# Sound wave particle question

1. Apr 8, 2006

### Grimhelm

I have recently been wrestling with this little problem:

I take a hot cup of powdered chocolate and stir it. I then tap the bottom of the cup repeatedly. The sound continues to increases in frequency/pitch as I continue tapping at a constant speed. After I stir the liquid, the sound returns to a low frequency. Tapping again creates the steady increase in frequency.

The question is, what is happening in the cup with the waves and particles created by the tapping that increases the frequency of the sound? Keep in mind that tapping the outside of the cup delivers the same result...

I am stumped, being a physics moron. :) Help anyone?

2. Apr 8, 2006

### Astronuc

Staff Emeritus
What does one mean by tapping? Is one stirring?

Also, is the chocolate powder in the bottom of the cup when one pours hot water into cup?

The distribution of the chocolate powder in the liquid or on the bottom of the cup will affect the mass distribution which in turn affects the frequency of sound. Similarly stirring the water in the cup will affect the frequency.

The more mass on a vibrating surface, the more resistance to motion, so the natural frequency would be lower, and the damping characteristics of the liquid will vary.

3. Apr 8, 2006

### Grimhelm

I simply tap a spoon on the bottom inside of the cup. Tapping the outside of the cup with the spoon similarly increases the pitch as tapping continues. Following your answer, could it be that creating waves in the liquid by tapping pushes the choco particles toward the center of the drink, away from the walls of the cup, thereby increasing the frequency?

4. Apr 8, 2006

### Astronuc

Staff Emeritus
If tapping inside redistributes the wet chocolate powder which accumulates on the bottom of the cup, that could change the pitch. I don't understand why tapping on the side of the cup would change pitch.

I tried an experiment earlier today with cold and warm water (but no cocoa powder). I tapped inside and out, with and without stirring, but no difference.

I know that adding powder to hot water changes the acoustic properties of a liquid, and frequency can be affected. Depth certainly can affect frequency, as well.

I need to buy some more cocoa powder tomorrow.

5. Apr 8, 2006

### Grimhelm

:) It has stumped me for years. Now, I am in training to be a teacher and this is one of my "inquiry" projects. I have pretty much narrowed it down to the particles of cocoa being the sole cause of the frequency change, but I can't figure out what they are doing to make the change! Tapping the outside of the ceramic cup does not work quite as well. After you buy up the cocoa shelf and mix yourself up a batch, just take a spoon and gently tap it against the bottom of a ceramic cup repeatedly and listen carefully! Thanks in advance for all of your help. What is even more strange to me is that re-stirring the liquid returns the pitch back to low. Argh.

6. Apr 10, 2006

### Grimhelm

Has anyone else gotten a chance to try this?

7. Apr 10, 2006

### HallsofIvy

You are also changing the density of the liquid as the chocolate dissolves. That will affect the speed of sound in the liquid and so the "natural frequency" of the cup-liquid system.

8. Apr 10, 2006

### Grimhelm

Yes. Strangely, as the chocolate powder dissolves more thoroughly, the phenomenon diminishes. So, I am presently concluding that it has something to do with the particles before they are fully dissolved.

9. Apr 10, 2006

### Astronuc

Staff Emeritus
It would be useful to attach an acoustic transducer and record the acoustic signature.

I think the change in frequency diminishes, but I believe with cocoa powder in the water, the frequency is different than without.

There is the matter of cocoa powder on the spoon (I observed this this morning). The powder sticks to the spoon and changes the spoon's acoustic properties.

The collection of cocoa powder on the bottom of the cup would also change the frequency. One idea is to note the frequency just after adding the cocoa powder and stirring. Then let is sit for several hours (but one will need to reheat the water) and then tap/stir and note any change in frequency.

I didn't see any effect while tapping on the outside, except where one taps will have a slight effect. The damping is much greater near the base of the cup than at the top, and damping can affect frequency.

10. Apr 10, 2006

### Meir Achuz

I think the "Grimhelm Effect" is due to standing wave patterns set up in the liquid (similar to what happens in a Kundts tube). Cocoa powder, as oposed to instant coffee, does not fully dissolve in the liquid, leaving a suspension of tiny cocoa particles distributed throughout the cup.
The cocoa particles act as a drag on oscillation in the liquid, making the overall tone lower than in the pure liquid.
When you tap the cup, standing wave patterns are set up in the liquid. These have nodal surfaces, where there is no oscillation. As the liquid oscillates, the suspended cocoa particles tend to rest at the nodal surfaces (similar to how the sand settles in a Kundts tube). This removes the cocoa particles from the body of the oscillating liquid, which thus increases the pitch of the oscillation. Stirring redistributes the cocoa particles.
The only test I can think of is to see how the effect varies with 1, 2, or 3 teaspoons of cocoa. I would use pure cocoa powder, because what is called "hot chocolate" is mostly sugar, which completely dissolves.
Another test would be to use sugar, which should have no effect until you put in too much to dissolve.
I have a tin ear so I am not sure whether I heard the effect or just imagined it.

11. Apr 10, 2006

### Grimhelm

A very interesting answer. I just wish I could visualize exactly what you mean by oscillations and nodes. :)

The sound is definitely real, though I believe two sounds may be overlapping, sort of like the plucking of a guitar string. You have the vibration of the string, but also the 'plink' that occurs when your fingernail plucks at the string itself. If you could explain your idea a little more for me, or perhaps give me a reference for some visual clue as to your meaning, I would be very grateful. Thanks! Oh, and I will look up a Kundts tube to gain a frame of reference... Thanks again!!!

12. Apr 11, 2006

### Meir Achuz

The nodes are like the nodes on a vibrating string or on a drum head.
If you put sand on the horizontal face of a vibrating drum, the sand will collect on the nodal lines of the drums oscillation.

