# Frequency difference when water splashes at different temperatures

When I pour hot water (near boiling) and cold water ($5 \unicode{x2103}$) from a height on a platform, there is a distinct difference in the sound that is generated. I feel that hot water splashing has a lower frequency than cold water splashing. What can be the possible reason behind this?

Edit 1: I used a tea kettle to heat the water and dropped it on a marble platform. I did the same experiment with cold (refrigerated) water using the same kettle. Height would be around 1.5m. There's a distinct difference between the sound produced.
Edit 2: I guess I won't need to do the experiment as @Deep suggested. Please view the link given by @Porges. Also, I was incorrect in relating the frequencies. Hot water makes higher frequency. Only thing is, how does bubbling make it more shrill?

• I would say viscosity is like string tension. High tension higher frequency. Feb 16, 2017 at 17:47
• What height did you drop the water from? and what surface was it hitting, to make the sound as it splashes? Feb 16, 2017 at 22:50
• Can you provide a video or measurement? It would be nice verify this isn't just your perception/nuances in your setup. Feb 16, 2017 at 23:23
• I may have misjudged the frequency, as people are pointing out it maybe the other way round. I would ask someone with better experience in music to help me out. Hopefully I would add the result of that experiment in a few days. Feb 17, 2017 at 5:28
• Here's a relevant NPR piece from a few years ago. npr.org/2014/07/05/328842704/what-does-cold-sound-like @ConfusinglyCuriousTheThird it has some recordings Feb 17, 2017 at 6:05

This is a guess since I have never done the experiment, but the viscosity of water falls by a factor of 5 on heating from 5°C to 100°C. The viscosity is one of the two factors (the other being density) that control the water flow, so it is quite reasonable to suppose that water at 100°C splashes in a noticably different way to water at 5°C.

I mentioned above that the density also affects the flow. However the density of water only changes by about 4% over this temperature range. So it seems likely that the change in the viscosity is the main factor.

• What would be the exact role of viscosity in the frequency of sound produced? Feb 16, 2017 at 13:16
• @AlphaRomeo: that's a good question and I don't know. Splashing is a very complicated type of flow, and working out what sound it makes and why is even more complicated. The reduced viscosity will obviously make a difference because the water will flow more easily, so presumably will splash farther. But for me to say anything more than this would just be guesswork. Feb 16, 2017 at 14:00
• Interesting! My intuition would have been rather that lower viscosity causes higher frequencies, since short wavelengths aren't damped as strongly. But that's obviously way too simplistic to be much use for predictions of such a highly nonlinear phenomenon. Feb 16, 2017 at 16:50
• I'm wondering how surface tension plays into this. Can this be addressed entirely with viscosity, or does it complicate our calculations considerably on its own? Feb 16, 2017 at 19:15
• Feb 17, 2017 at 11:24

My immediate guess is that it is because of the difference in viscosity due to temperature.

At 5 degrees celsius, water is around five times more viscous (dynamic viscosity ~ 1.5 mPa.s) than it is at 100 degrees celsius (dynamic viscosity ~ 0.3 mPa.s).

This means that when the cold water splashes, the droplets/jets will have less energy as viscous friction is absorbing some of the energy of impact. In the low-viscosity hot water, less of the energy from the fall is absorbed by viscous friction and so more is available to hit things and emit a higher frequency/ higher energy sound.

Other minor effects:

Surface tension is ~30% lower in the hot water (Surface tension and viscosity are parametrically related through temperature),

Density is 2.5% lower in the hot water

However, I just did an experiment with a mug of boiling water and a mug of chilled water and I've got to say I didn't notice the difference in the splashing sound. Maybe I need to do a more careful experiment.

Edit: did a more careful experiment and I noticed the slight change in pitch! Cool stuff! However I heard the change in pitch in the opposite direction to the one you describe, being slightly higher pitch for the hot water. My experiment was dropping water from either of two mugs (one boling water and one chilled) into a ceramic dish in the kitchen. Drop height of maybe 50cm, so probably shorter than your experiment.

There are a number of reasons:

The hot water has a lower density than cold water

Hot water will often be filled with tiny air bubbles, giving it a milky appearance. When cold water, with lots of dissolved air in it, is heated, its ability to hold dissolved air is reduced. The air is forced out of solution and into tiny bubbles.

But most important, hot water has a much lower viscosity than cold water. The viscosity of water at 70 degrees Celsius is about $\frac13$ the viscosity at 10 degrees Celsius. The hot water will flow more quickly through the pipes and splash differently when it hits a surface.

All of these will change the sort of sound the water makes in flowing through the pipes, and outside the pipes as well.

