Why can a velocity of a wave be negative?

• andorrak
In summary, the conversation discusses the concept of wave velocities and why they can be positive or negative. The participants also clarify that the equations provided are for simple harmonic motion and not waves. They explain that for waves to propagate, the equation should be in the form of cos(kx-wt) and the positive/negative velocity indicates the direction of the wave. The conversation concludes with a reminder to specify what type of wave is being discussed.
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))

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.

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the positive and negative velocity means different directions

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.

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)

andorrak said:
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.

1. Why can a velocity of a wave be negative?

The velocity of a wave can be negative because it is a vector quantity, meaning it has both magnitude and direction. In some cases, the direction of the wave may be opposite to the direction of propagation, resulting in a negative velocity.

2. What is the significance of a negative velocity in a wave?

A negative velocity in a wave indicates that the wave is moving in the opposite direction of its propagation. This can occur in situations where the wave is being reflected or refracted.

3. Can a negative velocity in a wave affect its frequency?

No, a negative velocity in a wave does not affect its frequency. The frequency of a wave is determined by its source and the medium it travels through, and is independent of its velocity.

4. Are there any real-life examples of waves with negative velocities?

Yes, there are several real-life examples of waves with negative velocities. One example is the reflection of sound waves off a moving object, such as a car. Another example is the refraction of light waves as they pass through different mediums.

5. How does the speed of a wave with a negative velocity compare to that of a wave with a positive velocity?

The speed of a wave with a negative velocity is still determined by its frequency and wavelength, just like a wave with a positive velocity. The only difference is the direction of propagation, with the negative velocity wave moving in the opposite direction at the same speed as the positive velocity wave.

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