# Mechanical Resonance

When a child on a swing is being pushed the amplitude of the oscillation increases rapidly only if the person pushing the swing does so in time with the natural period of the swing. This effect is called RESONANCE. It can be a real problem in building design if the frequency of swirls of air have the same frequency as part of the structure! The building oscillates with increasing amplitude and can eventually break up! Annoying buzzes can be produced in a concert hall if pieces of equipment such as fans fixed to the ceiling resonate when a note is played by the orchestra. Resonance can also be a problem when a car driving mirror vibrates as the car is being driven over an uneven road at a particular speed.

Resonance occurs in a vibrating system when a driving frequency is applied to the system which has the same frequency as the fundamental frequency of the oscillating object (or a simple multiple of it).

Resonance plays a very important part in the design of a musical instrument like a violin where the body of the instrument must resonate at a series of different frequencies, these frequencies being slightly different for each violin. This is made possible by the complex shape of the body and the material of which the violin is made. The wooden bars at the top of a marimba are made to have the same resonant frequency as the tubes hanging from them so that the air in the tubes resonates when the bars are struck.

Resonance is also essential in the tuning of a radio. The tuning circuit is varied so that its frequency is equal to that of the station you want to listen to - the signal fed to the amplifier is then large.

Any system usually resonates not at ONE frequency but over a small range of frequencies. The width of this range depends on the system itself.

STUDENT INVESTIGATION

Set up the apparatus shown in the diagram and by varying the frequency of the signal generator and hence the frequency of the vibration generator investigate how the resonance frequency of the loaded hack saw blade.

It will probably be necessary to clamp the apparatus to the bench to stop it moving about!

STUDENT INVESTIGATION
Investigate the spread of resonant frequencies for the following:
(a) a milk bottle containing air
(b) a tuning fork mounted on a resonant box

© Keith Gibbs 2010