`{:(,"Column I",,"Column II"),((A),"For a stationary wave",(p),"Vibrations are perpendicular to direction to wave propagation"),((B),"For a longitudinal wave",(q),"Amplitude of vibrations changes with time"),((C),"For a transverse wave",(r),"Amplitude of vibration does not change with time"),((D),"For a progressive wave",(s),"Vibrations are along the direction of wave propagation"),(,,(t),"Nodes and antinoes are formed"):}`

Answer

To solve the problem of matching the items in Column I with those in Column II, we need to analyze each statement in Column I and determine which statements in Column II are applicable to them.

### Step-by-Step Solution:

1. **For a stationary wave (A)**:
- **Vibrations are perpendicular to direction of wave propagation (p)**: This is incorrect. In a stationary wave, the wave does not propagate, so there is no direction of propagation.
- **Amplitude of vibrations changes with time (q)**: This is incorrect. In a stationary wave, the amplitude is fixed at each point and does not change with time.
- **Amplitude of vibration does not change with time (r)**: This is correct. The amplitude remains constant at each point in a stationary wave.
- **Vibrations are along the direction of wave propagation (s)**: This is incorrect. Again, since the wave is stationary, there is no direction of propagation.
- **Nodes and antinodes are formed (t)**: This is correct. Stationary waves have fixed points (nodes) where there is no displacement and points of maximum displacement (antinodes).

**Matching for A**: R, T

2. **For a longitudinal wave (B)**:
- **Vibrations are perpendicular to direction of wave propagation (p)**: This is incorrect. In a longitudinal wave, the vibrations are parallel to the direction of wave propagation.
- **Amplitude of vibrations changes with time (q)**: This is correct. In a longitudinal wave, as the wave travels, the amplitude can change due to energy loss.
- **Amplitude of vibration does not change with time (r)**: This is incorrect. As mentioned, the amplitude can change over time.
- **Vibrations are along the direction of wave propagation (s)**: This is correct. In a longitudinal wave, the particles move back and forth in the same direction as the wave travels.
- **Nodes and antinodes are formed (t)**: This is incorrect. Longitudinal waves do not form nodes and antinodes in the same way as stationary waves.

**Matching for B**: Q, S

3. **For a transverse wave (C)**:
- **Vibrations are perpendicular to direction of wave propagation (p)**: This is correct. In a transverse wave, the vibrations are indeed perpendicular to the direction of wave propagation.
- **Amplitude of vibrations changes with time (q)**: This can be correct depending on the context, but generally, in a simple transverse wave, the amplitude remains constant unless specified otherwise.
- **Amplitude of vibration does not change with time (r)**: This is also generally correct for ideal transverse waves.
- **Vibrations are along the direction of wave propagation (s)**: This is incorrect. In a transverse wave, the vibrations are perpendicular, not along the direction of propagation.
- **Nodes and antinodes are formed (t)**: This is correct. Transverse waves can also form nodes and antinodes.

**Matching for C**: P, R, T

4. **For a progressive wave (D)**:
- **Vibrations are perpendicular to direction of wave propagation (p)**: This can be correct if the progressive wave is transverse.
- **Amplitude of vibrations changes with time (q)**: This is correct. In a progressive wave, the amplitude can change as the wave travels.
- **Amplitude of vibration does not change with time (r)**: This is incorrect. Progressive waves can have changing amplitudes.
- **Vibrations are along the direction of wave propagation (s)**: This is correct. In a longitudinal progressive wave, the vibrations are along the direction of propagation.
- **Nodes and antinodes are formed (t)**: This is incorrect. Progressive waves do not form nodes and antinodes like stationary waves.

**Matching for D**: Q, S, P (if considering transverse)

### Final Matches:
- A: R, T
- B: Q, S
- C: P, T
- D: Q, S (and P if considering transverse)