# Vibrations in a rubber sheet

##### Demonstration

In this experiment oscillations are produced in a rubber sheet.

#### Apparatus and materials

• signal generator
• large loudspeaker
• xenon stroboscope
• sheet of rubber
• retort stand base & rod, 3
• boss and clamp
• large aluminium ring
• rubber band(s)
• 4 mm leads

additional apparatus for a closely-related experiment, Chladni plates

• square or round metal plate
• sand

#### Health & Safety and Technical notes

The diagrams above shows how to excite oscillations in a rubber sheet.

Stretch the sheet over the large metal ring, so as to be as evenly stretched as possible. Radial lines drawn on the rubber make the oscillations easier to see. Holding the sheet to the ring by a large rubber band makes it easy to make small adjustments to the evenness of the sheet's tension.

Place the loudspeaker below the ring and rubber sheet. Frequencies in the range 10 to 100 Hz are required, and the larger the power delivered by the loudspeaker, the better.

Safety note: Using the xenon stroboscope, teachers should be aware that frequencies around 7 Hz have been known to cause epileptic fits in certain people. Ask your students if any know that they are susceptible to this response.

#### Procedure

a Try a central position of the speaker first, and a low frequency. Raise the frequency gradually, looking and listening for the lowest resonance mode, in which the centre of the rubber sheet rises and falls, as in diagram (a) below.

The amplitude may be 10 to 20 mm at the centre.

b See diagram (b). At a higher frequency, with the speaker off centre, a mode of oscillation can be found in which the rubber surface tilts, one side rising as the other falls, the rim staying fixed of course.

c You may be able to produce several other modes of vibration. Is there a simple relationship between the resonant frequencies? Between the patterns obtained?

#### Teaching notes

1 The standing waves should be viewed stroboscopically, as well as by eye, to give students a clear understanding of their nature.

2 To show Chladni figures: Attach the metal plate centrally to the vibrator. Before switching the vibrator on, sprinkle sand on the plate to reveal the vibration pattern. Many modes of vibration exist. The resonant oscillations of car door or body panels are of this general kind.
Note the resonant frequencies. Are they simply related?

This experiment has yet to undergo a health and safety check.