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. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
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.
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.
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
View Answer
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.