Are there theories for the different sound in different volume of beaker?

[s0610038]

This question just pop out from my mind when my brother played with the glass cups with different volume of water in it to produce some kind of music

When I tried to do some research on net I found not much informations
So just want to know that are there any theories that proved the volume of liquid in beaker have some kind of relations which connected to the sound that produced when my brother use a chopstic to hit on the cup? Thanks so much for that

Cheers

 

[Fewmet]

My high school students have been working on this question, although they focus more on the questions of running a wet finger around the rim to get a sound, not on striking the glass.

Most people find the surprising thing is that the frequency lowers as more water is added. Two years ago one group found a tight correlation between the frequency and the square of the volume. They also found that a denser fluid produces a lower frequency.

The first attempt (last year) to repeat that experiment produced substantially different results. There were other attempts a few weeks ago. I have yet to review them, though.

The data remains unclear, but several points suggest that the sound comes from the vibrations of the glass and that the water constrains that to lower the frequency.

 

[s0610038]

So there isn't any physics theory shows that the volume of the water in those glasses have a clear relationship with the sound produced? If there is, i would like to have a look of that Physics Law

Well actually i am a having a physics assessment which i can choose whatever topic i want. So if you were me, will you choose this one as a assessment topic? or you will do other topics? If you do, please have a further discussion. Thanks for that mate

Cheers

 

[Fewmet]

So there isn't any physics theory shows that the volume of the water in those glasses have a clear relationship with the sound produced? If there is, i would like to have a look of that Physics Law

Well actually i am a having a physics assessment which i can choose whatever topic i want. So if you were me, will you choose this one as a assessment topic? or you will do other topics? If you do, please have a further discussion.

Someone might have worked out an explanation for this, but there is not a clear answer to me that comes from physical principles. I have not looked very hard to see if there is a broadly accepted answer since I'd like to see it worked out by my students.
I don;t know what the requirements are for your assessment, so I cannot advise you whether this is a good topic.

There was just another thread going about the physics of wrestling. That looks like a promising topic. Some aspects are

• landing slowly to decrease the forces acting
• lifting an opponent off the ground to limit his ability to push you
• using leverage to flip an opponent

If sound interests you, I can suggest a few ideas about that.

 

[JArkinstall]

The physics is quite well defined in this area if you simply model the bottle as a cavity with length L - where L (in terms of the bottle) is the distance between the top of the bottle and the surface of the liquid. Fill up the bottle some more and you're reducing L.

In such a cavity, the standing sound waves created have wavelength such that a displacement node (pressure antinode) is at the base of the cavity (the water surface) and the opposite at the opening, as shown in the following image I found via google:

And voila. Shorten L by filling up the bottle, and you're making a shorter wavelength therefore higher frequency :)

Not sure if I explained it very well but, if you're not sure, do some googling on "Standing Waves".

 

[s0610038]

All of these help so much. I am so interested in this topic now.
So please correct me if I am wrong.
The idea that I got was the frequency of the sound is proportional to the volume of the water in the beaker. And once the water surface closer to the top of the beaker the higher frequency we got.
Is that right?

 

[KingNothing]

All of these help so much. I am so interested in this topic now.
So please correct me if I am wrong.
The idea that I got was the frequency of the sound is proportional to the volume of the water in the beaker. And once the water surface closer to the top of the beaker the higher frequency we got.
Is that right?

Sort of. In your case it may be that simple, but certainly not in the general case. Glasses with different shapes will produce different sounds, as will striking the glass in different places. It depends on the properties of the liquid (water in this case).

As someone said, the physics of this are extremely well understood. But you are not going to find an equation for your specific example. Instead there are a wealth of equations dealing with the shape of a cavity, the fluid filling a cavity, and resonant frequencies based on those.

 

[s0610038]

Sort of. In your case it may be that simple, but certainly not in the general case. Glasses with different shapes will produce different sounds, as will striking the glass in different places. It depends on the properties of the liquid (water in this case).

