# Explanation of Rayleighs work on vibrations of liquid droplets

• M_1
In summary, the conversation discusses calculating the vibrational energy of a water droplet using Rayleigh's work from 1879, but with some simplifications and difficulties in understanding the calculations. The speaker also mentions looking for a more accessible presentation of Rayleigh's work in a thesis or master thesis. A link is provided for a thesis on the subject that may be helpful.

#### M_1

Hi,

I'm trying to calculate the vibrational energy of a water droplet for a given vibrational amplitude.
Rayleigh wrote about this in Proc. R. Soc. Lond., volume 29, 1879, "On the Capillary Phenomena of Jets", Appendix II, but he makes some simplifications (as I understand it) and I also have problems following parts of his calculus.

Is anyone aware of a thesis or master thesis or similar on this subject where the work of Rayleigh is presented in a more accesible way?

Thanks!

I don't know what level of detail you want to go into, but does the derivation involve the spherical wave equation? If you calculated the amplitude from that and then introduced the water tension to get the work wouldn't we get a relatively accurate measure of the vibrational energy?

1 person

## 1. What is the significance of Rayleigh's work on vibrations of liquid droplets?

Rayleigh's work on vibrations of liquid droplets is significant because it laid the foundation for understanding the behavior of fluids and their interactions with sound waves. This work led to the development of the Rayleigh-Plesset equation, which is used to model the oscillations of bubbles in a liquid, and has applications in various fields such as acoustics, meteorology, and oceanography.

## 2. What is the Rayleigh-Plesset equation and how is it used?

The Rayleigh-Plesset equation is a mathematical model that describes the dynamics of a gas bubble in a liquid. It takes into account factors such as surface tension, pressure, and viscosity to predict the behavior of the bubble under the influence of an external force, such as sound waves. This equation is used in various fields, including medical ultrasound imaging, underwater acoustics, and sonar technology.

## 3. How did Rayleigh's work contribute to our understanding of sound waves?

Rayleigh's work on vibrations of liquid droplets helped us understand the behavior of sound waves in fluids. He showed that when a droplet vibrates, it creates a sound wave that travels through the surrounding fluid. This discovery led to the understanding of how sound waves interact with different types of fluids, such as air and water, and how they can be used in various applications.

## 4. What are some practical applications of Rayleigh's work on vibrations of liquid droplets?

Rayleigh's work has practical applications in various fields, such as medical imaging, sonar technology, and weather forecasting. The understanding of sound waves in fluids has led to the development of medical ultrasound imaging, where sound waves are used to create images of internal body structures. Sonar technology, which uses sound waves to detect and locate objects underwater, also relies on the principles of Rayleigh's work. In addition, his work has contributed to our understanding of how sound waves affect weather patterns and ocean currents.

## 5. How did Rayleigh's work on vibrations of liquid droplets impact the field of acoustics?

Rayleigh's work had a significant impact on the field of acoustics. His study of the vibrations of liquid droplets led to the understanding of how sound waves travel through different mediums and how they can be manipulated. This work also paved the way for advancements in acoustics, such as the development of more accurate models for sound wave propagation and the design of more efficient acoustic devices.