What Do Wave Number and Phase Constant Mean in Wave Equations?

[lha08]

Homework Statement

Could anyone explain to me what exactly the wave number (k) represents and what it means in the equation 'cause it's kind of confusing me...Also, there's also the phase constant that i don't really understand as well: phase difference= k(deltax)-w(delta t)...One last confusion, is it possible for a transverse wave to travel in the negative x direction (positive w value) while the particle velocity is positive? Thanks

Homework Equations

The Attempt at a Solution

 

[diazona]

Wave number basically represents the number of times a wave oscillates in a given distance. It's the spatial equivalent of frequency (which itself is the number of times a wave oscillates in a given time).

As for the phase constant, in a sense it's a way of keeping track of a particular position on a wave. There's an image on Wikipedia that might be helpful to you.