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Group Velocity of Waves refers to the velocity at which the overall shape or envelope of a wave group propagates through a medium. It represents the speed at which wave energy is transmitted.
The calculator uses the formula:
Where:
Explanation: This formula calculates the group velocity by dividing the wave power per unit crest width by the total energy per unit area.
Details: Calculating group velocity is essential in wave mechanics and oceanography for understanding how wave energy propagates through different media and for predicting wave behavior in various conditions.
Tips: Enter wave power per unit crest width in watts (W) and total energy per unit area in joules (J). Both values must be positive numbers.
Q1: What is the difference between phase velocity and group velocity?
A: Phase velocity is the speed at which individual wave crests move, while group velocity is the speed at which the overall wave envelope or energy propagates.
Q2: In which applications is group velocity important?
A: Group velocity is crucial in optics, acoustics, seismology, and oceanography for understanding energy transport in wave phenomena.
Q3: Can group velocity exceed the speed of light?
A: In certain dispersive media, group velocity can exceed the phase velocity, but it cannot exceed the speed of light in vacuum according to special relativity.
Q4: How does dispersion affect group velocity?
A: In dispersive media, different frequency components travel at different speeds, causing the group velocity to differ from the phase velocity.
Q5: What are typical values for group velocity in water waves?
A: For deep water waves, group velocity is typically half the phase velocity, while for shallow water waves, group velocity approaches the phase velocity.