- #1
unscientific
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Homework Statement
Homework Equations
The Attempt at a Solution
Is my initial assumption wrong?
unscientific said:Homework Statement
Homework Equations
The Attempt at a Solution
Is my initial assumption wrong?
rude man said:No, it's right.
unscientific said:But I seem to be missing out on a 1/vph term..
Group velocity refers to the speed at which the overall shape or envelope of a wave moves, while phase velocity refers to the speed at which the individual crests or troughs of a wave move. In simpler terms, group velocity is the speed of the wave as a whole, while phase velocity is the speed of the individual parts of the wave.
Group velocity and phase velocity are related by the dispersion relationship, which describes the relationship between the frequency and wavenumber of a wave. The group velocity is equal to the phase velocity multiplied by the group index, which is a measure of how much the phase velocity changes with respect to the frequency or wavenumber.
The ratio between group velocity and phase velocity can provide insight into the behavior of a wave. For example, when the group velocity is equal to the phase velocity, the wave is said to be non-dispersive, meaning that all parts of the wave travel at the same speed. When the group velocity is less than the phase velocity, the wave is said to be dispersive, meaning that different parts of the wave travel at different speeds.
The properties of the medium, such as its density, elasticity, and viscosity, can affect the group velocity and phase velocity of a wave. In general, the group velocity and phase velocity will be higher in a medium with lower density and higher elasticity. Viscosity, or the resistance to flow, can also affect the wave speed, particularly for waves traveling through fluids.
No, the group velocity and phase velocity can only be equal for non-dispersive waves. For dispersive waves, the group velocity and phase velocity will have different values, and the ratio between them will depend on the dispersion relationship of the specific wave. Examples of non-dispersive waves include sound waves in air and electromagnetic waves in a vacuum.