The Sound Produced by a Dripping Tap is Driven by Resonant Oscillations of an Entrapped Air Bubble

Samuel Phillips,Peter Jordan,Anurag Agarwal

doi:10.1038/s41598-018-27913-0

Abstract

This paper details an investigation into the characteristic ‘plink’ sound produced by water droplets impacting a liquid surface, such as those falling from a dripping tap. Modern high-speed video and audio capture techniques have been applied to this problem for the first time. Previous literature investigating the underwater sound produced has been validated, with the key sound producing feature both above and below the water confirmed to be the entrainment of a small underwater air bubble. Recorded sound frequencies have been shown to align with the theoretical natural oscillation frequency of the entrained bubble, confirming this to be the driver of the characteristic ‘plink’ sound. For the first time these oscillations of the entrained bubble have been directly observed on video footage. An investigation into the effect of underwater reverberation showed that the airborne sound field is not simply the underwater field propagating through the water-air interface, as had previously been assumed. An alternative hypothesis is that the oscillating bubble induces oscillations of the water surface itself, giving a more efficient mechanism by which the underwater bubble drives the airborne sound field. A model for this new hypothesis produces good agreement with experimental data.

Highlights

Further studies into the fluid mechanics of splashes persisted, including work by Macklin and Metaxas[10] among others, but little interest was shown in the sound-production mechanism until the late 1980s when it was suggested that the distinctive underwater sound signature of a drop impact could allow a simple hydrophone to be used to measure oceanic rainfall
This study provides the first detailed investigation into the airborne sound produced by drop impacts, applying modern high-speed video and sound measurement techniques to the problem for the first time
A high-speed video of this drop impact was taken at 30,000 fps with the camera positioned horizontally. Key frames from this video are shown sequentially in Fig. 3, from which it is clear that the key features highlighted by Franz[9] are accurate; the impact creates a cavity, which begins to recoil; a small air bubble is trapped under the water in a process referred to as bubble entrainment

Summary

Introduction

Further studies into the fluid mechanics of splashes persisted, including work by Macklin and Metaxas[10] among others, but little interest was shown in the sound-production mechanism until the late 1980s when it was suggested that the distinctive underwater sound signature of a drop impact could allow a simple hydrophone to be used to measure oceanic rainfall This required a relationship between the size of a raindrop and the frequency of the sound it produced to be found, and led to extensive research into the underwater sound generated by individual drop impacts. These experimental findings were supplemented by the analytical work of Oquz and Prosperetti[14], Guo and Ffowcs-Williams[15] and Longuet-Higgins[16] Whilst these initial studies were limited to low impact velocities and small drops, Snyder[17] and Jacobus[18] took advantage of the 26 m tall drop facility at the Naval Postgraduate School in Monterey, CA, to test drops of various sizes falling at their terminal velocities. This allows accurate causal links between the fluid dynamics of of the drop impact and the radiated sound field to be provided

Methods

Results

Conclusion