Explain this (changing pitch in coffee mug)

[Keith_W]

I recently came across this phenomenon and its explanation, and I posted this video to my WhatsApp chat group with my former university classmates. None of us have degrees in acoustics and our formal learning in physics stopped at high school. It provoked a rather spirited discussion, at the level of a whole bunch of 50 year olds with extremely rusty recollections of high school physics.

The question is this:

I made a mug of coffee this morning and stirred it vigorously. Then I tapped the rim of the mug. Listen to the pitch. Why does the pitch go up?

We have since googled the answer here but this provoked even more arguments. And then my friend repeated the experiment with frothed milk:

... which shows the opposite result of what we would expect if the explanation in the spoiler is to be believed.

Anybody want to have a shot at explaining this phenomenon? Don't worry, this topic was created in the "fun topics" subforum so nobody's reputation will be ruined

 

[dweeeeb2]

air bubbles damped the system ?

 

[ernestcarl]

I recently came across this phenomenon and its explanation, and I posted this video to my WhatsApp chat group with my former university classmates. None of us have degrees in acoustics and our formal learning in physics stopped at high school. It provoked a rather spirited discussion, at the level of a whole bunch of 50 year olds with extremely rusty recollections of high school physics.

The question is this:

I made a mug of coffee this morning and stirred it vigorously. Then I tapped the rim of the mug. Listen to the pitch. Why does the pitch go up?

We have since googled the answer here but this provoked even more arguments. And then my friend repeated the experiment with frothed milk:

... which shows the opposite result of what we would expect if the explanation in the spoiler is to be believed.

Anybody want to have a shot at explaining this phenomenon? Don't worry, this topic was created in the "fun topics" subforum so nobody's reputation will be ruined

Yeah... it's fairly obvious foam/bubbles have something to do with it. I forgot the exact technical explanation, though... something about standing waves frequency changing as the density distribution changes.

 

[JayGilb]

Maybe it the rotational speed of the liquid that is making the pitch change ?

 

[dweeeeb2]

Its actually a space time phenomenon. As speed increases time slows. You’ll notice the pitch goes up as the speed decreases, which can be counter intuitive until you factor in gravity. As time has been slowed the gravitational forces increase to delay the sound escaping to our ears. Quite simple really.

 

[NTK]

Bubbles in liquid significantly reduce the "stiffness" (bulk modulus) of the fluid, and hence can significantly reduce its speed of sound. This affect sound propagation in the fluid and how the sound waves interact with structure at the fluid/structure boundaries (acoustic impedance). This phenomenon is also used to mask naval vessels.

Prairie-Masker - Wikipedia

en.wikipedia.org

 

[Keith_W]

OK, I will explain my theory and why it doesn't work.

1. bubbles in a liquid changes the density of the liquid.
2. the speed of sound varies according to the density of the liquid. Higher density = faster speed of sound.
3. the sound produced is the result of a standing wave between the bottom and the top of the mug. This is a quarter wavelength, similar to bass standing waves in our listening rooms. Because we are not changing the height of the mug, the wavelength remains constant.

We know that c = f * lambda (c = speed of sound, f = frequency, lambda = wavelength)

Therefore, if c increases, then f increases along with it, which produces the rising pitch.

So far, so good, right? This explains the first video.

My friend disagreed. His theory is that the different viscosity of the bubbles in the liquid dampens the vibration of the walls of the mug differently. He reasoned that a more viscous fluid (no bubbles) would dampen the vibrations more than a less viscous fluid (with bubbles). So he performed the second experiment.

A glass containing flat milk was tapped. Then the milk was agitated with a whisk and tapped again. This time, the bubbles caused the pitch to increase (as you can hear). I do not have an explanation for this. My model would predict the pitch to decrease. There is something else going on, and I have no idea.

 

[NTK]

1. bubbles in a liquid changes the density of the liquid.
2. the speed of sound varies according to the density of the liquid. Higher density = faster speed of sound.
3. the sound produced is the result of a standing wave between the bottom and the top of the mug. This is a quarter wavelength, similar to bass standing waves in our listening rooms. Because we are not changing the height of the mug, the wavelength remains constant.

We know that c = f * lambda (c = speed of sound, f = frequency, lambda = wavelength)

Therefore, if c increases, then f increases along with it, which produces the rising pitch.

First, speed of sound is inversely related to density. The huge influence of the bubbles is that they reduce the stiffness of the liquid (liquid with lots of bubbles is a lot easier to "compress" into a smaller volume than without). From: https://www.win.tue.nl/~sjoerdr/papers/boek.pdf

 

[Keith_W]

Do you have an explanation for the second video, where introduction of bubbles into the milk froth increases the pitch compared to flat milk?

 

[Curvature]

Do you have an explanation for the second video, where introduction of bubbles into the milk froth increases the pitch compared to flat milk?

