Wave Velocity in Dispersive Medium – Rankers Physics

Waves and its Characteristics: Practice Problem & Solution

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

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Waves and its Characteristics. Understanding the underlying formula is key to arriving at the correct answer below:

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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