As someone said, the physics of this are extremely well understood. But you are not going to find an equation for your specific example. Instead there are a wealth of equations dealing with the shape of a cavity, the fluid filling a cavity, and resonant frequencies based on those.

So can i use the laws of waves to prove that the distance between the water surface and the end of the beaker did affect the sound provided. Then use some data loggers to prove that the frequency did increase once the water surface closer to the end of the beaker?

As i am using the same shape of beaker , i think i can take the shape problem as a control variable? thanks so much to answer my annoying question :)

Wish best

 

[KingNothing]

So can i use the laws of waves to prove that the distance between the water surface and the end of the beaker did affect the sound provided. Then use some data loggers to prove that the frequency did increase once the water surface closer to the end of the beaker?

As i am using the same shape of beaker , i think i can take the shape problem as a control variable? thanks so much to answer my annoying question :)

Wish best

Sort of. The properties of the glass material and the properties of the water both have an effect on the sound.

 

[s0610038]

Thanks for that =] Problems solved!

 

[nasu]

In the case under discussion, the sound is produced by the vibration of the glass (and the water in it). The frequency (and so the pitch) will depend on the elasticity and mass of the glass as well as the shape and size. The normal modes are characteristic to the glass rather than to the air above the water. Adding water increases the mass and the damping of the system so the frequency decreases, in general, when you add water.
The motion is somehow similar to that of a bell. The pitch of the bell is tuned by slightly reshaping the bell on a lathe. Does not depend on the height of the air column inside the bell.

 

[sophiecentaur]

I'm not so sure that the resonance is due to the air in the glass. The natural resonance of such a small and open ended cavity would be a very high (ultrasonic, even) frequency and the Q would be extremely low (very short reverberation time). It seems more likely to me that the resonance involves the mass of water and the flexing of the stem of the glass or the bowl shaped envelope of the glass. The simplest form of this type of harmonic oscillator is a mass on a spring. The frequency of that oscillation is
1/(2π√(k/m)) where k is the spring constant and m is the mass. That would tie in with the observation that more water in the glass produces a lower note.

Rats - I just read the same basic thing in the previous post. But here it is anyway.

When tuning bells, they make the 'end' of the the bell thinner to raise the pitch and the 'waist' of the bell thinner to lower the pitch. Glockenspiels (and quartz crystals) have the frequency adjusted by making the middle thinner to lower the frequency and the ends thinner to raise it. With a glass of water, all you can do is to vary the mass. but I guess that thinner glasses would tend to produce lower notes than thicker ones.

 

[Fewmet]

In the case under discussion, the sound is produced by the vibration of the glass (and the water in it).

I don't think it is the vibration of the water. Two of my students just completed tests on that. They dropped dried food coloring into the water and sounded the glass by running a finger around the rim. They saw a gentle swirl in the dissolving dye, but convinced it was caused by the residual motion from the filling of the glass with water.

Adding water increases the mass and the damping of the system so the frequency decreases, in general, when you add water.

I see how increasing the mass of the vibrating element would lower the natural frequency, but is that what is going on here? Do you see some mechanism by which increased mass increases vibration?

Do you see how damping the vibration increases frequency rather than decreasing the amplitude?


Edit: I apologize. In the penultimate question I confused the effect. The frequency does decrease so that is compatible with nasu's assertion.

 

[Fewmet]

In the case under discussion, the sound is produced by the vibration of the glass (and the water in it).

I don't think it is the vibration of the water. Two of my students just completed tests on that. They dropped dried food coloring into the water and sounded the glass by running a finger around the rim. They saw a gentle swirl in the dissolving dye, but convinced it was caused by the residual motion from the filling of the glass with water.

Adding water increases the mass and the damping of the system so the frequency decreases, in general, when you add water.

I see how increasing the mass of the vibrating element would lower the natural frequency, but is that what is going on here? Do you see some mechanism by which increased mass increases vibration?

Do you see how damping the vibration increases frequency rather than decreasing the amplitude?


