Phase velocity facts for kids

Ocean waves moving across the water. The red dot shows the phase velocity, and the green dots show the group velocity.

The phase velocity of a wave is how fast a specific part of the wave, like its highest point (the crest), seems to travel. Imagine a ripple in a pond; the speed at which the peak of that ripple moves is its phase velocity.

This speed depends on two main things:

• The wavelength (λ), which is the distance between two matching points on a wave, like from one crest to the next.
• The wave period (T), which is the time it takes for one complete wave to pass a certain point.

You can find the phase velocity using a simple formula:

This means the phase velocity (v_p) is the wavelength (λ) divided by the wave period (T).

Understanding Phase Velocity

When you look at a wave, like an ocean wave or a sound wave, you see its shape moving. The phase velocity tells you how fast that shape is moving. For example, if you watch a specific crest of a wave, its speed is the phase velocity.

Sometimes, different parts of a wave can travel at different speeds. This is especially true for waves that are made up of many different frequencies. However, the phase velocity focuses only on how fast a single, specific part of the wave's pattern moves.

Phase Velocity vs. Group Velocity

It's important to know that phase velocity is not always the same as group velocity.

• Phase velocity is the speed of a single point on the wave, like a crest or a trough.
• Group velocity is the speed at which the overall shape or "envelope" of a group of waves travels. This is often the speed at which energy or information is carried by the wave.

Imagine a group of ocean waves. The individual waves (crests and troughs) might move faster or slower than the whole group of waves. If the individual waves move faster than the group, they appear to form at the back of the group and disappear at the front. If they move slower, they appear to form at the front and disappear at the back.

Examples of Phase Velocity

• Light waves: In a vacuum, light waves always travel at the speed of light, which is their phase velocity. However, when light travels through materials like glass or water, its phase velocity can change.
• Sound waves: The phase velocity of sound waves depends on the material they are traveling through. Sound travels faster in water than in air, for example.
• Ocean waves: For deep water waves, the phase velocity can be different from the group velocity. This is why you might see individual wave crests moving faster than the overall wave pattern.

Images for kids

• 

  This shows a wave packet where the phase velocity is faster than the group velocity.

• 

  Here, the wave's group velocity and phase velocity are moving in opposite directions.

• 

  This image shows how many small waves (blue) combine to form a larger wave packet (red). The blue dots show the phase velocity of the small waves, and the red line shows the group velocity of the whole packet.

See also

In Spanish: Velocidad de fase para niños