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The dispersion law for a certain type of wave motion is ω = (c2k2 + m2)1/2  where ω is the angular frequency, k is the magnitude of the propagation vector and cm are constants. The group velocity of these waves approaches :
  • a)
    vg → c as k → ∞
  • b)
    vg → 0 as k → ∞
  • c)
    vg → 0 as k → 0
  • d)
    vg → c as k → 0
Correct answer is option 'A,C'. Can you explain this answer?
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The dispersion law for a certain type of wave motion is ω= (c2k2...

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The dispersion law for a certain type of wave motion is ω= (c2k2...
The relationship between the wave's frequency (f) and its wavenumber (k). It describes how the wave speed changes with the wave's frequency or wavelength.

In general, the dispersion law can be expressed as:

ω = ω(k)

where ω is the angular frequency of the wave and k is the wavenumber.

For different types of wave motion, the dispersion law may take different forms. Some common examples include:

1. Linear dispersion: In this case, the dispersion law is given by ω = ck, where c is the phase speed of the wave. This means that the wave's frequency is directly proportional to its wavenumber.

2. Nonlinear dispersion: In some cases, the dispersion law may not be linear. The relationship between ω and k can be a more complex function, involving higher powers of k or non-linear terms. This is particularly common in waves that exhibit wave-breaking or wave-steepening behavior, such as ocean waves.

3. Anomalous dispersion: In certain materials or systems, the dispersion law may have unusual behavior. This is known as anomalous dispersion. For example, in some cases, the wave speed may decrease as the frequency increases, leading to a negative dispersion or dispersion inversion.

The specific form of the dispersion law depends on the properties of the medium or system in which the wave is propagating. Different materials or systems can exhibit different dispersion characteristics, resulting in waves with different relationships between frequency and wavenumber.
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The dispersion law for a certain type of wave motion is ω= (c2k2 + m2)1/2 whereωis the angular frequency,kis the magnitude of the propagation vector andc,mare constants. The group velocity of these waves approaches :a)vg→ c as k→ ∞b)vg→ 0 as k→ ∞c)vg→ 0 as k→ 0d)vg→ c as k→ 0Correct answer is option 'A,C'. Can you explain this answer?
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