• That suggests a simple experiment to separate the effects: keep the water just short of boiling for a little while to get rid of the dissolved gas. Feb 16, 2017 at 9:44

As others have said, the significant viscosity difference between hot and cold water is a major reason for the difference in splashing sounds.

Another reason, especially for water near boiling, is how much more likely micro-boiling is. As water is splashed there will be significant shock waves thru it, which really are variations of the pressure about the median. For water that is near boiling, it only takes a little extra negative pressure to make it actually boil. This causes temporary micro-bubbles to form, then collapse again as the pressure increases. These small but sudden expansions and contractions surely cause some additional sound. They also likely change the overall viscosity of the water, and its sound transmission properties.

I don't have any direct evidence or measurements of this, but I suspect the effect is significant enough to change the sound of splashing. One way to test this is to splash the same temperature hot water at different air pressures.

This is not a reply to your question. This was too long for a comment, so I am posting it here.

I don't know what experiment you did to arrive at the conclusion you have mentioned. I do experiments in laboratory, and given how much preparation goes into properly conducting even a seemingly simple experiment, I am always a bit suspicious about home-made experiments (I am not saying you are wrong). You can do the following blind experiment to verify your conclusion (if you have not done it already).

Ask someone else to pour hot water and cold water from predetermined height for predetermined amount of time, repeatedly and in random sequence. You must stand far enough to ensure that you can only hear the sound of splashing, but are far removed from the place of pouring so that you can neither see nor feel the effects of hot water (such as rising vapors, hotness etc.). After listening to each pouring write down whether hot or cold water was poured, while the person pouring water notes the same. After sufficient number of trials, say at least 20-30 trials, compare your predictions with what actually happened. If you have guessed better than what pure chance would allow (I would be inclined to believe the result if you got it right at least 90% of the time) then your conclusion is most probably correct, and deserves a serious attempt at explanation. You can also ask assistance from someone with a musical ear (one who can easily make out a change in the pitch of the sound) if that helps.

• Alright, would try that Feb 17, 2017 at 5:24
• Deep, you should know better than to post comments as answers. Frankly, an easier method is to record the sound, and analyze the frequency content - this does not rely on perception, would not require 30x repetitions, and would yield and would provide data for further analysis... Feb 17, 2017 at 6:59
• I'm surprised there is any skepticism about the different sounds. I routinely use sound to tell me when hot water has gotten thru the pipes to a faucet. The splashing sound in the sink is noticeably different. Try it. If you want to detect a quantitative difference, take recordings and analyze them as @Conf said. But just a simple test is enough to convince yourself the effect is real. Feb 17, 2017 at 18:39
• @ConfusinglyCuriousTheThird You are right in that I should not have posted a comment in the answer section. May be I should have written it as multiple comments. As regards your way of doing experiments it is definitely better, but my intention was to propose something simpler and less expensive to be done at home. Recording the sound and analyzing frequency content requires more expertise than what I assumed for the OP.
– Deep
Feb 18, 2017 at 4:47
• @OlinLathrop I have not the done the experiment myself (may be I should). If you have done it carefully enough and are able to tell the difference, then that means the effect is real.
– Deep
Feb 18, 2017 at 4:50

Let me take a stab at answering the question, even though I have nothing but my intuition, logical reasoning and a little scientific knowledge to go by.

I believe that the main component of the splashing sound generated by a falling stream of a liquid is due to the breaking up of the liquid while falling. The more viscous the liquid is, the larger are the droplets that it breaks up into. Naturally, the more droplets there are, the higher the frequency they hit the surface they fall upon. As stated in John Rennie's answer, hot water has lower viscosity than cold water, so if this explanation is correct then we have the answer.

Now we could test this hypothetical explanation relatively easily to a certain degree. It predicts that keeping everything the same but increasing the height would yield a higher frequency, because the liquid stream will break up into tinier droplets. Also, the size of rain drops seem to correlate with the 'pitch' of rainfall in the manner predicted by this hypothesis. Next we should check that liquids at the same temperature but with different viscosity (water, sugar syrup, oil) really does change with frequency. Finally we should compare liquids that have the same viscosity (preferably with some at different temperatures) and see if the frequency obtained is the same.

• By the way, there is certainly a threshold height for each liquid, below which there is little splashing and hence little sound, and above which there is splashing. There is a secondary effect that you can observe if you have a tap that can generate a very steady thin stream of water, where the stream will have sinusoidally varying width near the impact surface. I believe (from prior humming experiments) that this effect is mostly due to the resonant frequency of the impact surface. For metal sinks, I expect this secondary effect to generate the same frequency regardless of liquid viscosity. Feb 18, 2017 at 12:24