Why can a velocity of a wave be negative?

[andorrak]

Hi yall,

Im trying to understand waves and I am wondering why the velocities are negative sometimes and or positive.

I think that the velocities are negative because of the slope of the wave as it is coming down? I just want to completely understand it and am a little confused.

Like the equations i use are x(t)-Acos(wt+(phi)) or v(t)=-Awcos(wt+(phi))

 

[Pengwuino]

Strictly speaking, I wouldn't call those waves. They're just sines and cosines (by the way your velocity is not correct, it should not have the negative sign and should be sin(wt + phi) instead. The derivative you calculated is simply the slope.

When people talk about the velocity of a wave, they're typically talking about something propagating as cos(kx - wt) where k is the http://en.wikipedia.org/wiki/Wave_number" . The former being the velocity of the wave you're probably thinking about, the latter being something when you talk about frequencies that are not constant.

 

[azureth]

the positive and negative velocity means different directions

 

[andorrak]

yea that was a mistype.

But why can't the velocities always be positive? I seem to feel like the wave is always moving in one direction unless it's reflected back at me.

 

[azureth]

the two equations you offer are for simple harmonic motion,not waves.so if the velocity is negative,it means the direction of it is opposite from displacement(or x in your first equation)

 

[Pengwuino]

yea that was a mistype.

But why can't the velocities always be positive? I seem to feel like the wave is always moving in one direction unless it's reflected back at me.

You have to specify what you're talking about. Like azureth is saying, what you have could tell you about the velocity of a simple harmonic oscillator such as a spring. The positive/negative tells you about whether or not it's traveling to the left or right.

When you're talking about say, waves in the air or a vibration you make on a string that actually propagates, your propagation has to be something like cos(kx - wt). If you plotted this function for various times of 't', you'd find a wave that propagates in the positive-x direction.