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: 153
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 'Question about pressure of a liquid'
I am looking at pressure in liquids and I am testing my idea. The vertical tube is 100m, the contraption is filled with water. The vertical tube is very thin(maybe 1mm^2 cross section). The area of the base is ~100m^2. Will he top half be launched in the air if suddenly it cracked?- assuming its light enough. I want to test my idea that if I had a thin long ruber tube that I lifted up, then the pressure at "red lines" will be high and that the $force = pressure * area$ would be massive...
I feel it should be solvable we just need to find a perfect pattern, and there will be a general pattern since the forces acting are based on a single function, so..... you can't actually say it is unsolvable right? Cause imaging 3 bodies actually existed somwhere in this universe then nature isn't gonna wait till we predict it! And yea I have checked in many places that tiny changes cause large changes so it becomes chaos........ but still I just can't accept that it is impossible to solve...
Hello! I am generating electrons from a 3D gaussian source. The electrons all have the same energy, but the direction is isotropic. The electron source is in between 2 plates that act as a capacitor, and one of them acts as a time of flight (tof) detector. I know the voltage on the plates very well, and I want to extract the center of the gaussian distribution (in one direction only), by measuring the tof of many electrons. So the uncertainty on the position is given by the tof uncertainty...
Back
Top