# Detailed Description of Resonance in Sound and Mechanics

If a diving springboard is bent and then allowed to vibrate freely, it oscillates with a frequency which is called its natural frequency. When a diver on the edge of the board begins to jump up and down repeatedly, the board is forced to vibrate at the frequency of the jumps; and at first, when the amplitude is small, the board is said to be undergoing forced vibrations. As the diver jumps up and down to gain increasing height for his dive, the frequency of the periodic downward force reaches a stage where it is practically the same as the natural frequency of the board. The amplitude of the board then becomes very large, and the periodic force is said to have set the board in resonance.

A mechanical system which is free to move, like a wooden bridge or the air in pipes, has a natural frequency of vibration, f, which depends on its dimensions. When a periodic force of a frequency different from f is applied to the system, the latter vibrates with a small amplitude and undergoes forced vibrations. When the periodic force has a frequency equal to the natural frequency f  of the system, the amplitude is a typical curve showing the variation of amplitude  with frequency. Some time ago it was reported in the newspapers that a soprano who was broadcasting had broken a glass tumbler on the table of a listener when she had reached a high note. This is an example of resonance. The glass had a natural frequency equal to that of the note sung, and was thus set into a vibration sufficiently violent to break it.

The phenomenon of resonance occurs in other branches of physics other than Sound and Mechanics. When an electrical circuit containing a coil and capacitor is ‘’tuned’’ to receive the radio waves from a distant transmitter, the frequency of the radio wave is equal to the natural frequency of the circuit and resonance is therefore obtained. A large current then flows in the electrical circuit. A dark line in a continuous spectrum, an absorption line, is an example of optical resonance. Thus some of the yellow wavelengths from the sun’s spectrum are absorbed by molecules of sodium vapour in cooler part of the sun’s atmosphere, which are set into resonance.

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Sharpness Of Resonance

As the resonance condition is approached, the effect of the damping forces on the amplitude increases. Damping prevents the amplitude from becoming infinitely large at resonance. The lighter the damping, the sharper is the resonance, that is, the amplitude diminished considerably at a frequency slightly different from the resonant frequency.  A heavily damped system had a fairly flat resonance curve. Tuning is therefore more difficult in a system which has light damping. The effect of damping can be illustrated by attaching a simple pendulum carrying a pith bob, and one of the same length carrying a lead bob of equal size, to a horizontal string. The pendula are set into vibration by a third pendulum of equal length attached to the same string, and it is then seen that the amplitude of the lead bob is much greater than that of the pith bob. The damping of the pith bob due to air resistance is much greater than for the lead bob.

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Resonance In A Tube Of Pipe

If a person blows gently down a pipe closed at one end, the air inside vibrate freely, and a note is obtained from the pipe which is its fundamental. A stationary wave then exists in the pipe, with a node N  at the closed end and an antinode A at the open end.

If the prongs of a tuning-fork are held over the top the pipe, the air inside it is set into vibration by the periodic force exerted on it by the prongs. In general, however, the vibration are feeble, as they are forced vibrations, and the intensity of the sound heard is correspondingly small. But when a tuning-fork of the same held over the latter, the air inside is set in resonance by periodic force, and the amplitude of the vibration is large. A loud note, which has the pipe, and a stationary wave is set up with the top of the pipe acting as an antinode and the fixed end as a node. If a sounding turning –fork is held over a pipe open at both ends, resonance occurs when the stationary wave in the pipe has antinodes at the two open ends; the frequency of the fork is then equal to the frequency of the fundamental of the open pipe.