## The sound of hot tea

23.11.2008 16:25

One thing that I was wondering about for some time is why when I pour boiling water from a kettle into a cup, the bubbling sound it makes seems different than when I fill it with cold water. I found it curious, but I never gave it much thought. I always guessed it that if I wasn't just imagining this difference it was more likely the effect of the container from which I was pouring water, not the temperature of the water itself. I never tried filling a cup with cold water from a kettle to check this assumption.

Photo by Mr. T in DC CC BY-ND 2.0

That is until the coffee machine in the office broke down. That forced me to use the office water cooler to make tea. You see, this particular water cooler has two identical faucets: one for chilled and one for hot water. And this time it occurred to me that the sound is still different, even when the two faucets are identical in shape. So I went on and made an experiment in controlled circumstances to come to the bottom of this.

I made a simple replica of the important parts of the water cooler: a funnel with an empty ceramic cup below it, so that when the funnel was quickly filled up, the water trickled down into the cup over the period of around 20 seconds (diameter of the opening was 3 mm, volume of water was 200 ml). I recorded the sound with a microphone placed over the top of the cup. The funnel was high enough that the flow became turbulent.

I did 10 measurements, 5 with water at room temperature and 5 with freshly boiled water just below 100°C. For each measurement I cut out a 10 s long part 3 s into the recording to ignore any transient effects of filling the funnel. On those cut-outs I made a discrete Fourier transform.

This figure shows all 10 measured spectra superimposed. Measurements with hot water are red, while those with cold water are blue.

The most obvious difference is the nicely defined peak at 3000 Hz: it raises in frequency for almost 500 Hz with hot water. Also noticeable is that hot water spectra are on average weaker than cold water between 6000 to 12000 Hz.

So it looks like there is a noticeable difference. The question remains what mechanism causes it.

One factor that contributes to the sound is the ringing of the ceramic cup, excited by the falling water. To get the resonant frequencies of an empty cup I did an impulse response test without any water in it (i. e. I hit the cup and recorded the spectrum of the 'ding' sound):

As you can see this particular cup design resonates strongest at around 2500 Hz, so I'm confident that the similar peak in the spectra in the previous figure is connected with the same cause - the resonant frequency is probably higher when the cup is partly filled with water. I'm not sure why the peak moves with temperature though. Mechanical resonant frequencies of solid objects do change with temperature, but the rate observed here seems a bit excessive. It's also possible that difference in water viscosity caused the hot cups to fill up faster and so resonate at higher frequencies during the measurement interval I used. Some more measurements of responses of an empty cup at different temperatures may clear this up.

The change in higher frequencies is a bit trickier to explain. After a bit of browsing it turned out that I'm not the only one asking such silly questions. For example, the change can be attributed to tiny water droplets of condensed steam in the air according to this post at Yahoo Answers. It seems a plausible explanation to me, although I can't think of a simple way to test it.

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