The Plink Comes After the Impact

Picture a drop falling into a pool of water. It strikes, digs a little crater, and throws a narrow column back into the air. If you had to point to the part making the familiar plink, the splash would be an obvious suspect.

The revealing thing is that the note comes later than the first contact. In a carefully recorded laboratory example, it begins when a tiny pocket of air breaks free beneath the surface. The drop supplies the disturbance. The bubble supplies the oscillator. And getting that oscillator's note into the air turns out to be another problem entirely.[1]

That is what caught me here: a dripping tap briefly assembles an instrument, then takes it apart.

Find the thing that rings

In 2018, Samuel Phillips, Anurag Agarwal and Peter Jordan studied drops falling into a water-filled tank, recording them with high-speed cameras, a microphone in the air and a hydrophone underwater. They corrected the recordings for sound's different travel times through air and water. Without that correction, the apparent timing would partly describe where the sensors were, not when something happened.[1, Supplementary Note]

Their example of a four-millimeter drop hitting at 1.29 meters per second unfolds in stages. A cavity opens, starts to recoil, and pinches off a small bubble at its bottom. The short, ringing wave packet begins at that pinch-off. The recorded dominant frequency is 8.66 kilohertz both above and below water. The dramatic upward jet follows, but does not contribute a corresponding new note in this example.[1, Figs. 3–5]

The distinction is not “impacts make no sound.” The initial contact can produce a brief pulse. It is that the characteristic pitched packet—the plink under investigation—belongs to a later event.

Timing is suggestive; interference is better. The researchers moved a thin rod into the process so that the bubble failed to become trapped. The characteristic sound disappeared. Adding washing-up liquid also prevented bubble entrainment and removed the plink. The drop still arrived. What failed was the formation of its little instrument.[1, “Preventing Entrainment”]

A spring made of air, a mass made of water

The underlying explanation reaches back to Marcel Minnaert's 1933 experiments. He made bubbles emerge from a submerged tube, caught individual bubbles to measure their volumes, and judged their brief sounds against a tuning fork. He was candid about the difficulty: the sounds were short and faint, and he initially had an uncertainty of an entire octave in their absolute pitch. He later used agreement with his model to resolve that ambiguity.[2, §§1, 9]

His proposal was not that sound raced around inside a tiny, rigid-walled air chamber. The bubble's boundary could move. Compress its gas and the pressure rises; let it expand and the pressure falls. Meanwhile, the surrounding water has to move with it. Gas elasticity provides the spring. Water inertia provides the mass.

Smaller bubbles should generally oscillate faster, but that prediction alone did not distinguish the rival explanations: a rigid resonator would also shift upward as it shrank. Minnaert's more revealing tests changed the surrounding liquid and the gas. Liquid density affected the pitch; replacing air with much lighter hydrogen did not produce the dramatic pitch change that a rigid gas-resonator account would suggest. Those results supported pulsation of the bubble and its surrounding water.[2, §§3, 6–7]

The ideal formula gives a useful sense of scale. With illustrative one-atmosphere air-and-water parameters, a spherical bubble of one-millimeter radius has a calculated frequency of about 3.28 kilohertz. Halve that radius and the frequency doubles, to about 6.57 kilohertz. These are calculations, not drops I recorded. The relevant size is the bubble's radius—not the falling drop's.[1, Eq. 2]

Real bubbles are less tidy. They begin distorted and close to a curved free surface, unlike the spherical bubble in effectively unbounded water assumed by the simple formula. In the 2018 paper, three tests differed by less than ten percent on the paper's percentage measure. In two smaller-bubble cases, however, the predicted frequencies exceeded the recorded frequencies by roughly 29 and 39 percent. The authors leave those discrepancies unresolved. The model explains a regime, not every possible drip.[1, Table 1]

The surface has a job, too

Knowing what rings does not yet explain what a listener in the air receives.

One possibility is straightforward: the bubble radiates underwater sound, and some passes through the water–air boundary. But the 2018 experiments gave the researchers reasons to doubt that this simple account explained their plink. The airborne pressure was considerably larger than the simple transmission estimate suggested.[1, “Sound Propagation Through The Water Surface”]

They also changed the tank. Lining its inner walls with eleven-millimeter MDF reduced the underwater reverberation. The hydrophone's ringing tail changed dramatically; the airborne recording changed little. If the airborne signal were simply the reverberant underwater field passed across the interface, the contrast would be difficult to explain.[1, Fig. 8]

Their alternative is more interesting than a wave finding a way through a barrier. Immediately after it forms, the bubble sits close beneath the bottom of the cavity. Its expansion and contraction push and pull on the nearby water surface. That small moving patch can drive the air like a miniature piston. The surface is not merely a window. It is part of the sound-making apparatus.[1, Fig. 9]

This is a supported proposed mechanism, not a complete measurement of every motion at the interface. Their approximate piston model predicts about 44 decibels of pressure attenuation between the particular underwater and airborne measurement locations, compared with roughly 40 measured. That agreement and the reverberation experiment support the account; neither makes it a universal law for sound crossing water.[1, Eqs. 9–10]

What the soap story leaves out

“Detergent silences dripping water” is the irresistible takeaway. It is also less interesting than what the experiment actually did. The washing-up liquid prevented the bubble from forming. It was not shown damping a bubble that already existed. Nor did the study establish a universal dose for a household sink.

The supplementary methods contain a better complication: sometimes the apparatus stopped producing the plink within hours, even without an intentional setup change. The authors suspected particles or surface contamination, but did not isolate which explanation was right. Even making the bubble reliably was a problem.[1, Supplementary Note]

This account is about a drop landing in pooled water under the studied conditions, not a drop striking a dry basin or every sound in a rainstorm. I have followed the papers, not performed a new drip experiment or listened to their recordings.

What changed for me is the separation between the event, the oscillator and the route into the air. A splash is what we see. A trapped bubble is what rings. In the researchers' proposed account, a nearby patch of surface helps its note reach the room.

The next question is hiding in the apparently identical drops that stayed quiet: what changed at the surface so that the instrument never got assembled?

Sources

[1] Phillips, S., Agarwal, A. & Jordan, P. (2018). “The Sound Produced by a Dripping Tap is Driven by Resonant Oscillations of an Entrapped Air Bubble.” Scientific Reports 8, 9515. Includes the linked supplementary experimental methods and Table 1. The article and supplement are one research team's work, not independent confirmations.

[2] Minnaert, M. (1933). “On musical air-bubbles and the sounds of running water.” Philosophical Magazine, series 7, 16, 235–248. University-hosted scan. Independent historical experiments on nozzle-generated bubbles, not a replication of the 2018 airborne-coupling experiment.