When a tightly stretched band is plucked, it vibrates and produces sound. Let's understand this phenomenon in detail.

1. Vibrations:
- When the band is plucked, it is displaced from its equilibrium position and then released.
- Due to the tension in the band, it tries to return to its original position.
- However, due to inertia, it overshoots the equilibrium position and moves in the opposite direction.
- This back-and-forth motion continues, creating vibrations in the band.

2. Sound Production:
- As the band vibrates, it pushes and pulls the surrounding air molecules.
- This creates a series of compressions and rarefactions in the air, forming sound waves.
- The sound waves travel through the air as longitudinal waves, reaching our ears.
- When these waves enter our ears, they cause vibrations in the eardrums.
- The vibrations are then transmitted to the brain, which interprets them as sound.

3. Pitch and Loudness:
- The pitch of the sound produced by the vibrating band depends on its frequency of vibrations.
- A higher frequency of vibrations produces a higher pitch, while a lower frequency produces a lower pitch.
- The loudness of the sound depends on the amplitude of the vibrations.
- Greater amplitude produces a louder sound, while smaller amplitude produces a softer sound.

4. Factors affecting sound production:
- The tension in the band: Higher tension results in higher frequency vibrations and produces a higher-pitched sound.
- Length and thickness of the band: Longer and thicker bands produce lower-pitched sounds.
- Material of the band: Different materials produce different sounds due to variations in their properties.

In conclusion, when a tightly stretched band is plucked, it vibrates due to the tension in the band. These vibrations create compressions and rarefactions in the surrounding air, producing sound waves. The pitch and loudness of the sound depend on the frequency and amplitude of the vibrations, respectively. Several factors, such as tension, length, thickness, and material of the band, affect the sound produced. Therefore, the correct answer is option 'D' – the vibrating band both vibrates and produces sound.

D