Plink: The Tiny Bubble Behind the Dripping Faucet

One night, while staying with a friend whose roof had a leak, acoustic engineer Anurag Agarwal couldn't sleep. The culprit was the sound of water dripping, drop by drop, into the bucket placed under the leak. The next day, he talked it over with his friend and another visiting academic. All three were surprised to realize that no one had ever actually pinned down what produces that sound. Agarwal leads the Acoustics Lab at the University of Cambridge's Department of Engineering, so he decided to find out.

The answer was published in June 2018 in the journal Scientific Reports. The "plink" of a drop doesn't come from the drop itself. It comes from a minuscule bubble of air, and the surface of the water acts as the loudspeaker.

A Puzzle More Than a Century Old

Water drops have fascinated scientists for a long time. In 1908, British physicist Arthur Worthington published "A Study of Splashes," which contains the earliest known photographs of drop impacts. They show the drop carving a small crater into the water. The crater then snaps shut and sends a column of liquid shooting upward.

Around 1920, several researchers turned their attention to the sound. Some believed the air cavity resonated, a bit like a bottle when you blow across it. Others, including future Nobel laureate C. V. Raman, noticed that below a certain drop height, the drop made no sound at all. All of them already noted that a small air bubble sometimes stayed trapped beneath the surface.

In 1933, Belgian physicist Marcel Minnaert derived a formula for the natural vibration frequency of a submerged bubble. He closed his paper with a lead to follow: it remained to be checked whether the sound of falling drops might share the same origin as the sound of bubbles. The question didn't come back into focus until the late 1980s, and for a very practical reason. Oceanographers hoped to measure rainfall at sea simply by listening to its sound underwater with a hydrophone. In 1989, American researcher Hugh Pumphrey and his colleagues showed that the trapped bubble was indeed the main source of sound underwater.

One question remained: how does that sound, produced underwater, reach our ears through the air?

Filming a Drop at 30,000 Frames per Second

Anurag Agarwal teamed up with Peter Jordan, a researcher at the Pprime Institute (CNRS, University of Poitiers, France), who was spending a term at Cambridge, and with Sam Phillips, a final-year engineering student. The study was in fact carried out as part of Phillips's master's thesis. The team set up a water-filled tank, an ultra-high-speed camera, a microphone in the air, and a hydrophone in the water, then recorded hundreds of impacts.

Take a typical case described in the paper: a drop 4 mm across (about 0.16 inch) falls from 8.6 cm (about 3.4 inches) and hits the water at roughly 1.3 m/s (about 4.3 feet per second). Filmed at 30,000 frames per second, it digs a crater with a radius of just over 2 mm. As the crater closes, it traps an air bubble at its base, which eventually settles at about 0.7 mm in diameter.

The surprise came from lining up the footage with the audio. According to the researchers, the initial impact, the formation of the crater, and the jet of water that shoots up are all practically silent. The sound starts at the exact moment the bubble breaks away from the bottom of the cavity. The microphone and the hydrophone then pick up the same dominant frequency, 8.66 kHz in this particular case. Toward the end of the study, an even faster camera (75,000 frames per second) made it possible, for the first time, to watch the bubble swell and shrink in step with the recorded sound.

The Singing Bubble

An air bubble in water behaves like a tiny spring. The air inside compresses and expands, while the surrounding water acts as the mass. When the bubble suddenly pinches off from the cavity, it gets a kick and starts to "ring," like a struck bell, for just a few oscillations.

Minnaert's formula links the pitch of that note to the size of the bubble: the smaller the bubble, the higher the sound. A bubble with a 1 mm radius lands around 3 kHz. The millimeter-scale bubbles from faucet drips climb to around 8 to 10 kHz. In three of the Cambridge tests, the measured frequency differed from the one predicted by the 1933 formula by less than 10%. The researchers called that agreement remarkable, given how hard it is to measure a distorted bubble from a video frame.

Since bubble size varies from one drop to the next, so does the note. That's what gives a drip its irregular, almost melodic quality.

The Water Surface as a Loudspeaker

Until then, the prevailing hypothesis held that the sound produced underwater simply passed through the surface into the air. The trouble is that the boundary between water and air is a very poor acoustic bridge. Calculations predicted a loss of about 70 dB, while the Cambridge team consistently measured around 40 dB. The airborne sound was far too loud for that explanation to hold.

