Sunday, May 2, 2010

Coffee sounds

I was at a dinner last week with physicists and mathematicians from the College, along with a visiting scientist who was on campus to give a lecture. During dinner, I suggested that it was possible to identify by ear the difference between pouring hot water and pouring cold water. As we ate our dessert, I did a small demonstration. I poured ice-cold lemonade into a china cup, then poured hot coffee into an identical cup. A few of the diners didn't notice a difference. Most of us did hear the two liquids differently, but no one could accurately describe what we had heard: "more tinkly", "more splashy", "higher", "lower" were some of the descriptive words we suggested.

This weekend I conducted a more careful experiment, making a sound recording of each.
I poured very hot water (fresh from the tea kettle) from my teapot into a mug:  pouring hot water
Then I poured chilled water (fresh from the fridge) from the same teapot into the same mug:  pouring cold water

Do you hear a difference?

My wife said she thinks the cold water sounds higher pitched.  I agreed (she has a very good ear), but I was unsure.  I loaded these recorded sound files into Audacity and computed the power spectra.

 In the following figure, the hot water spectrum is shown in the upper view, with the cold water spectrum in the lower.

The first few peaks (114 Hz, 175 Hz, 358 Hz, 444 Hz, 536 Hz, 650 Hz) are common to both spectra.  I think this must be due to the physical properties of the teapot spout, the mug, and my kitchen.  Then comes the difference:  the strongest peak for the hot water is 895 Hz, while the strongest peak for the cold water is lower, at 780 Hz.   Overall, the strongest frequency of the hot water is 15% higher.  In terms of musical pitch, the MIDI digital music encoding format has a neat way to identify a pitch, given its frequency.  The standard reference pitch at 440 Hz is the musical note "A" above middle C on the piano.  MIDI calls this pitch number 69.  Every other pitch number is determined by the formula

p = 69 + 12\cdot\log_2 {(f/440)}
\,.

For us then, the hot water has a frequency component with pitch number 12.2 half-steps above A440, while the cold water has a strong frequency component 9.9 half-steps above  A440 ---  a difference of about one whole step.  This seems like a small difference to discern in two sequential experiments! And it is counter to our perception that the cold water had a higher pitch.  Maybe something else is going on.

I listened to the recordings a few more times, and realized that the last few seconds of each one are a lot different:


The last 2.5 seconds of
hot water.

The last 2.5 seconds of
cold water.

Notice that the end of the cold water sound much higher pitched than the end of the hot water.
Here are spectrum plots for the final 2.5 seconds  (upper view is hot water, lower view is cold water):

Notice that all the peaks up to about 1300Hz are the same in each case.  In the cold water spectrum, there are pronounced peaks at  about 2700 Hz, 4100 Hz and 5000 Hz.  There are none of these high frequency peaks in the hot water spectrum.

There is a difference at the beginning of the pour as well, with the cold water having a lower frequency sound.  The frequency difference  in the strongest peaks we saw in the full spectral decomposition is prominent in the first 2.5 seconds,  as illustrated by these final spectrum plots:




None of this explains why hot and cold pouring water have different sounds.  A quick Google search shows that this issue has been the subject of discussion boards from time to time.  The proposed physical causes are many and varied:  Temperature dependent changes in water viscosity, surface tension, density, and gas content.  There are suggestions that the mechanics of the pourer are different for hot and cold waters (like maybe we're naturally more careful with hot water).  Maybe the sound waves travel differently in the hot, swirling, steamy air inside the hot-water cup.  I'm eager to know the cause, but I'm not in a position to work it out now.  Maybe a later post!



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