Velocity proportional to wavelength?

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Velocity and wavelength are linked through two key equations: velocity equals frequency multiplied by wavelength, and de Broglie's equation relates wavelength to a particle's mass and velocity. As particles accelerate to high velocities, their wavelengths decrease, suggesting an inverse relationship between velocity and wavelength. However, the velocities in these equations refer to different concepts; the first is wave velocity (phase velocity), while the second pertains to particle velocity (group velocity). Understanding this distinction clarifies the relationship between velocity and wavelength in different contexts. The discussion highlights the complexity of these interactions in physics.
v_pino
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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 :)
 
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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.
 
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