# The hot chocolate effect

The Hot Chocolate Effect is a cool little experiment you can try at home right now. Take a cup of hot water and tap a spoon against the bottom of the glass. Then add your favourite hot chocolate powder and stir it in. Now tap at the bottom of the glass again. The more you stir, the lower the pitch! And if you keep on tapping on the glass after you’re done stirring, the pitch will gradually increase! Why!?

# On a diet? don’t worry

Here’s another equivalent form of the experiment that might be easier if you don’t have chocolate powder. Turn on your hot water tap and fill up a glass cup. Then tap on the bottom of the glass every few seconds. You should hear the sound gradually rise in pitch. Can’t try it out right now? Check out this youtube video. Don’t look at the explanations yet! Try to think about it yourself first!

Ok…

# Explanation of the hot chocolate effect

When you tap on the bottom of the cup, where does the sound come from? Well some of the sound is definitely transmitted through the air when you hit it, but most of it goes through the water. This is the first thing to understand. The sound waves travel through the water.
So what changes when you stir? One guess might be the speed of the water. But it’s not easy to see how that changes the pitch. So let’s move on. The next obvious thing that changes is the air bubbles. Initially, the hot chocolate has no bubbles, but stirring mixes in a lot of air with the water. If you did the second form of the experiment, initially the water had a lot of bubbles but the bubbles eventually go away.

## how do bubbles change the pitch?

Well what does change the pitch? We know that we hear sounds because of a standing wave inside of the water or hot chocolate. The boundary between the liquid and the air actually reflects back the wave. Don’t believe me? Try putting your water proof phone in the sink and playing a song. It’ll be a lot quieter! Let’s say there’s a standing wave in the water. Then the frequency is proportional to the speed of the wave for a given wavelength. Notice that each harmonic still has the same wavelength because the height of the bottle doesn’t change.

So why does the speed change? Let’s look at the difference between water and air. When you push on water, it’s immediately responsive. Since it’s essentially incompressible, your displacement will be quickly transferred to neighbouring areas of the water. But how about air? Air is easily compressed, so if you push on it, it’ll take some time for the effect to felt elsewhere. Which medium gives you faster sound waves? Obviously water! The speed of sound in water is $1484 \, m/s$ while the speed of sound in air is just \$343 \, m/s\$. That’s a huge difference!

So what do bubbles do to the hot chocolate? It makes it less responsive which decreases the speed. A smaller speed gives you a lower frequency which gives you a lower pitch! As you mix, you increase the air bubbles which lowers the pitch. But when the bubbles gradually leave the drink, the pitch goes back up.

Next time you’re having hot chocolate, tell your friends about the hot chocolate effect!