# Why are higher frequencies amplified less by filling a bottle with warmer water instead of colder water?

Out of curiosity I was trying to figure out what makes the sound of hot water versus cold water filling a bottle different, but I'm unable to find any explanation as to why such differences occur.

The image above is an FFT of a bottle being filled with water at 20°C, and the one below is an FFT of the same bottle being filled with water at 70°C. These are FFTs taken at the halfway point of filling the bottle (synced with a video) but throughout the filling of the bottle, it seems that for the bottle being filled with hot water, higher frequencies are not amplified at all?

I'm aware that the bottle can act as a resonant cavity that amplifies certain frequencies as the bottle is filling up, and those frequencies come from the sound generated by water hitting the bottle/water surface within the bottle. Many people discussing this in forums and articles talk about the lower viscosity of hot water, but I don't understand how this would contribute towards the effect I've observed, and there are even some articles contradicting what I've observed, highlighting that hot water would actually result in a higher pitched sound due to more splashing of water.

From what I've read it seems that in hot water, bubbles produced when hitting the surface of water are generally smaller than bubbles formed the same way in cold water, and intuitively that could imply that the overall amplitude is lower, but I'm not sure if this is useful towards this question.

When using a cup instead of a bottle, I noticed that there was the presence of some higher frequencies, but the lower frequencies when filling the cup with hot water were more prominent still, so I was wondering if the shape of the resonator could have anything to do with this disappearance of the higher frequencies.

Would there be any explanation that could address the attenuation of higher frequencies when using hot water? Thank you!

This is a picture of the bottle used. It's about 22cm in height, and I placed my microphone about 1cm away from the bottle opening when recording the sound. I did not really maintain a constant flow rate, but I did use a funnel fixed at 20cm above the bottle opening and poured water through the funnel in order to fill the bottle. In this case I'm not sure, but I don't think that the flow rate would play a major part in such attenuation of the sound.

• A photo showing the material and shape of the bottle, the location of the microphone, and anything else touching the bottle (like your hands) during the measurement could be helpful. Apr 15, 2019 at 16:17
• There are so many variables involved here in addition to the issue of hot water versus cold water. The experiment would have to be carefully done to make sure that the effect is really due to hot versus cold water rather than some other factor. Were the water flow rates for the two measurements exactly the same? Were the faucet-to-bottle distances the same? Do the two graphs shown correspond to times when the amount of water in each bottle at that instant were the same? If you were writing this in a paper, you would have to show that you considered all these possible factors.
– user93237
Apr 15, 2019 at 20:42
• @Samuel Weir I didn't manage to conduct a very exact experiment as this was out of curiosity and not for a paper. I fixed a funnel exactly at 20cm above the mouth of the bottle and poured the water through the funnel. If I have the time perhaps I'll try something to keep the flow rate more constant. The microphone was also fixed about 1cm from the mouth of the bottle. I used a glass bottle with a relatively narrower neck, like a beer bottle. I left the bottle resting on a tabletop when I recorded the audio, but that shouldn't have too much of an effect? Apr 16, 2019 at 10:49

## 1 Answer

probable answer: water full of bubbles attenuates sound transmission much better than water with no bubbles. Hot water when mixed vigorously with air will readily fill with bubbles because its surface tension is less than that of cold water and the hot water likes to vaporize into the bubbles, making them last longer. Those bubbles will preferentially kill off the high frequencies and leave the lows more or less alone.

You can easily test this by shaking up hot and cold water and observing the bubble density.

• Why will bubbles "kill off" these higher frequencies? Does it have a damping effect on the vibrations of the air resonating inside the bottle? I don't really understand the mechanism behind this, sorry. When you refer to the hot water vapourising into bubbles, will that be an observable effect as well or do these pockets of gas dissolve quickly into the water? I don't recall really seeing a larger amount of bubbles when pouring hot water instead of cold. Apr 16, 2019 at 10:50
• @CassandraLee I'm guessing it is because high frequencies do not go around things very well, just like sound. Higher frequency sound doesn't travel as well around or through objects as well as lower frequencies. Why? I think it is because for the same amount of energy, the amplitude in a high frequency pressure wave is less. Dec 8, 2020 at 23:07
• Another damping mechanism (thermomechanical): A high vapor pressure means more water condensing/expanding as it vibrates. Absorbing and releasing latent heat repeatedly to the walls. Due to finite thermal resistance energy will get lost. Jun 19 at 4:21