Wave Velocity in Dispersive Medium – Rankers Physics
Topic: Waves
Subtopic: Waves and its Characteristics

Wave Velocity in Dispersive Medium

Assertion (A): Wave velocity is equal to group velocity in a non-dispersive medium.
Reason (R): A non-dispersive medium is one in which the wave velocity is frequency dependent.
 
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution:

In a non-dispersive medium, the phase velocity (wave velocity) \(v_p\) is constant, meaning it does not depend on frequency. In this case, group velocity \(v_g\) equals \(v_p\). So (A) is true. Reason (R) is false because a non-dispersive medium has wave velocity independent of frequency.

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