- #1
rlduncan
- 104
- 1
What are the equation(s) for circular waves such as pebble dropped in a pond.
rlduncan said:I am studing the equation y=sinkx/x^2 and find that the second order differential equation found for this equation is Bessel like, but not identical to Bessel functions. The first derivative term, for example, is off by a constant.
ZapperZ said:Are you sure it is not
[tex] y=\frac{sin^2(kx)}{(kx)^2}[/tex]
which is the Fraunhofer diffraction equation? If it is, then I don't see the connection with asking for circular water waves.
Zz.
rlduncan said:If you graph just sinx/x^2 where k=1 then you get a damped sine curve in which the wavelength is constant. I assume for ripples on a pond the wavelengths are constant and I was trying to make a connection if any.
When a pebble is dropped in a pond, it creates a disturbance on the surface of the water. This disturbance causes the water molecules to move in a circular pattern, creating circular waves that emanate from the point of impact. These waves can be described using mathematical equations known as circular wave equations.
The size and shape of the pond, the density and viscosity of the water, and the force with which the pebble is dropped can all affect the circular wave equations. Additionally, any obstacles or reflections in the pond can also alter the equations.
Circular wave equations are a fundamental part of fluid dynamics, which is the study of how fluids, such as water, behave and interact with their environment. These equations help us understand and predict the motion and behavior of fluids, which has many practical applications in fields such as engineering and meteorology.
Yes, circular wave equations can be used to model a variety of different types of waves, including sound waves, electromagnetic waves, and seismic waves. These equations can also be applied to other fluid systems, such as air or gas, to study their behavior and interactions.
Studying circular wave equations allows us to better understand the behavior of fluids and how they interact with their surroundings. This knowledge has many practical applications, from designing structures that can withstand waves to predicting the behavior of natural phenomena like ocean currents and weather patterns. Additionally, studying these equations can also lead to advancements in fields such as acoustics and optics.