Standing Wave in a Metal Rod
standing waves - longitudinal waves - compressional waves - resonance
What it shows:
Longitudinal standing waves in solids.
How it works:
A metal rod is not unlike an organ pipe with both ends open. Holding it exactly in the middle will
force the simplest, or fundamental, mode of vibration -- the ends will be free to vibrate maximally
and the center will be a node. The fundamental frequency happens to be 2.26 kHz. As with a
pipe open at both ends , the rod will vibrate at all the odd as well as even harmonics - one need
only change the holding position which will force a node at that location. For example,
holding it 1/4 of its length from one end allows the 2nd harmonic (4.52 kHz) while suppressing
the others, 1/6 will produce the 3rd (6.78 kHz), 1/8 the 4th (9.04 kHz) and finally, 1/10 the 5th
at 11.30 kHz.
The rod is aluminum and measures 1/2" in diameter by 1.16 meters long.
1
The nodal points mentioned above are marked on the rod. The easiest way of performing the demo
is to simply hold the rod (between finger and thumb) vertically and hit the end onto the floor. Because
of its high Q, it will ring for a surprisingly long time. If the floor happens to be carpeted, a gentle tap
with a hammer on its end will do just as well. But much more impressive is if you rub the rod
between the thumb and index finger of your other hand (you should practice this). The resonance
builds up to almost painful volume and is quite amazing. It works best if the metal rod is lightly rubbed
with rosin so that the rubbing becomes a "stick-slip" motion.
If desired, the demonstration can be used to measure the speed of sound in aluminum (5,240 m/s for
this particular alloy). In the fundamental mode of vibration, the wavelength of the sound emitted will
be twice the length of the rod. The frequency is measured with a microphone and oscilloscope or
frequency counter.
Setting it up:
If the lecturer plans to just hit the rod on the end, no preparation is needed. But the rubbing
technique of exiting a resonance should be tried and practiced beforehand. It's not difficult once
you get the hang of it. Performing the demonstration in lecture sometimes results in failure,
probably due to nervousness (sweaty hands). This can be avoided by having a rag and some
alcohol handy to clean any grease or moisture off the fingers just prior to the demonstration.
Comments:
Simple, quick, and dramatic. Rating ***
1 The rod was found that length and there was no reason to cut it to a different length