The phenomenon you are referring to is known as time reversal symmetry in sound waves. When a sound wave undergoes time reversal, it means that the wave is played backward in time. The inverse of a sound wave, where the wave is reversed in time, does indeed sound similar to the original wave.
The reason for this similarity lies in the mathematical properties of sound waves. Sound waves are described by wave equations that are linear and time-invariant. Linearity means that the superposition principle holds, allowing multiple sound waves to combine without affecting each other's properties. Time invariance means that the properties of the sound wave remain constant over time.
When a sound wave is reversed in time, the physical processes that generate the wave, such as the vibration of air molecules, also reverse. However, the mathematical equations describing the wave itself do not change. As a result, the wave's shape, frequency content, and other characteristics remain the same when played backward in time.
This time reversal symmetry is not a universal property and may not apply to all physical phenomena. However, in the case of sound waves in a linear and time-invariant medium, it is a notable characteristic that allows the inverse of a sound wave to sound similar to the original.