Wave Velocity vs. Particle Velocity – Rankers Physics

Waves and its Characteristics: Practice Problem & Solution

Assertion (A): For a given medium in a wave, particle velocity varies w.r.t. time, while the wave velocity is independent of time. Reason (R): For propagation of mechanical wave, medium must have the properties of elasticity and inertia.  
(1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
(2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(3) (A) is true but (R) is false
(4) 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:

Particle velocity in a wave is oscillatory and time-dependent, while wave velocity in a homogeneous medium is constant. So, Assertion (A) is true. Mechanical waves require elasticity for restoring force and inertia for propagation. So, Reason (R) is true. However, (R) explains wave propagation conditions, not the difference in velocities.

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