# Oscillations and Waves in Fluids

• I
• Tazerfish
In summary, the Brunt-Vaisala frequency describes the frequency of oscillation in a fluid with a density gradient, but it is unclear how this can be applied to the oscillation of air behind mountains. The concept is based on the assumption of constant density, which does not make sense for air. However, understanding gravity-driven waves and basic mechanical and electric oscillations can help make sense of this concept. Derivations for mathematical descriptions of waves in water, air, and string/spring systems can provide a better understanding of wave motion.

#### Tazerfish

I first wanted to ask a very specific question:
There is something called the Brunt-Vaisala frequency.
It describes the frequency of oscillation in a fluid with a density gradient.
Because if a parcel of fluid is pushed up or down from its stable state it will oscillate around it.

What i don't get is why this can be applied to the oscillation of air behind mountains.

One of the fundimental axioms you derive this from is that your fluid parcel has a constant density.
And with air does not make any sense.
A bit of air would simply expand (violating constant density)
and slightly cool when going up and then pretty much stay where it is.
Vice versa when going down.
Wouldn't it ?

But this got me thinking ...
I actually don't really understand gravity driven waves.(Maybe waves in general )
(We didn't have them in school yet.)
(Although we did have basic mechanical and electric oscillations.)
Even the miraculously simple equations for wave speed in water don't really make sense to me.
If somebody had nice derivations for mathematical desciptions of these things i would really appretiate it:
Water/Air Interface (basically ocean) waves
Atmospheric waves (stratified)
Waves on a String or spring ...

Posting some links with reasonably "easy" derivations would really help me out.
I think this and many other questions about waves would solve themselves if i knew a little more about them in general.
Sorry i know this question is a little dumb and the only person who finds it interesting or would be helped is probably me, but i am going to ask it anyways and hope for some replies.

Waves in air are pressure changes - which means density changes ... since a rarifaction is, by definition, a change in particle density in a volume.
However - the math is about oscillations around the mean ... when the sources are talking about a pressure gradient they usually mean the mean pressure is changing smoothly, and there are oscillations about that. This should makes sense because you can already think of the speed of sound in still air... even though the presence of the sound means the air is not still.

There are no "nice" derivations in the sense of "simple" ... the waves in nature are described by the maths of waves. We can derive wave motion for different situations by applying Newton's Laws to models of the situation. You get how you can have wave motion for a mass on a spring right? Have you seen coupled mass-on-spring or pendulums?

For bulk materials you may want to start here:
http://www.acs.psu.edu/drussell/Demos/waves/wavemotion.html
... and realize that the difference between states of matter is how strongly the particles are coupled to each other ...

For the maths, brace yourself and look up "damped driven harmonic oscillator" and "wave equation" and "helmholtz equation".
It is a common exercise for senior college students to derive the helmholtz equation for simple systems like an infinite line of small masses separated by massless springs.

Tazerfish

## 1. What are oscillations and waves in fluids?

Oscillations and waves in fluids refer to the movement of fluids, such as water or air, in a back and forth or up and down motion. This can be caused by external forces, such as wind or pressure changes, or by internal forces, such as gravity or buoyancy.

## 2. What is the difference between oscillations and waves in fluids?

Oscillations refer to the back and forth or up and down motion of a fluid, while waves refer to the propagation of this motion through the fluid. In other words, oscillations are the individual movements of particles, while waves are the overall pattern of movement.

## 3. How are oscillations and waves in fluids important in everyday life?

Oscillations and waves in fluids play a crucial role in various natural phenomena, such as ocean waves, tides, and weather patterns. They are also used in engineering and technology, such as in the design of ships and aircrafts, and in medical applications, such as ultrasound imaging.

## 4. What factors affect the behavior of oscillations and waves in fluids?

The behavior of oscillations and waves in fluids can be influenced by various factors, including the properties of the fluid (such as density and viscosity), external forces (such as wind or gravity), and the shape and size of the container or body of fluid.

## 5. How can we study oscillations and waves in fluids?

There are various methods for studying oscillations and waves in fluids, such as mathematical models and simulations, experiments in a laboratory setting, and observations in natural environments. This allows us to better understand and predict the behavior of fluids and their impact on our daily lives.