Weird science

[Wowbagger]

Dez made himself some hot chocolate earlier and noticed that the note made by striking the cup with his spoon was lower when he stirred the chocolate and rose as the stirring slowed down. The hot chocolate was made with blue-top milk.

https://twitter.com/deniswalker/status/548253060641075200 refers.

He also tried the same thing after stirring hot water but the note remained the same.

Wossgoinon?

[Kim]

Inconclusive results here with hot water and a variety of mugs and cutlery.  Definitely doesn't work with cold.  Didn't fancy a hot chocolate, so haven't tried that.

Ti spork and the periodic table^[1] mug seemed to work best, but it's *extremely* sensitive to the part of the spoon you hit the mug with, so would need to construct a mug-tapping robot to enable blind testing...


_{[1] Our most scientific mug.}

[Wowbagger]

That's Boxing Day spoken for then. 

[barakta]

It probably is and all...  Professor Branestawm is on iPlayer and Kim's been watching it so will have _^IDEAS

[Jaded]

I've noticed that, from years back. I have put it down to the tension in the mug changing as the inside heats up rapidly and then the outside more gradually.

[Wowbagger]

It has to be to do with the lengthening of the sound waves - the longer they are, the deeper the note. It occurred to me that the waves spread out from the point of striking the edge of the mug in the manner of the ripples in a pond when you throw in a stone. If the fluid is still, then they can be no longer than the diameter of the mug. If the fluid is stirred, i.e. spiralling, the waves are being stretched around the inside of the mug and can therefore be longer.

Why does the viscosity of the fluid make a difference? Presumably the waves pass through a viscous fluid less easily than a mobile one. If that is the case, then water, being less viscous, would not affect the sound waves to the same degree.

More testing in the morning with cold milk, whole and semi-skimmed.

Dez is suggesting custard and making fluids of varying viscosity using cornflour. Once a fluid gets beyond a specific viscosity, then stirring it becomes a problem.

[Dez]

I have produced a video of our further experimentations available at https://www.youtube.com/watch?v=u17CnKFjav4

Professor Branestawm is on iPlayer and Kim's been watching it so will have _^IDEAS

I'd not heard of that until I saw Jonathan Ross's tweet about it and meant to check it out. It'll have to wait though. Need to finish listening to the Christmas Day Infinite Monkey Cage!

[Kim]

I don't think the spiralling has anything to do with it, more likely a change in density caused by the distribution of milk fat or air...  Try stirring in a non-circular manner, or bubbling it with a straw or something.

I think it's density that'll affect the speed of sound (and therefore the wavelength of the standing wave) in the fluid rather than the viscosity, though a more viscous fluid will trap bubbles of air (which must make the greatest difference to density, I mean, the milk isn't going anywhere, even if it's clumping together) for longer (hence pure water doesn't work).

ETA: Though, thinking about it, does stirring the drink *really* trap that much air?  Surely the volume would have to increase substantially for it to affect the speed of sound, and you'd see that as a change in level...?  I think we need a physicist.

[Diver300]

It has to be to do with the lengthening of the sound waves - the longer they are, the deeper the note.

That isn't correct, as it could be to do with the change in the speed of sound. The formula is v = f • λ, where v is the velocity, f is the frequency λ is the wavelength, and what I think is happening here is that the speed of sound is varying, which seems far more likely than the wavelength varying.

(If the speed of sound were fixed, because the medium were fixed, then there would have to be a change in dimension. That is how the notes of wind instruments are changed, as they all work with air)

There are two possible mechanisms that I can see.

1) It could be due to the heating distribution within the walls of the mug. The chocolate heats the cup from the inside, while air cools it from the outside. Stationary hot chocolate is a worse conductor of heat than moving hot chocolate, so there will be less heat loss and as smaller temperature difference between the inner surface of the mug and the outer surface, so less stress in the material. When the chocolate is stirred, more heat is transferred to the mug, so the is a bigger temperature difference, and more stress in the material. The more stress in the material of the cup, the stiffer it becomes, raising the note.

