Phase velocity greater than propagation velocity

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Phase velocity and propagation velocity are equal in the given scenario with a wavelength of 4 meters, frequency of 30 cycles/sec, and a wave propagation velocity of 120 m/s. To achieve a phase velocity greater than propagation velocity, adjustments to the wave number or angular frequency are necessary. This phenomenon is not exclusive to electromagnetic waves; it can occur in other wave types under specific conditions. The discussion seeks numerical examples illustrating how varying these parameters can lead to a phase velocity exceeding propagation velocity. Understanding these relationships is crucial for analyzing wave behavior in different contexts.
morrobay
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With:
wavelength = 4 meters
frequency = 30 cycles/sec
period, T, = .033 sec/cycle
wave propagation velocity = 120 m/s
wave number ,k, = 2pi/wavelength = 1.57 radians/meter
angular frequency, w, = 2pi/T = 188.5 radians/sec
phase velocity = w/k = 120m/s
In the above propagation velocity equals phase velocity
Question: what values here would vary so that phase velocity is greater than propagation velocity ?
 
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atyy said:

I have a copy of the above but that is in reference to EM waves.
Is it only in the case of electromagnetic waves where phase velocity can be greater than propagation velocity ?

If not then I would like to see a numerical answer to my original question
 
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