# Determining direction of wave propagation from the phase?

• AxiomOfChoice
In summary, the phase of a wave is determined by the equation \phi = \vec k \cdot \vec r - \omega t. The direction of wave propagation can be determined by taking the derivative of the phase with respect to time, which gives the velocity of the wave. The direction of propagation is in the direction of the wave vector \vec k.
AxiomOfChoice
Suppose you know the phase of a wave is given by

$$\phi_1 = \vec k \cdot \vec r - \omega t.$$

How can you determine in which direction this wave is propagating? I guess, more specifically, how does a wave described by this phase differ from a wave described by the phase

$$\phi_2 = \vec k \cdot \vec r + \omega t$$

I may not have provided enough detail...please tell me if I haven't! Thanks.

(I was always under the impression that it was the wave vector $$\vec k$$ that carried the information about which way the wave was propagating, but recent discussions in my E&M class have caused me to question this belief.)

You first need to define your time progression. If your standard is good ole e^{-i\omega t}, then the phase dependence is given by:

$$\mathbf{k}\cdot\mathbf{r}-\omega t$$

The wave propogates in the \hat{k} direction. If you have

$$\mathbf{k}\cdot\mathbf{r}-\omega t$$

as your phase progression then you must have changed your time convention to e^{i\omega t} or you are missing a minus sign here where the actual dependence is e^{-\phi_2} in which case we are progressing in the -\hat{k} direction, but this information is not given in what you have.

Take r vector to be in the direction of k vector.
Now, take kx-wt=A (some constant phase) and differentiate it with respect to t . you get dx/dt=w/k which is the velocity of the point whose A(phase) is constant, and hence velocity of wave . It is called phase velocity. Direction of the propagation is the direction of k vector.

http://www.actionurl.com/jpxp

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## 1. How do you determine the direction of wave propagation from the phase?

The direction of wave propagation can be determined from the phase by analyzing the slope of the wave on a graph. If the slope is positive, then the wave is propagating in the positive direction. If the slope is negative, then the wave is propagating in the negative direction.

## 2. Can the direction of wave propagation be determined from the phase of a single point?

No, the direction of wave propagation cannot be determined from the phase of a single point. The phase only provides information about the position of a point on the wave and not the direction of propagation.

## 3. How does the wavelength affect the determination of wave propagation direction from the phase?

The wavelength does not affect the determination of wave propagation direction from the phase. The phase of a wave is independent of its wavelength and only depends on the position of a point on the wave.

## 4. Is it possible to determine the direction of wave propagation from the phase of a standing wave?

No, it is not possible to determine the direction of wave propagation from the phase of a standing wave. In a standing wave, the phase at each point is constant and does not change with time, therefore it does not provide information about the direction of propagation.

## 5. How accurate is determining the direction of wave propagation from the phase?

Determining the direction of wave propagation from the phase is a reliable method as long as the wave is a simple sinusoidal wave. In more complex waveforms, such as those with multiple frequencies or harmonics, the phase may not accurately represent the direction of propagation.

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