2) Air entrapment in the hot chocolate lowers the speed of sound in the liquid. It only needs a tiny volume of air to lower the speed enough if that is the mechanism. The formula for speed of sound in a fluid is:-

 

where:

K is a coefficient of stiffness, the bulk modulus (or the modulus of bulk elasticity for gases);
ρ is the density.

Now liquids are not very compressible, so K for them is very high, so high that the speed of sound in water is around 5 times that in air, in spite of the fact that water is around 800 times as dense as air, water being around 15,000 times harder to compress than air.

So a tiny amount of air in the hot chocolate will lower the stiffness lots (think of small air bubbles in hydraulic brakes) and will therefore lower the speed of sound by enough to be heard.

(As a demonstration of the huge reduction in the speed of sound that air in a fluid can have, hold a full tub of Swarfega in one hand and tap the tub with the other hand. The tub will wobble. Swarfega is largely water, but has air bubbles in it, so its density is nearly as high as water, but its stiffness is really low, due to all the bubbles. The result is a speed of sound as low as few m/s, and the wobble is the shock of it being hit reflecting off each side, and doing so slowly enough to be felt, far too slowly to be heard)

[T42]

My father pointed out this effect back in the fifties.  His idea was that if he tapped long enough the bottom of the mug would fall off.  Dear mama kyboshed the advance of science.

[Wowbagger]

Diver300's hypothesis 1 can be tested with cold milk. There will be little change in temperature when the milk has come out of the fridge, but what there is will be in the opposite direction: the surface of the mug will be warmer than that of the fluid, by about 18 deg C. I would imagine that the temperature difference using hot cocoa is about 40 deg C.

I find it hard to believe that a crude implement like a teaspoon could introduce bubbles fine enough to make the sort of difference we are talking about. In the case of cocoa (this is good quality Montezuma's spiced mandarin flavour) I would think it is far more likely to be the high fat content, especially combined with whole milk. Effectively it's a mixture of fat and water. Fat floats, but stirring mixes it reasonably thoroughly. As the moving fluid slows down, so the fat rises to the surface. A test comparing whole milk with semi-skimmed should establish that.*

There is another factor we haven't considered. The improbability drive could be at work. Beware of the petunias.

*Edit: I would think that fat would be more fluid at higher temperatures. Hot milk might work better than cold.

[mattc]

I think we need a physicist.

Well as you asked ...

Fortunately lots of physicists - incluing some bloke called Bragg - have already studied this to save me the trouble.
If your bookshelves are well stocked,  read this:
"The hot chocolate effect" in the American Journal of Physics -- May 1982 -- Volume 50, Issue 5, pp. 398-404 

Or for a lighter look: http://www.kilty.com/coffee.htm

It's mainly about 3 related effects:
-  as Divers300 said,  trapped air affects the speed of sound.
- But on top of that is the complexity of different modes of vibration in the fluid/cup. (e.g. vertical and radial modes).
- Then there is how the human ear/brain perceives pitch. The sound your cup makes is not one pure frequency, so your brain "hears" a different pitch to what you might see on an oscilloscope.

The trapped air effect is relevant to froth on beer,  sugar stirred into tea,  and many other scenarios.

[rr]

If I remember rightly cornflour/water mixtures are non-newtonian Bingham plastics. Could be a very interesting experiment.

[David Martin]

at the right ratios, yes they do behave as non-newtonian fluids. At higher water/flour ratios it behaves like a normal fluid.

[Wowbagger]

This still works, although to a lesser extent, with hot semi-skimmed milk with one sugar. Without the sugar I think it worked a little, but the change in tone was very small. I didn't try with cold milk.

I think the viscosity of the fluid is relevant. Cocoa powder in whole milk is a pretty viscous brew, semi-skimmed milk a lot less so. The dissolved sugar makes it "sticker" and therefore marginally more viscose. I wonder what honey does?

[Diver300]

The viscosity of the fluid will help to trap air bubbles.