For a guitar, there is an opposite effect. A plucked string vibrates in a large number of modes ("harmonics" or "overtones"). The higher overtones move faster, gettilng more air resistance, and so die out faster. This makes the pitch decrease (all in about a second). Our hears this as "twang". The tw is high pitched, and the ng low pitched.
A violin string, with a continuous pull does not have the twang.

13. Apr 11, 2006

### Meir Achuz

It should have the apostrophe.

14. Apr 11, 2006

### Grimhelm

Okay, I think I am very close to an answer. This morning I put minimal amounts of cocoa into a clear cup of hot water. I stirred. Tapping produced an immediate increase in pitch in direct relation to the amount of particles rising to the top of the water. I then tried the same thing with cold water. The particles hovered in the cold water and there was no change in pitch. Therefore I am concluding that it is simply heat pushing the particles of cocoa to the top of the water very rapidly, thus chnaging the density of the liquid itself and thereby creating an upward change in pitch. What do you think?

15. May 31, 2006

### jrs

hot coco and the rising pitch

First. Hi gang. First post here. I saw this thread and had to comment. As you'll see I've pondered this subject before.

31 May 2006

My current theory(s) on this follow. I should say that although they're hypotheses, I haven't come up with a good experiments to test them.

1.
In the hot coco, the particles of sugar are in the process of dissolving and as the solution sits the particles settle to the bottom of the mug. This settling changes the density of the solution and causes a rise in the mug's pitch. When the solution is stirred the particles are redistributed and the pitch resets to it's lower tone.

2.
The pitch isn't related to the density, but rather to the physical distribution of particles in the solution (like particles in a Kundt's tube).

3.
It's a bubble effect and has to do with bubbles of air rising to the surface as the solution dissolves.

4.
Something else that I haven't thought of, or some modification of 1, 2, or 3.

I'm not satisfied with these hypotheses however. Though I dare someone to disprove hypothesis #4. None explain the observation of the apparent relationship to the rate of change of the pitch and the temperature of the water.

-- Jonathan

Here's too much experimental data for you guys to chew over. but it might be worth your perusal:

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21 March 1998
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Mugs were filled with hot milk and hot cocoa mix was added. 1 pack of cocoa mix is 1 oz. While tapping the bottom of the mug with a spoon, while stirring the cocoa, it was noticed that pitch of the sound of the tapping was rising with each tap. Soon it was noticed that stirring the cocoa reset the pitch from the higher note that it had risen too back to a lower pitch.

The effect was that the pitch of the tapping of the spoon on the inside bottom of the mug filled with hot cocoa would rise until the cocoa was stirred, which would lower the pitch.

this was quite astonishing to the two experimenters. the cocoa was consumed.

next, an equivalent volume (about 200ml) of cold water was put into the same mug. the mug was tapped in a similar fashion and no noticeable pitch change occurred.

the cold water and mug wa placed in a microwave and heated until the water was steaming hot. the mug was again tapped and still no noticeable pitch change occurred. hot cocoa mix was added to the hot water and instantly the rising pitch was noticeable by both experimenters. again, the pitch would drop to a lower note when the hot cocoa was stirred.

the mug was placed in the freezer.

meanwhile a nearly identical mug (nearly identical: same manufacturer, different decoration) was filled with cold water and a plain powdered gelatin packet. (1/4 oz packet). It is worth noting that this second mug had also been filled with hot milk and cocoa mix initially and the same rising pitch effect was observed in it as well.

filled with cold water and gelatin, no pitch change was noticed when the inside bottom of the mug was tapped with a spoon. two more 1/4 oz gelatin packets were added to the cold water until the cold water was super-saturated with gelatin mix. with a super-saturated mixture of gelatin in cold water a just noticeable rise in pitch was heard. it was much slower than that of the hot cocoa and the experimenters didn't have the patience to spend time trying to ascertain how high the pitch would rise because the effect was just barely noticeable.

the gelatin and water were heated in the microwave until the water was warm, but not yet hot or steaming. the rising pitch was more noticeable and seemed to rise faster that when the solution had been colder.

the gelatin and water mixture was heated in the microwave until it was steaming hot. the inside bottom of the mug was again tapped with a spoon and the sound made by the tapping undeniably rose in pitch and, just like with the hot cocoa, the pitch would drop back down to a lower note each time the mixture was stirred.

it was noticed that the rise in pitch continued whether or not the experimenters tapped the mug with the spoon. this was deduced because while tapping it was heard the the pitch would rise at a constant rate with respect to time. if the tapping was stopped and then resumed some time later the pitch of the sound would be at a note consistent with that constant rise in pitch. it was not the case that each tap rose the pitch by a certain amount; for if this was so, the pitch would have risen with respect to the number of taps rather than time.

the effect was much more noticeable with hot cocoa and water than with gelatin and water.

the mug was removed from the freezer while the water and cocoa mix was still a liquid. the bottom of the cold cocoa was tapped with a spoon in a similar fashion and one of the two experimenters claimed to notice a rise in pitch. the other experimenter didn't notice any such effect.

the gelatin mixture was emptied and canola oil was added to the mug and the inside bottom of the mug was tapped with a spoon. no noticeable rise in pitch was heard.

the canola oil was headed and again no noticeable rise in pitch was heard while tapping with the spoon.

it should be noted that there seemed to be no noticeable difference whether the inside bottom of the mug was tapped or whether the outside bottom of the mug was tapped.

the cold cocoa (which had been in the freezer) was re-heated in the microwave until it was steaming hot. when the bottom of the mug was tapped with a spoon the rising pitch was not heard. this quite surprised the experimenters.

16. Sep 19, 2007