Shattering Wineglass

resonance - driven oscillator - normal modes of vibration

What it shows:
Sound waves of the right frequency are used to excite a wineglass in one or two of its normal modes of vibration. Stroboscopic illumination makes it possible to actually see the vibrations in apparent slow motion. When the intensity of the sound is increased, the large undulations of the glass exceed its elastic limit and cause it to shatter. This can be done in the fundamental or next higher normal mode of vibration ... a beautiful and dramatic example of resonance.

How it works:
A tunable audio-oscillator/power-amplifier/loudspeaker combination is used to generate sound waves of approximately 120 dB (very loud) and within ± 1/2 Hz of the resonance frequency of the glass.

The resonance frequency of the glass must first be determined before lecture (the method is described in Setting it up). However, its sound should be demonstrated to the audience by either tapping the glass or (better) rubbing its rim with a moistened finger. It should be emphasized to the class that the frequency of the sound is all important to exciting resonance vibrations; shear volume (intensity) won't do a thing if it's off resonance. This is demonstrated first so that students aren't left with the impression that any loud high note will break a glass.

Stroboscopic illumination is used to make the rapid oscillations (typically 500-700 Hz) visible. Rather than "freezing" the motion, the strobe frequency is set slightly above or below the resonance frequency resulting in an apparent slow vibration at the beat frequency (difference between strobe and wineglass frequencies).

The wineglass can be "played with" for a while before increasing the volume to the point at which it shatters. This is done by slowly increasing the volume in steps so that the audience has time to appreciate the incredible distortions the glass manages to survive before its elastic limit is exceeded. The fundamental mode of vibration is that in which the rim vibrates with two-fold symmetry and assumes a ellipsoidal-like shape, alternating in orthogonal directions (see figure 1 following the Comments). Peak-to-peak amplitudes have sometimes been as much as 5 or 6 mm (8-10% of the rim's diameter). The wineglass can also be excited (and shattered) in one of its higher normal modes of vibration. The strongest of these is a mode in which the rim of the glass vibrates with three-fold symmetry (six nodes). The peak-to-peak amplitude of the excursions are much less than in the fundamental mode (2 or 3%). This is a fine opportunity to point out to the class that, unlike one-dimensional simple harmonic oscillators, the higher mode frequencies are not multiples (harmonics) of the fundamental frequency and indeed, the ratios of the resonance frequencies are different for every glass. 1

Setting it up:
Choose a large wineglass whose sides don't curve in too much at the top. The wineglasses we have been using for the last decade or so are white wine stem glasses. 2   Although they all look very similar, their resonance frequencies vary over roughly a 600 Hz range with an equally unpredictable Q. The lower frequency glasses tend to flex more dramatically (because of thinner walls) and ring longer. Thus the glasses should be carefully selected in the store (take a 512 Hz tuning fork and ignore the puzzled and anxious looks of the salespeople as you strike their glasses). Back in the Preparation Room, the resonance frequency of each glass must be determined to an accuracy of ± 1/2 Hz. The quickest and easiest way of making this measurement is to use a microphone/preamp/frequency counter, 3   strike the glass gently with a rubber bung, and record the average value of several measurements. To identify the higher frequency mode of vibration you will have to use an audio spectrum analyzer. 4

The loudspeaker used to excite the glass is a midrange transducer capable of generating 120 db or more of acoustic power. Ours is a JBL 5   Professional Series model 2482. We have removed the horn from the driver and mounted the driver in the middle of a solid oak baffle (measuring 38 cm square and 2.54 cm thick). This allows us to take advantage of the 1/r2 intensity increase, by placing the wineglass close to the loudspeaker (1 to 2 cm).The driver handles a maximum of 60 watts input and so is protected with a 1.5 A fast-blow fuse. It is much cheaper to replace a fuse than a new voice coil!

The source of the audio signal is a function generator and power amplifier. Any combination capable of generating a finely tunable sine wave with up to 60 watts of power will do the job. We happen to use an IEC model F34 function generator and a Hafler model DH-200 power amplifier. The fine frequency control is not fine enough for this application and so we additionally use a very simple low voltage source (0-60 mV) on the VGA input of the function generator. The circuit is shown in figure 2, following the Comments. The 10-turn potentiometer gives us a fine tuning resolution of about 1 Hz/revolution. The TTL output of the function generator is used to monitor the frequency.

To achieve a ± 1/2 Hz accuracy in frequency, the frequency counter of choice must be able to deliver 4 significant figures in the 400 to 1 kHz range. Ours happens to be an instrument designed for high frequencies 6   and so it is necessary to use the period function of the instrument to obtain the desired accuracy. Thus, calculate the inverse of the resonance frequency and work with that. The stroboscopic illumination 7   should be adjusted so that it shines down at a 45° angle. The strobe is calibrated in RPM so the resonance frequency must be converted to these units. The video camera, equipped with an 80mm zoom lens, is mounted on a tall tripod opposite the strobe and too looks down at a 45° angle. This lighting brilliantly highlights the rim of the glass (where all the action is). Begin with a wide angle shot to give the audience a sense of orientation and a good view of the whole glass and then zoom in so that the rim of the glass dramatically fills the video screen.

Comments:
Be sure to wear safety goggles! This demonstration has all the ingredients of The Perfect Demo and is an all-around favorite. It will arouse a round of applause from even the most taciturn audience. Rossing (see References) has published some marvelous photographs (holographic interferograms) showing six modes in a wineglass. Rating ****





References:
T.D. Rossing, J Acoust Soc Am 95, 1106-1111 (1994). "Acoustics of the glass harmonica"
A.P. French, AJP 51, 688 (1983). "In Vino Veritas: A study of wineglass acoustics"
R.E. Apfel, AJP 53, 1070 (1985). "Whispering waves in a wineglass"

1 For example, one glass had resonance frequencies of 601.5 and 1427.5 Hz (1:2.37) for the two modes while another had 700.0 and 1765 Hz (1:2.52); these ratios are close but different!
2 KROSNO brand 13 oz Birgitta Goblet, made in Poland and available for about $6 each from Crate & Barrel (in the Boston area)
3 Our Tektronix model 2236 oscilloscope has a built-in digital counter/timer/multimeter
4 The Hewlett Packard model 3560A Dynamic Signal Analyzer is very convenient to use for this purpose.
5 James B. Lansing Sound Inc., Los Angeles CA
6 Hewlett Packard model 5302A, 50 MHz Universal Counter
7 General Radio model 1540 Strobolume. The maximum rep rate is 25,000 RPM, or 417 Hz. For glasses above this frequency (most of them are), divide the RPM by 2 or, if necessary, 3 and strobe at that rate. The higher-frequency mode may even require strobing at 1/4 the frequency.