \mathrm{~cm}.$$

Answer

20 cm.

Answer provided by https://www.AssignmentExpert.com