Sorry about the duplicate post. I have no idea how that happened...

 

[KingNothing]

I don't think it is the vibration of the water. Two of my students just completed tests on that. They dropped dried food coloring into the water and sounded the glass by running a finger around the rim.

It's neither. The sound you hear is the vibration of the air in your inner ear. The glass, the water in it, and the air around it all vibrate. What makes you believe that your students could observe the vibration of water? Even a 500 Hz tone means the molecules move back and forth 500 times per second. The human eye is not the proper measurement device.

 

[Fewmet]

What makes you believe that your students could observe the vibration of water? Even a 500 Hz tone means the molecules move back and forth 500 times per second. The human eye is not the proper measurement device.

They were looking for a change in rate of the dispersal of the dye in he water. The thinking was that over several minutes there would be evident change. In light of your objections, I see that expectation might not have been duly verified. I find it plausible, but admit it is untested.

It's neither. The sound you hear is the vibration of the air in your inner ear. The glass, the water in it, and the air around it all vibrate.

I am suspicious. I get that the sound is transmitted by air. The volume is great, though, while the amplitude of the glass vibration is so small. Just as a guitar string is barely audible without a resonator, the vibration of the glass seems too slight to generate such a volume.

Can you say where your explanation comes from? Is it drawn from principles you can cite? I'd love to know how to test the phenomenon experimentally...my students and I have only seen indirect approaches.

 

[s0610038]

So the topic seems confused me right now
Does it mean that the frequency of the sound waves which produced from their around, the glass and the water will decrease when the volume of the water in the beaker increase?
Is my concept right? Is there anything to do with the distance between the water surface and the top of the glass? Please correct Me if I am wrong

Coz my teacher just told me that the physics theory behind the sound from hitting the beaker is not related to the Colum's law. He said that when I hit the beaker, the physics behind is that the vibration of the beaker and not about the air frequency in the beaker

I am so confused now and I really wish some help

Thank you for that

 

[KingNothing]

He said that when I hit the beaker, the physics behind is that the vibration of the beaker and not about the air frequency in the beaker

The air moves, no? The air, water, and beaker are all vibrating.

 

[s0610038]

Yes I know they all vibrating once the chopstic hit the beaker.
But is the vibration theories will be much more likely to apply in this case?
Or it's really related to the Colum's Law?

 

[KingNothing]

They were looking for a change in rate of the dispersal of the dye in he water.

Why would you expect a change? The sound may move the atoms of the water back-and-forth on a very small scale, but it would not at all change the time-averaged movement of them. Just as shouting across a room does not cause a breeze.

I am suspicious. I get that the sound is transmitted by air. The volume is great, though, while the amplitude of the glass vibration is so small. Just as a guitar string is barely audible without a resonator, the vibration of the glass seems too slight to generate such a volume.

What we perceive as "high volume" actually carries very little acoustic power. Take for example, the gravitic energy recovered by dropping a penny a single meter. A penny weighs 2.5 grams, so this energy is about .0025 kg * 9.8 m/s^2 * 1 m = 0.0245 joules. Say this tiny amount of energy, in a time of 0.5 seconds (making the power about 0.05 watts), is tranformed 100% into acoustic energy entering your ear. This means it will have an intensity of 97db, enough to make a person go deaf!

I say this because the force with which you are striking the beaker is probably much greater than a penny dropping to the floor, and you seemed to express some disbelief about the volume of sound generated.

 

[Fewmet]

So the topic seems confused me right now
Does it mean that the frequency of the sound waves which produced from their around, the glass and the water will decrease when the volume of the water in the beaker increase?
Is my concept right? Is there anything to do with the distance between the water surface and the top of the glass? Please correct Me if I am wrong

Coz my teacher just told me that the physics theory behind the sound from hitting the beaker is not related to the Colum's law. He said that when I hit the beaker, the physics behind is that the vibration of the beaker and not about the air frequency in the beaker

I can see why you find this confusing. We've been exploring possible answers to your original question. You have different people telling you different things about what is going on. This is especially hard when one of them is your teacher. It is hard to know if he or she is the kind of teacher who will be pleased to have you argue with what he or she says, or will be irritated by it.

