B Sinusoidal wave function of t and x

AI Thread Summary
It is possible to characterize a sinusoidal wave in both time and spatial domains, starting with parameters like amplitude, angular velocity, and frequency. The angular velocity can be expressed in terms of frequency, which relates to wave velocity and wavelength. The wave number is defined as 2 pi divided by the wavelength, and the movement along the x-direction is represented by vt. The discussion clarifies that the focus is not on disturbances from equilibrium but rather on the evolution of the sine wave across these domains. The derivation presented is coherent and aligns with the principles of wave mechanics.
Ennio
Messages
26
Reaction score
2
TL;DR Summary
Starting from the domain of t, is it possible to express the sinef function under the domain of movement?
Greetings,

is it possible to characterize a sinusoidal wave in the domain of time and then pass into the domain of movement along x direction?
I start with: a is the amplitude of the sine function and ω is the angular velocity. t is the time. I can express the angular velocity in funct. of the frequency n. In turn, n is velocity of the wave valong x divided its wavelength. Now, 2 pi over lambda is the wave number k and vt is the movement along x.
Does my derivation make sense to you?

1661530866936.png

E.
 

Attachments

  • 1661530736287.png
    1661530736287.png
    9.2 KB · Views: 155
Physics news on Phys.org
Are you trying to describe the disturbance ##y## from equilibrium
  • for a single particle located at ##x=X_P## in a medium as time evolves? ##y(X_P,t)##
  • for the shape of a string (made up of a string of particles) at a certain time ##T_0## ? ##y(x,t=T_0)##
  • for the shape of a string (made up of a string of particles) as time evolves? ##y(x,t)##
 
robphy said:
Are you trying to describe the disturbance ##y## from equilibrium
  • for a single particle located at ##x=X_P## in a medium as time evolves? ##y(X_P,t)##
  • for the shape of a string (made up of a string of particles) at a certain time ##T_0## ? ##y(x,t=T_0)##
  • for the shape of a string (made up of a string of particles) as time evolves? ##y(x,t)##
not exactly a disturbance from equilibrium but rather the description of the sine wave evolution i nthe two domains.
 
Thread 'Gauss' law seems to imply instantaneous electric field'
Imagine a charged sphere at the origin connected through an open switch to a vertical grounded wire. We wish to find an expression for the horizontal component of the electric field at a distance ##\mathbf{r}## from the sphere as it discharges. By using the Lorenz gauge condition: $$\nabla \cdot \mathbf{A} + \frac{1}{c^2}\frac{\partial \phi}{\partial t}=0\tag{1}$$ we find the following retarded solutions to the Maxwell equations If we assume that...
Hello! Let's say I have a cavity resonant at 10 GHz with a Q factor of 1000. Given the Lorentzian shape of the cavity, I can also drive the cavity at, say 100 MHz. Of course the response will be very very weak, but non-zero given that the Loretzian shape never really reaches zero. I am trying to understand how are the magnetic and electric field distributions of the field at 100 MHz relative to the ones at 10 GHz? In particular, if inside the cavity I have some structure, such as 2 plates...
Back
Top