Phase velocity and wave propagation velocity

[morrobay]

Homework Statement

wavelength = 3m
frequency =25 cycles/sec
period T = 1/frequency = .04 sec/cycle
wave propagation velocity =75 m/s
wave number K = 2pi/wavelength= 2.09 radians/m
angular frequency w = 2pi/T = 157 radians/s
phase velocity Vp = w/k = 157/2.09 = 75meters/second

----------------------------------------------------------------x = 200 meters, t= 2.66 s

In the above propagation velocity = phase velocity.

What would vary here for phase velocity to be greater than propagation velocity ?
]

 

[jbsteele]

Homework Equations Phase velocity = angular frequency/wave numberVp = w/KThe Attempt at a SolutionFor the phase velocity to be greater than the propagation velocity, the angular frequency would need to be greater than the wave number. In other words, w>K. This would mean that the period, T, would need to be less than 2pi/K.

 

[baba89]

I would like to clarify that phase velocity and wave propagation velocity are two different concepts. Phase velocity refers to the speed at which a particular phase of a wave (such as the peak or trough) travels, while wave propagation velocity refers to the overall speed at which the wave moves through a medium.

In this scenario, we can see that the phase velocity is equal to the wave propagation velocity, which means that the wave is traveling at a constant speed without any changes in its phase. However, it is possible for the phase velocity to be greater than the wave propagation velocity. This can occur if the wave is traveling through a medium with varying properties, such as a medium with different densities or refractive indices. In such cases, the phase velocity may change while the overall propagation velocity remains constant.

For example, imagine a wave traveling through a medium with regions of high and low density. In the region of high density, the wave may travel slower, causing the phase velocity to decrease. However, the overall propagation velocity may remain the same as the wave moves through the medium. Therefore, in this case, the phase velocity would be greater than the wave propagation velocity.

In conclusion, while the phase velocity and wave propagation velocity are equal in this scenario, it is possible for them to differ in cases where the wave is traveling through a medium with varying properties. It is important to understand the difference between these two concepts in order to accurately analyze and interpret wave behavior.