Can the shape and amount of water in a glass affect the sound it produces?

[OJA]

I'm doing a project on a water xylophone, and I have a couple questions about it. Please site your sources because we need all the help we can get. Thanks =D

1) How does the shape of the glass affect the sound the water produces.
2) Why does more water in a glass lower the frequency of the note?
3) How does the height of the glass affect the frequency of the note produced by the water?

Thanks for all your help

 

[Bobbywhy]

OJA, Welcome to Physics Forums. This is a place where real scientists, engineers, and other experienced experts can help guide you in learning science.

As for you water xylophone questions:

1. The water does NOT produce the sound. The glass above it does. Yes, the shape will affect the sound. You may experiment with various shapes to discover this.

2. When you add water to a bottle, the pitch or frequency gets lower. This happens because as you add water, you also add more mass to the bottle — the combined mass of the bottle plus the water. More mass results in a slower/lower vibrating frequency, and less mass produces a faster/higher vibrating frequency.

3. The height of the water in the glass is directly related to question No. 2

I did a fast Google search for "water xylophone" and found many articles. I recommend two, both by the same author(s). The first shows you how to construct, has interactive sound examples, and is great fun. The second reference is an excellent scientific explanation with questions and answers about exactly how the xylophone functions. Let us know how your project goes.

http://www.philtulga.com/water.html
http://www.philtulga.com/MSSActivities.html

 

[Michael C]

1. The water does NOT produce the sound. The glass above it does.

I don't think that's right. In any case it would seem to be contradicted by what you say just afterwards:

2. When you add water to a bottle, the pitch or frequency gets lower. This happens because as you add water, you also add more mass to the bottle — the combined mass of the bottle plus the water. More mass results in a slower/lower vibrating frequency, and less mass produces a faster/higher vibrating frequency.

The sound must be produced by the vibrations of both glass and water.

Here's my understanding of the effect of adding water: the sound is lower because sound waves travel about three times faster in glass than they do in water. When water is added to a glass, part of the vibrating wave travels though the water instead of through the glass.

 

[sophiecentaur]

The natural frequency of vibration relates to stiffness and mass. Stiffer - higher frequency and more massive -lower frequency. A glass of water is a complicated structure and there won't be a simple formula but the above basics will always apply. You have a flexible glass (with stiffness) and it's loaded with water (the mass - which isn't the flexing part; you could replace it with a ring of masses, stuck to the side of the glass).
So, as you add water to the glass, you are increasing the mass so the pitch will drop. A thinner (less stiff) glass would also vibrate slower.
This contrasts with blowing over the top of a bottle, when the resonating item is the air in the bottle. Adding water will reduce the volume of air, which reduces the mass, so the pitch will go up (see Helmholtz Resonator). A pipe is easier to analyse because you are setting up an identifiable standing wave in the air column and there will be a resonance when the length of tube is a quarter wavelength of the tone.

 

[Michael C]

The natural frequency of vibration relates to stiffness and mass. Stiffer - higher frequency and more massive -lower frequency. A glass of water is a complicated structure and there won't be a simple formula but the above basics will always apply. You have a flexible glass (with stiffness) and it's loaded with water (the mass - which isn't the flexing part; you could replace it with a ring of masses, stuck to the side of the glass).

I just tried that: I stuck a ring of pieces of wax around the side of a glass at about mid-height (the glass was as near to cylindrical as I could find, slightly narrower at the top than at the bottom). The result was mainly to dampen the vibrations: instead of ringing for a couple of seconds when tapped, the glass stopped audibly vibrating almost immediately. The sound was very slightly lower than before, difficult to ascertain exactly due to the brevity of the sound.

I also tried filling the glass to a certain level with rice. This had only the effect of damping the vibrations, without an audible difference in sound frequency. With the glass half full of rice, it produced the same note as when empty, but the sound decayed much faster. When the glass was almost completely full of rice, no note was discernible when the glass was tapped, just a dull noise.

This is quite different to what happens when the glass is filled with water. Adding water changes the frequency of the sound, but makes no noticeable difference in the length of time it takes for the sound to decay.

Since the water does not have a damping effect on the vibrations, is it reasonable to conclude that the vibrational waves are passing through both glass and water?

 

[sophiecentaur]

Good experimentation and the results don't surprise me - now you describe them. Wax and rice are very 'lossy' materials, whereas water will transmit sound without absorbing it. That would account for the longer reverb time, I think. If you could bolt a ring of masses (or glue them firmly) in a circle round the belly of the glass, then I think this would also lower the note but not shorten the reverb time because no energy would be lost. This would be like fixing lead fishing shot onto the string of a guitar to slow down its natural vibration compared with soggy putty, which would absorb some of the vibrational energy.

The resonance of the glass must be in the form of flexing of the whole of the bowl of the glass. The waves are also passing through the water from side to side of the glass. However, the speed of sound in water (a longitudinal wave) is extremely high compared with the speed of flexing waves in the glass so the water just behaves as a mass, loading the glass without dissipating the energy. For the water to be a part of the resonating system as anything other than a mass, there would need to be a significant transit time for the wave through it and there isn't. The water is 'incompressible' under these conditions and has very low viscosity so I think it must just act as a load on the surrounding glass without losing energy. The whole of the vessel can vibrate - bits going in and other bits going out, like the skin of a balloon and the water transmits force from one side to the other (or up and down - I don't know which) and to the water's surface, which probably moves up and down all at the same time as well as forming surface waves at times.

 

[AlephZero]

Since the water does not have a damping effect on the vibrations, is it reasonable to conclude that the vibrational waves are passing through both glass and water?

That's right. Pressure waves can travel through water with very little damping (whales can "sing" and communicate with each other through thousands of miles of ocean), but not through a pile of rice grains to any significant degree, because a grain in contact with the glass can "move out of the way" by changing the shape of the air gaps, rather than pushing againt the other grains.

It would be interesting to try a square shaped glass filled with metal ball bearings, of the right size to fit "exactly" into the glass like the atomic structure of a crystal structure...

 

[sophiecentaur]

That's right. Pressure waves can travel through water with very little damping (whales can "sing" and communicate with each other through thousands of miles of ocean), but not through a pile of rice grains to any significant degree, because a grain in contact with the glass can "move out of the way" by changing the shape of the air gaps, rather than pushing againt the other grains.

It would be interesting to try a square shaped glass filled with metal ball bearings, of the right size to fit "exactly" into the glass like the atomic structure of a crystal structure...

I think there would still be a lot of friction between the ball bearings during shear motion.