The correct answer is option 1: Reverberation.

Reverberation is a phenomenon that occurs when sound waves created in a big hall linger and persist due to repeated reflections. When sound waves are produced in a big hall, they bounce off the walls, ceiling, and other surfaces multiple times before they completely dissipate. This repeated reflection of sound waves causes them to overlap and create a continuous sound that lingers in the hall for some time after the initial sound has stopped.

Option 2: Dispersion refers to the spreading out or scattering of a sound wave as it travels through a medium, which is not relevant to the persistence of sound in a big hall.

Option 3: Refraction refers to the change in direction of a sound wave as it passes from one medium to another, which is also not relevant to the persistence of sound in a big hall.

Option 4: Diffraction refers to the bending of sound waves around obstacles or through openings, which is also not applicable to the phenomenon of sound persistence in a big hall.

So, the correct answer, in this case, is option 1: Reverberation.