There is a really valuable lesson here. Not everything is completely clear in science, and things are not decided by an authority saying something is true. You can look at any claim and judge it by how well it matches laws, principles and (most importantly) experimental results. That's what you are seeing going on. Claims are made. Questions are asked. Questions are answered in terms of principles and the way we know other things work.

But that doesn't answer your question.

I think we are all pretty confident that the glass vibrates, and that vibrates the air and what you hear is a vibration in the air. We also agree that the higher the water level, the lower the frequency of the sound.

 

[Fewmet]

What we perceive as "high volume" actually carries very little acoustic power. Take for example, the gravitic energy recovered by dropping a penny a single meter. A penny weighs 2.5 grams, so this energy is about .0025 kg * 9.8 m/s^2 * 1 m = 0.0245 joules. Say this tiny amount of energy, in a time of 0.5 seconds (making the power about 0.05 watts), is tranformed 100% into acoustic energy entering your ear. This means it will have an intensity of 97db, enough to make a person go deaf!

I say this because the force with which you are striking the beaker is probably much greater than a penny dropping to the floor, and you seemed to express some disbelief about the volume of sound generated.

Could it be that we hear the penny because it vibrates the surface on which it lands, increasing the volume of air that is moving and making the sound louder? (That is consistent with the fact that it is quieter on a softer surface.)

I think a better model for a vibrating glass would be a vibrating tuning fork that is not in a resonating box. I am reasonably sure I whack the fork on my elbow harder that I tap a glass with a pencil. The glass is far louder. And the glass that is sounded by running a finger around the edge probably surpasses 60 db.

(I'll have to pull out the the decibel meter and measure the penny and glass when this vacation is over and I get back into my lab).

 

[s0610038]

Okay. Is that mean the vibration of the glass cause the vibration of the air. All the sound that I heard was the sound of the vibrating air? I am still very confusing now:(
thanks for that

 

[Fewmet]

Okay. Is that mean the vibration of the glass cause the vibration of the air. All the sound that I heard was the sound of the vibrating air? I am still very confusing now:(
thanks for that

To me it looks most likely that the glass vibrates. That vibrates the air, and you hear the air vibrating.

I am not totally certain of that because
1) I do not see how the very small amplitude of the glass can make such a loud sound (especially if you think of making the sound by rubbing your finger rather than hitting the glass).
2) I do not see how a higher water level makes a lower frequency.

 

[Fewmet]

I'm not so sure that the resonance is due to the air in the glass. The natural resonance of such a small and open ended cavity would be a very high (ultrasonic, even) frequency and the Q would be extremely low (very short reverberation time). It seems more likely to me that the resonance involves the mass of water and the flexing of the stem of the glass or the bowl shaped envelope of the glass. The simplest form of this type of harmonic oscillator is a mass on a spring. The frequency of that oscillation is
1/(2π√(k/m)) where k is the spring constant and m is the mass. That would tie in with the observation that more water in the glass produces a lower note.

I really like the observation about the size of the air cavity. I know that the first resonance in a tube with one open end occurs at \lambda/4, so the wavelength will be much larger than the cavity. I started to estimate the cavity dimensions for the wine glasses I used in class, and that reminded me that you get a tone (by striking and running a finger around) with a glass that is full to the brim with water. That seems to rule out the air cavity as having an essential role in sound production. And the fact that you get a tone in an empty glass does the same for the water.

I don't think the stem can be involved in making the tone. You can wrap your hand around it and squeeze to damp the vibration and not affect the tone.

A student working on this last year noted that you can get a tone by running a finger around the circular base of a wine glass.

 

[s0610038]

To me it looks most likely that the glass vibrates. That vibrates the air, and you hear the air vibrating.

I am not totally certain of that because
1) I do not see how the very small amplitude of the glass can make such a loud sound (especially if you think of making the sound by rubbing your finger rather than hitting the glass).
2) I do not see how a higher water level makes a lower frequency.

