Final answer:
The medium through which sound cannot transmit is d. a perfect vacuum because it lacks particles to carry sound waves. Sound can travel through other mediums like liquid air, liquid water, and gaseous oxygen.
Step-by-step explanation:
The medium through which sound cannot transmit is a perfect vacuum. Sound requires a medium with particles that can vibrate and transfer energy from one to another. In a perfect vacuum, there are no particles to transmit these vibrations, hence no sound can travel through it. This is why explosions do not occur in space with sound - because space is largely a vacuum.
In contrast, sound can travel through liquid air, liquid water, and gaseous oxygen because these mediums contain particles that can collide and transfer sound waves. The speed of sound through these mediums can vary based on their density and elasticity. For example, sound travels faster through liquid water than air because water is more dense, allowing particles to transmit the sound waves more efficiently.