This has been driving me mad...

June 17, 2009 8:54 AM

What governs the pitch of a glass as you rub your finger along the rim?

Clearly, if you put more water in a glass, the pitch goes down, contrary to what I would naïvely expect. I would assume that what produces the sound is the vibration of whatever glass is lying above the level of the water; thus more liquid would mean shorter rim which should, by this train of thought, be a higher pitch. But this isn't the case.

I've seen the explanation once that this is because a glass is like a tuning fork: The heavier the "fork" is (i.e. the more water in it), the deeper the pitch. But this also can't be true: I've tried filling a glass partway, and adding a few coins into it, and the pitch doesn't change. So this explanation doesn't wash.

To compound this, there's the fact that if you tilt a partially full glass (and so the water runs up the side), the pitch drops accordingly. So it seems more to be a function of "how high the water is" in the glass, in some sense.

So what it is? What produces the pitch you hear? Bonus points if you can describe a relatively simple experiment to show why your answer is the correct one.

posted by vernondalhart to science & nature (10 comments total)

As you add water, the amount of vibrating material increases, slowing down the vibrations. Since there is more material to vibrate, a lower pitch is produced.

Also, related to your coin experiment, the water exerts significant pressure on the glass itself, whereas the coins don't really. The water also vibrates more (and passes on that vibration to the glass more ) than the coins do if you do the finger-on-the-rim thing.
posted by olinerd at 9:08 AM on June 17

As you add more water, it damps the glass, slowing down the natural frequency of the instrument.
posted by notsnot at 9:12 AM on June 17

Elasticity and inertia affect the pitch. The coins you added would not add much more mass/inertia than their volume equivalent in water.
posted by weapons-grade pandemonium at 9:14 AM on June 17

The entire glass is vibrating, from point at the base where you're holding it up to the point of contact with your rubbing finger.

Water dampens the vibrations (hah!). It's not so much the water level that matters, but how much surface area of the glass is incident to the water mass; that's why tilting the glass lowers the frequency.
posted by qxntpqbbbqxl at 9:16 AM on June 17

Just like a string, a glass can be excited at a number of different frequencies. When you move your finger around the rim, you're driving some resonance that dominates based on the conditions of the glass. By adding water, you dampen vibrations. Frequencies that have many oscillations in the water (thus high pitches) will be more affected than ones which are long and have less variation in the water.

Think of standing waves on a string. There are always nodes, where the material is standing still. If you happen to only dampen vibration at the nodes, not much happens. If you dampen vibration just outside the node, a bit more happens, but how much depends on what we mean by "just outside." A high frequency will have its nodes spaced very closely, so you start damping that resonance greatly by damping a relatively small region. That same region, if applied to a low frequency resonance, is only vibrating a little bit (since the node is still not moving), and thus loses less energy.
posted by Schismatic at 9:30 AM on June 17

If you use a liquid other than water, you'll get different results, too, because the specific gravity of the liquid will dampen the sound more or less efficiently. A glass filled with whole milk or high-alcohol liquor will sound lower and higher, respectively, than water.
posted by Cool Papa Bell at 9:33 AM on June 17

Ben Franklin was fascinated by this as well and invented one of the most hauntingly lovely musical instruments based on these principles - the glass armonica. It's played by touching wet fingers to various sized spinning glass bowls. In this case it's the size of the bowls that affect the pitch, with the largest bowls producing the lowest tones.
posted by platinum at 9:54 AM on June 17

This was a surprisingly neat question to think about; thanks. Here's some background that might help you understand some of the other answers.

As everyone else has noted, a glass is a little like an oscillatory spring: it resists distortions, and in particular has some restoring force that depends linearly on how much you distort it. Like most other oscillatory systems, it has "normal modes" of oscillation -- a set of characteristic frequencies at which the system (in this case your wine glass) will respond to perturbations. Those frequencies depend on the material -- on its "springiness" and its mass, effectively -- but not (at least, not much) on how rapidly or strongly you perturb the system. That's why, for instance, the pitch you get when you run your finger over a wineglass can't be significantly altered by moving your finger faster or slower.

Those characteristic frequencies scale like the square root of (k/m), where k characterizes the "springiness" and m characterizes the mass -- or, equivalently, where k and m relate the potential and kinetic energy of the glass to its displacement.

(There is a nice description of the basic wineglass-singing effect at the Cornell Center for Materials Research, though it doesn't directly address your question.)

Now you can start to think about what happens when you add water. Hand-wavingly, the water is forced to vibrate along with the glass, but probably doesn't change the potential energy part of the story much (i.e., the "springiness" of the glass+water system is similar to that of the glass alone). So, in the above equation, the effective mass m goes up while k remains the same -- so the frequency drops. This is a little like your "tuning fork" argument. I actually found a few papers on this sort of thing, including one by A.P. French called In Vino Veritas: A study of wineglass acoustics. (This is slightly different than saying the oscillation is "damped" by the water, though that is probably true at some level too. Damping would also imply a shift in frequency, but would also suggest that the ringing from a wine-filled glass would die out significantly sooner than the ringing from an empty glass -- I'm not sure this is true, but will certainly experimenting with a nice glass of wine when I get home. In the name of science, of course.)

As you point out, this picture seems a bit too simplistic. Some of the other answers above point out effects that are probably relevant -- e.g. the properties of the material in the glass matter. I found a few other papers that attempted to deal with this problem in a semi-serious way: e.g., this one, which essentially looks at the pressure perturbations produced in the wine/water as the glass distorts. I have not tried to work through any of these in great detail.

That paper by A.P. French closes with the following few sentences, which I thought were kind of great: "Obviously the observations and analysis described in this paper cannot be regarded as very fundamental physics. The subject of classical mechanical vibrations has no mysteries, but even so a serious test of its predictions would call for better defined physical systems than a random set of ordinary wineglasses. Nonetheless, it is satisfying to see how physical analysis can be applied, with some success, to real wineglasses and other such vessels that can be found in any household. The analysis is, to be sure, rather unreasonably heavy in relation to the importance (or lack of it) of the specific topic, but it does exemplify the power of the energy method for the analysis of relatively complex vibrating systems."

Metafilter: rather unreasonably heavy in relation to the importance (or lack of it) of the specific topic
posted by chalkbored at 1:41 PM on June 17

It would be really interesting to fill a wineglass with an equivalent volume of mercury and water, and see how the pitch differs. Might be a little aggressive for home or school experimentation, though.
posted by jenkinsEar at 2:48 PM on June 17

jenkinsEar, good idea. I just made a glass harmonica with water and with corn syrup (density ~1.3 g/cc).

My wineglasses have two shapes: one with a bowl which is widest about one-third of the way from the bottom to the top, and one where the widest point is about halfway. Adding water so that its level is above the widest part of the bowl changes the pitch as other commenters have described: the increased water mass lowers the pitch. In this regime an equal volume of corn syrup produces a noticeably lower pitch. Also the corn syrup glass is noticeably harder to play, and doesn't resonate for as long as the water glasses. The corn syrup is apparently a better damper than water (which you can tell just by shaking them both).

If the water level is below the widest part of the glass, I hear either no change in pitch or that more water raises the pitch: right now I have six glasses, each with more water than the next, that play (nearly empty) C#, C, C#, B, A, G (nearly full). So the competition between vibrations in the glass and in the liquid is clearly pretty complicated.

I'm looking forward to reading chalkbored's citations. The American Journal of Physics mostly contains articles from people with a strong interest in education, so they tend to be pretty enlightening.
posted by fantabulous timewaster at 3:52 AM on June 18