Pitch is subjective. I.e., the name for a subjective perception of frequency. But if we look at a spectrogram:

Spoiler

(Milk flat, voice, milk frothed.)

The frequency components haven't shifted. They've been dampened. What you hear as a change in pitch is a change in the relative strength of various frequency components.

But this is the coffee:

Spoiler

Only some specific components shifted, not all, so you can identify those as relating to the turbulent, hot liquid.

 

[Curvature]

Wanted to add three things about listening tests.

1. Controls, controls! Lot of changes between the two examples that weren't acknowledged and confounded the ear. Different cup, different liquids, different stirring, and I'm guessing the milk was cold and the coffee hot.

2. Ear training. I did not hear a change in spectral distribution (pitch), but I did hear the change in amplitude/level of resonance.

3. The milk example represents a change in FR. Interesting that it was not interpreted as such.

 

[NTK]

For the milk, it looks like the froth had increased the damping (which resulted in much higher rate of energy dissipation), and the ringing duration is much shortened while the mode frequencies were about the same.

This happens with other liquids too. One of my former big bosses told us during a business trip to Ireland that to judge whether the Guinness is ready to drink after it is poured is to wait until the sound from tapping the glass with a coin is no longer a thud (most bubbles have rose to the top). It is collaborated with this post:

https://www.fodors.com/community/europe/ireland-trip-report-may-june-2004-a-439666/page2/#post5594565

 

[Curvature]

For the milk, it looks like the froth had increased the damping (which resulted in much higher rate of energy dissipation), and the ringing duration is much shortened while the mode frequencies were about the same.

I think the damping effect was as strong as it was because the glass is lightweight.

 

[Keith_W]

@Curvature wow thank you for doing that! I had a good look at your spectrograms.

Frothed milk. The first tap (on the left) produces a spray of frequencies from low to high. After the milk is frothed, some frequencies are damped more than others. In this case, the lower frequencies have been attenuated more, while the higher frequencies have been attenuated less. This produces the illusion that more bubbles in the glass = higher pitch, when in reality it is selective attenuation of frequencies.

This is the coffee spectrogram. Unlike the frothed milk experiment, this shows that the rising frequency / pitch of the taps is actually being generated from the taps, i.e. it is not arising from attenuation of pre-existing frequency components.

My take from this is that the coffee experiment and frothed milk experiment demonstrate two different phenomena.

The coffee experiment validates Wikipedia's article on the Hot Chocolate Effect.

The milk experiment demonstrates another phenomenon. I suspect it has something to do with how resonant the thin glass vessel is, and the influence of the difference in viscosity and therefore dampening of the thin glass walls, which selectively reduces the attenuation. Lower frequencies (long wavelengths) are being selectively attenuated because it requires a larger surface to vibrate.

Do you think my theory is off the walls here?

 

[Hiten]

Coffee mug sound may be shephard tone audio illusion.
Link
at around 1:50 in the link

 

[Keith_W]

Coffee mug sound may be shephard tone audio illusion.
Link
at around !:50 in the link

Great reply. I think from analysis of the spectrograms, we have demonstrated that the frequency is actually rising with the coffee mug experiment. It might explain the frothed milk experiment though.

 

[dweeeeb2]

Pitch is subjective. I.e., the name for a subjective perception of frequency. But if we look at a spectrogram:

Spoiler

View attachment 336077

(Milk flat, voice, milk frothed.)

The frequency components haven't shifted. They've been dampened. What you hear as a change in pitch is a change in the relative strength of various frequency components.

But this is the coffee:

Spoiler

View attachment 336090

Only some specific components shifted, not all, so you can identify those as relating to the turbulent, hot liquid.

This is soooo ASR. Love it

 

[Hiten]

I think from analysis of the spectrograms, we have demonstrated that the frequency is actually rising with the coffee mug experiment.

Probably moving liquid molecules has more exposure to adjacent molecules to transfer vibrational energy ? Which will not be the case for settled/settling liquid.

 

[Keith_W]

I just realized something. If the pitch of the mug is due to a standing wave, then we should see n0, n1, n2, etc. components of other supported standing waves in the same container of fluid.

From @Curvature's spectrogram:

Red = n0. Blue = n1.

Regrettably there is no scale included with the spectrogram. But I am willing to bet that the n1 component is twice the frequency of n0. @Curvature can you confirm please? If this is true, it confirms that the rising pitch is due to the speed of sound in water.

Also, if we know the frequency of these waves, I might be able to calculate the speed of sound in the water, since I know the height of my vessel. I would love to see if it corresponds.

 

[MCH]

i don't have an explanation for either video, just wanted to bring up that milk is not an homogeneous fluid, but an emulsion, and is not perfectly newtonian. Might be your friend is up to something with his viscosity explanations.