Drip drip drip ... the science of a dripping tap

It turns out that the science behind why dripping taps sound the way they do is a lot more complicated than we first thought, and this week scientists at Cambridge University have solved the riddle of the reason why a drip sounds the way that it does. Chris Smith spoke to engineer Anurag Agarwal to find out why on earth he started studying the sounds of a dripping tap...

Anurag - I was visiting a friend in Brazil and it was the rainy season and it was raining very heavily. The bedroom I was in had a small leak and what my friend did was placed a bucket underneath as one would normally do to collect the water. At the beginning everything was fine but after about half an hour or so I started to hear the annoying plink noise that you hear with a dripping tap let’s say in your sink.

So initially this was very annoying and kept me awake but then I quickly became curious. I wanted to know why it was making this loud sound.

Chris - And critically, why the sound had changed. When the bowl was empty your didn’t get a sound and then as it got a threshold amount of water in it it began to make the plink plonk noise that you get.

Anurag - Yes.

Chris - And so the physicist and engineer in you kicked in and said I have to design an experiment to work this out?

Anurag - That’s right. We advertised it as an undergraduate project and we found a smart student, Sam, to work on it.

Chris - You’ve brought a demo: bowl, water, syringe. What are you going to do with them?

Anurag - Yes, I’ve got them here. I’ve got a full bowl with water, and I’ve got a syringe full of water, and what I’m going to do is I’m going to squeeze this syringe and release drops into this bowl full of water.

Chris - Before you do it in the water though, you did say that when you were in your bedroom in Brazil that when the bowl was empty to start with there was no sound so we’d better test that first.

Anurag - I have an empty bowl here, and if I squeeze my syringe in this, I’m just about to do it, the first drop is coming down…

Chris - Right. We’re listening really carefully.

Anurage - It’s hit, second drop.... third drop… fourth drop. As you can see this is very silent.

Chris - No, I can’t hear anything.

Chris - Okay. Proved by experimentation. I believe you. Then the bowl gets full.

Anurag - Now the bowl is full and I’m going to do the same thing again. I’m squeezing now. First drop…

Chris - Yeah. I’m definitely hearing the noises. Can I ask you to try something because you’re doing nice little individual drip, drip, drip. What happens if you do a more rapid stream?

Anurag - If I do this…

Chris - Now that is different. That’s louder. Is that the same thing but just many many times over so it sounds louder, or is there something else exciting going on?

Anurag - the mechanism here is different. We have just finished the research for this and it’s about to be published.

Chris - Ah. So you’re not going to give the game away?

Anurag - No. You’d have to invite me again.

Chris - How did you then go about modeling that then in order to work out what is going on.

Anurag - This is the interesting thing. When the water drop falls on a hard surface it makes almost no sound but, at the same time, when it’s falling on a soft surface it’s making a lot of sound, an annoying sound. This is counterintuitive.

So what’s happening is when the water drop falls on a soft surface like the water surface, the water surface caves in because of the mass of the drop following.

Chris - Ah, you mean the actual surface sinks a bit under the momentum of the falling drop?

Anurag - Exactly. And then what happens is that this cavity that’s formed wants to close because with the surface tension water wants to get back to its original level. But it does so very quickly, and in doing so it entraps an air bubble underneath. And this air bubble oscillates or pulsates at 5,000 hertz which is 5,000 times a second, and that’s the source of sound that we hear.

Chris - And it’s right in the middle of speech frequencies so we’re actually quite tuned into that.

Anurag - Actually it’s in the middle of the annoying speech frequency, which is between 1 kilohertz and 5 kilohertz. Other examples would be a baby crying which is in that frequency as well.

Chris - It’s very elegant you’ve been able to find out how this works, but can you extrapolate this and do anything useful with the model?

Anurag - One thing we can do with the model is to predict the amount of rainfall on an ocean. Because once we know the frequency that we are measuring we can tell what the raindrop size is, and from that we can estimate the amount of rainfall.

Chris - So what, would you put a hydrophone - a microphone under water - and listen to the rain falling on the ocean?

Anurag - Exactly that. That’s what we would do.

Chris - How do you resolve where the rain is falling? Because the water’s going to transmit vibrations from all over the place over a big area, small area. How do you resolve all of that?

Anurag - Localisation is hard but we can tell the total amount of rainfall so we can do a sum of all the rain that’s falling.

Chris - Forgive my ignorance, but is that a big problem facing marine scientists and hydrologists then trying to work out how much rainfall’s at sea? Because if there’s no-one there to measure it it’s a little bit of ‘who cares’ situation isn’t it?

Anurag - Well, if you are interested in the total amount of rainfall in a season and normally we do it overland in a certain place, then that could be interesting. But that’s not what motivated us.

Chris - No, indeed. And any other applications for that apart from getting someone a first?

Anurag - That was the best project in the year so the student was happy.

Chris - I’m not surprised. Very very exciting.

Anurag - But there is another application which is to synthesise sound. It is very hard to synthesise these kind of sounds. That’s because you would think that most of the sound is coming from the initial impact when the drop falls on the water surface, but from what I’ve said that’s not what happens. That initial impact is completely silent. It’s only when you get this bubble entrapped underneath, which is a few milliseconds after the initial impact do you get the sound.

Chris - Does that mean then it’s really hard to make an artificial raindrop sound?

Anurag - Yes, because people up to now didn’t know how to make it.

Chris - They were doing it wrong?

Anurage - Yes.

Chris - So you can solve that?

Anurage - Yes.

Chris - So can we look forward then to much better sounding rainfall made artificially in Hollywood movies and cartoons?

Anurag - Oh yes. Absolutely.

Chris - Have you licensed this? Have your protected this, or can everyone just read your paper and rip this off now?

Anurag - I think it’s pretty easy.