The researchers then ran a second test. They lined the walls of the tank with MDF panels just under half an inch thick to cut down on underwater reverberation. The hydrophone signal changed noticeably, but the microphone signal didn't. If the airborne sound were just the underwater sound passing through the surface, both would have changed in the same way.

So the team proposed another mechanism. Right after it forms, the bubble sits very close to the bottom of the crater, which hasn't closed up yet. As it vibrates, it pushes and pulls directly on that patch of surface, which starts oscillating at the same frequency. This small disk of water then works like a piston, or like the cone of a loudspeaker, pushing on the air above it. The mathematical model built on this idea predicts a loss of about 44 dB, very close to the 40 dB measured. For the "plink" to be clearly audible, then, the bubble has to form as close as possible to the bottom of the cavity.

A Squirt of Dish Soap, and Then Silence

If the bubble is the source of the sound, preventing it from forming should bring silence. The researchers confirmed this in two ways. First, with a thin rod placed in the water that mechanically kept the bubble from breaking away: no sound. Then, by adding dish soap to the water: the bubble didn't form, and no sound was produced.

Dish soap is a surfactant, meaning it lowers the surface tension of water, the very force that makes the crater snap shut so violently. According to the authors, small changes in surface tension are enough to affect how the bubble forms. They draw a household tip from this. A few drops of dish soap in the bucket under a leak, or in the sink under a dripping faucet, could ease that maddening noise until the plumber shows up. The idea wasn't entirely new: back in 1989, Hugh Pumphrey had found that adding liquids that reduce surface tension made the characteristic peaks between 14 and 16 kHz vanish from the sound of artificial rain.

And oil? It has the same effect. In 2009, a team at the University of Hull, in the UK, was working on an acoustic rain gauge that measures raindrop size from the sound of drops landing in a tank of water. For that device, the bubbles' ringing was unwanted noise. The researchers found that an oil film on the surface prevented bubbles from forming. They still ruled it out, because it required too much upkeep in the field. Work from Johns Hopkins University, presented in 2014, observed the same phenomenon with layers of crude oil: films between 10 and 400 micrometers thick suppress bubble formation under raindrops. The authors attribute this most likely to the drop in surface tension, from about 72 to 28 mN/m. On a sea slicked with oil, rain simply doesn't sound the same.

Why Some Drops Stay Quiet

Some drops from the same faucet sing and others don't. Pumphrey had already shown why: for a given drop size, the bubble forms reliably only within a narrow range of impact speeds. Researchers call this "regular entrainment." Outside that range, the bubble forms poorly or not at all, and the drop stays quiet. According to the studies cited by the Cambridge team, regular entrainment hasn't been observed for drops smaller than 1 mm or larger than 5 mm in diameter.

Large raindrops falling at full speed follow a different sound mechanism, tied to the jet that shoots up after impact. It was studied using an 85-foot drop tower at the Naval Postgraduate School in Monterey, California. One of those studies even found a direct link between the sound energy of an impact and the temperature difference between the drop and the water. That detail echoes a phenomenon I've already explored: the sound difference between hot water and cold water.

From the Lab to the Studio

The Cambridge researchers acknowledge that their study grew out of pure curiosity. Still, they see two possible uses. The first is more accurate rainfall measurement. The second speaks directly to sound professionals: in 2018, the team considered that no one had yet produced a convincing synthesized water drop sound for video games or movies. Knowing that everything hinges on a bubble that rings for a few milliseconds, at a pitch set by its size, offers a starting recipe.

In the meantime, Foley artists keep recording real drops. For anyone who wants to try, the behavior described by the researchers suggests a few simple levers: the drop height, the drop size, and how clean the water is, since a trace of dish soap may be enough to silence everything. It's reminiscent of another bubble-related acoustic oddity, the hot chocolate effect, where bubbles in a mug change the pitch of a spoon tapping against it. And if you enjoy everyday sounds explained by physics, don't miss why shoes squeak.

Tonight, if a faucet keeps you awake, you'll know it isn't a collision but a one-millimeter bubble singing for a few thousandths of a second at the bottom of a tiny water crater. Have you ever noticed that some drops "plink" and others don't? Have you ever tried the dish soap trick in the bucket?