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First of all: This is a different question than Why is boiling water loud, then quiet?, although the answers might be similar.

When I wake up, I boil some water for a cup of tea. It happens quite often that I do something else for 10-15 minutes and forget the water, so I boil it again. I noticed that boiling the water the first time is much louder than boiling it the second time.

Why is this the case? Did the air dissolved in the water disappear and therefore it became more quiet? How long would it take until the water has again air (I'm sorry, I know this is linguistically wrong, but I don't know how to write it correct). Is there any simple way I could get air again into the water to check if it's only the air?

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up vote 7 down vote accepted

Water could have small pockets of air dissolved inside it, and given enough time they will rise to the surface on their own.

Now when you boil water, what happens is that the vapour pressure at the water surface is equal to the atmospheric pressure, and liquid water gets turned into water vapour. This process does help the trapped pockets of air reach the surface more quickly, since the water molecules are moving around a lot during boiling. So after one boil, there is less water in your kettle, but there is also a lot less air dissolved in the water.

As the question you linked to pointed out, some of the sound comes from the dissolved air bubbles hitting the surface, and with less air that is less sound. Also quoted is the vapour bubbles that are produced at the bottom of the kettle (where the heating is). A vapour bubble is basically a bubble of water vapour, as the name suggests. The pressure of the water vapour is higher than the pressure of the water around it, so it rises upward to the surface. This produces a sound (quoting the paper linked in the question) of about $35 - 60$ $KHz$.

But the second time you boil the water, the water isn't at room temperature. It's quite a bit higher. Therefore I suspect that less vapour bubbles are produced near the bottom (since the pressure of the surrounding water is higher than at room temperature, because it's hotter) and thus overall less sound.

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Typical human cannot hear sound with frequency higher than 20 kHz – hwlau Dec 13 '12 at 10:20
@hwlau If you read the paper linked in the question, they also mention that air bubbles hitting the surface of water is ~ $100$ $Hz$, which we will hear. I'm wondering if there are any sources of sound that they haven't pointed out that will contribute though. – Kitchi Dec 13 '12 at 13:45

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