|MadSci Network: Physics|
Thank you for the interesting question and for the opportunity to turn my kitchen into a laboratory! Before I discuss why the pitch sounds lower when tapping a cup after adding a hot liquid, let me address some of the related questions in the archives.
When I searched the MadSci Circumnavigator, I found two similar questions that inquired about rising pitches. The first, "Hot Chocolate and rising pitch when tapping on bottom of cup" deals with the sound rising for a fixed amount of fluid. This is different from your question where the amount of fluid is changed, so the results of the two experiments are not relatable. (William's answer to that question, by the way, is very good.) The second question, "why does the sound made by a spoon 'clinking' a cup of coffee rise in pitch", could not be reproduced by either Uli Dammer or myself. Uli suggested that perhaps it had to do with the specific cup or coffee mixture.
Getting back to your question, tapping your cup after adding hot water causes the material of the cup to vibrate and produce sound. The water, however, dampens these vibrations. The less water there is in the cup, the faster the cup vibrates, and the higher the pitch. Conversely, the more water there is in the cup, the slower the cup vibrates, and the lower the pitch. After trying many different types of cups (coffee mugs, glasses, and jars), many different types of liquid (water, coffee, tea, and milk), and many different temperatures (ranging from chilled to boiling), I can tell you that temperature and liquid density have very little influence on the resulting pitch. What really matters is how much fluid you've added.
Here's another interesting experiment to try while we have out lots of cups with varying levels of liquid: instead of tapping the cups, blow over them. This effect is the opposite of tapping the cups! The cups with the more water in them make higher pitched notes. This is because now it is the air, and not the glass, vibrating. Shorter columns of air will have a higher pitch when you blow, just as shorter columns of water have a higher pitch when you tap them.
I hope I've answered your question.
James R Holliday
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