Velocity proportional to wavelength?

Click For Summary
SUMMARY

The discussion centers on the relationship between velocity and wavelength, specifically through two key equations: velocity = frequency x wavelength and de Broglie wavelength = Planck's constant / (mass x velocity). It is established that as particles are accelerated to high velocities, their wavelengths decrease, indicating an inverse relationship between velocity and wavelength. The velocities referenced are distinct; the first pertains to wave velocity (phase velocity), while the second relates to particle velocity in de Broglie's theory (group velocity).

PREREQUISITES
  • Understanding of wave mechanics and the wave equation.
  • Familiarity with de Broglie's hypothesis and quantum mechanics.
  • Knowledge of Planck's constant and its significance in physics.
  • Basic grasp of frequency and its relationship to wavelength.
NEXT STEPS
  • Study the concept of phase velocity versus group velocity in wave mechanics.
  • Explore the implications of de Broglie's wavelength in quantum physics.
  • Research the applications of Planck's constant in modern physics.
  • Examine the relationship between frequency, wavelength, and energy in electromagnetic waves.
USEFUL FOR

Students of physics, particularly those studying wave mechanics and quantum theory, as well as educators and researchers interested in the principles of particle behavior and wave-particle duality.

v_pino
Messages
156
Reaction score
0
There are two equations I know of that link velocity and wavelength:

1 velocity = frequency x wavelength

2 de broglie wavelength= Planck's constant/ (mass x velocity)

I read that 'When particles are accelerated to high velocities, they have low wavelengths'.
This means that velocity has to be inversely proportional to wavelength, and this would come from the second equation. But why?

Thanks :)
 
Physics news on Phys.org
The velocity in v=f*lambda is the wave velocity of a wave.
The velocity in 2 is the velocity of particle in de Broglie's conjecture for the wavelength of the wave function associated with the particle's motion.
 
In other words: they are not the same velocity, but two different ones; the first is also called "phase" velocity, the second "group" velocity.
 

Similar threads

  • · Replies 10 ·
Replies
10
Views
7K
  • · Replies 8 ·
Replies
8
Views
3K
  • · Replies 17 ·
Replies
17
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 25 ·
Replies
25
Views
4K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 14 ·
Replies
14
Views
2K