## 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.