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# Why does the pitch of tapping with a teaspoon rise in a mug of hot milk? Answered

Need: Ceramic mug (shape doesn't matter), hot semi-skimmed or full-fat milk, metal teaspoon. When I give the milk a good stir, then begin to tap the bottom of the mug (inside) with the spoon, the pitch of tapping rises gradually. When I stir the milk thoroughly & then start tapping again, the pitch resumes its ascent from the original lowest note. If I only give a partial stir, the pitch resumes partway up from the lowest note. What's going on?

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## 5 Replies

Dr.Bill (author)2009-09-19

geeze! I thought I was the only one that noticed stuff like that.

Karred (author)2009-02-07

BeanGolem has most of it right on the money, the only thing missing is that when you heat milk up its resistance lowers (not exactly the right wording, but i've been up for thirty hours, sue me! ;D ), basically when you change the thickness/quantity of the item inside the glass your going to change how the glass resonates, with light crude oil if I remember right its +5 degrees to make a note sharp in a glass, -5 degrees to make it flat, so +10 degrees for a full note. (Farenhite (my spelling and grammar brain dieded a horrible death three hours ago) Degrees, not Celsius/Centigrade, +10 degrees C would be enough to make you wish you melted your hand when you grab the glass) Happy Milk tiem! :D

Karred (author)2009-02-07

I was backwards, the cooler it gets, the sharper the note, because the resistance is higher, my bad! I'll go to sleep now! :D

killerjackalope (author)2009-02-05

I have an answer somewhere, I'll give the science later...

BeanGolem (author)2009-01-30

This is intriguing. I just did a little experiment at my desk. Case 1: Full mug of water. No stirring. Tap on side of glass. Result 1: A certain pitch of tappy noise Case 2: Drink half of the water in mug. No stirring. Tap on side of glass. Result 2: Pitch has gone up Case 3: Drink all of water in mug. No stirring. Tap on side of glass. Result 3: Pitch has gone up again. Conclusion: The level of water in the mug affects the system's natural frequency. The higher the water in the mug, the lower the tapping noise frequency (opposite of rubbing the rim of a wine glass). As you spin the fluid in the mug, it rises towards the outside and lowers in the middle. This causes the effective height of liquid in contact with the glass to rise, resulting in similar behavior to my experiment. Combining both of our observed results, it would appear that the volume or mass of water inside the cup has much less influence over the pitch than the height of the water in contact with the mug does. I would guess that this all has to do with the vibration of the vertical section of the mug. If you think of the mug wall as a vibrating spring, it has a certain natural frequency -- the pitch you would hear with an empty glass. When you take a certain portion of that mug wall and coat it with water, it is like adding mass to that spring, which would lower its natural frequency. Thinking of the whole mug, the more of the wall that is covered by water, the more mass there is lowering the frequency of the empty mug. That's just my guess :D