Well i am not making the sound by rubbing your finger rather than hitting the glass, i am actually going to use some object to hit on the glass.

But, to me, the hardest thing is to know the theory behind this vibration and how can i record these data.. I am really interested in this topic and i really want to make the idea clear
thanks so much for helping

 

[s0610038]

A student working on this last year noted that you can get a tone by running a finger around the circular base of a wine glass.

it seems interesting experiment, can you talk a little bit more about your student experiment?

 

[nasu]

I found this page that discuss the vibration of a glass with water:

http://www.ccmr.cornell.edu/education/ask/index.html?quid=1143

It don't see any references but it may be a good starting point.
The modes shown are similar to some vibration modes of a bell.

 

[Fewmet]

it seems interesting experiment, can you talk a little bit more about your student experiment?

There have been seven or eight related experiments. For all, the goal is to develop an understanding of what is going to make the sound when you hit or rub a wine glass. The first experiments (from two years ago) used a Vernier microphone and LoggerPro software to record the sound made when running a finger around the rim. They used an FFT graph in LoggerPro to display the frequencies. One always produced a much higher peak, and they recorded that one. They ran a regression analysis and found a strong linear relationship between the frequency and the square of the volume of water added to the glass.

That group then repeated the experiment several times with different salt solutions and sound the same results hold for a denser liquid, but the frequencies produced are lower. They had heard that a cornstarch/water mix ("http://www.wellesley.edu/childstudy/pages/oobleck.html" ") is a "non-Newtonian fluid", so tried that and got the same results (although it was very hard to measure the volumes of the mix accurately).

They ran into a problem that you (s0610038) might see if try anything like this. The FFT analysis cannot report on every single frequency. The one they used reported frequencies in groups of about 20 Hz. That means they would sometimes make as many as four additions of water, be able to hear a change in frequency, not get get a measurable change in frequency.

Work by a student last year did not get the same results. I suspect it is because she had a different method for selecting the peak frequencies. The discrepancy is still under investigation.

Another round of experiments was just completed last week. One got the same results as the original group. Those workers also measured the depth of the water.

Two other recent experiments compared the sounds of rubbing versus tapping, focusing on the peak frequency and also on the overtones. I have attached the data from one of them. Note that this is the preliminary phase of experimenting with tapping, and the methods are still rough. (I haven;t even carefully reviewed the report yet.) Don't read too much into the numbers. You see in the data the problem I described with getting the same frequency for different volumes. They might have done better to add 50 mLs at a time.

That group's write-up reports that a third overtone (close in frequency to the second) appeared when there were 80 mLs in the glass. It's precise frequency was not recorded. They noticed, however, that the height of the third overtone's peak gradually increased from that point on. At the same time the second overtone peak decreased. That means that the third overtone grew louder (relative to the second overtone). Another group doing similar work with Tibetan singing bowls noticed the same thing.

One interesting preliminary result seen in the data below is that the first overtone is very close to three times the the frequency of the tonic (i.e., the lowest frequency). Musically, that makes it a fifth. The relationship is not nearly so tight in the data from tapping.

I will encourage the students to try find a sensible way to average the data to deal with the repeated frequencies. I think it will turn out that the experiment needs to be run again using bigger volume increments.

 

[Fewmet]

I found this page that discuss the vibration of a glass with water:

http://www.ccmr.cornell.edu/education/ask/index.html?quid=1143

It don't see any references but it may be a good starting point.
The modes shown are similar to some vibration modes of a bell.

That's interesting. I have thought about that mechanism (I like to describe the finger as "chasing the nodes" around the perimeter of the glass). There has to be more going on to explain the overtones that are produced.

The Earth has multiple whole-body vibration modes set off by earthquakes. Even something as apparently simple as tuning fork vibrates in http://www.vibrationdata.com/animation.htm" . It seems likely that there is another mode of vibration acting along the vertical axis.