Can group velocity be greater than phase velocity?

Thread starter Halo CX
Start date Apr 6, 2015
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Group Group velocity Phase Phase velocity Velocity

In summary, group velocity and phase velocity are two different measures of the speed of a wave. Group velocity describes the overall movement of a wave, while phase velocity describes the speed of individual oscillations within the wave. It is possible for the group velocity to be greater than the phase velocity, which occurs when the wave packet is dispersed or compressed. The properties of the medium, such as its refractive index, can affect these velocities. Real-world examples include ocean waves and the dispersion of light in a prism.

Apr 6, 2015

Halo CX

Is it possible for a group velocity of any wave disturbance to be greater than its component phase velocities?

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Apr 6, 2015

nasu

Homework Helper

Yes, sure.

Go to the actual youtube page to see various cases.

Apr 6, 2015

Halo CX

Thank you for the you tube clip.

Related to Can group velocity be greater than phase velocity?

1. What is the difference between group velocity and phase velocity?

The group velocity refers to the speed at which the envelope of a wave packet travels, while the phase velocity refers to the speed at which the individual wave crests propagate. In other words, the group velocity describes the overall movement of a wave, while the phase velocity describes the speed of the individual oscillations within the wave.

2. Is it possible for the group velocity to be greater than the phase velocity?

Yes, it is possible for the group velocity to be greater than the phase velocity. This occurs when the wave packet is dispersed or spread out, causing the envelope of the wave to travel faster than the individual wave crests.

3. Can group velocity be negative?

Yes, group velocity can be negative. This occurs when the wave packet is compressed or shortened, causing the envelope of the wave to travel backwards in the opposite direction of the individual wave crests.

4. How does the medium affect the group and phase velocities?

The properties of the medium, such as its refractive index and density, can affect the group and phase velocities of a wave. In general, the group velocity is influenced by the dispersion of the medium, while the phase velocity is influenced by the medium's refractive index.

5. What are some real-world examples of group velocity being greater than phase velocity?

One example of this phenomenon is seen in ocean waves, where the group velocity can be greater than the phase velocity due to the varying depths of the ocean floor. Another example is in the dispersion of light in a prism, where the different frequencies of light travel at different speeds, causing the group velocity to be greater than the phase velocity.