Two wires are welded together end to end. The wires are made of the same material, but the diameter of one is twice that of the other. They are subjected to a tension T. The thin wire has a length L and a linear mass density μ. The combined wire is fixed at both ends and vibrated in such a way that two antinodes are present, with the node between them being right at the weld. a. What is the frequency of vibration? b. What is the length of the thick wire?
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
Two wires are welded together end to end. The wires are made of the same material, but the diameter of one is twice that of the other. They are subjected to a tension T. The thin wire has a length L and a linear mass density μ. The combined wire is fixed at both ends and vibrated in such a way that two antinodes are present, with the node between them being right at the weld.
a. What is the frequency of vibration?
b. What is the length of the thick wire?
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