Final answer:
Sound waves travel faster through the boiling water than through the water vapor above it because liquids are denser than gases and the particles are closer together, allowing sound to transmit more efficiently. Additionally, the temperature and pressure of the medium influence sound speed, with higher temperatures and pressures resulting in faster sound propagation.
Step-by-step explanation:
The speed at which sound waves travel depends on the medium they are moving through. Sound waves move faster through liquids such as water than they do through gases like water vapor because the particles in a liquid are more closely packed together than in a gas. Therefore, a sound wave will move faster through a pot of boiling water than it will through the water vapor above the pot.
Additionally, the temperature of the medium affects the speed of sound; the hotter the medium, the faster the particles move, and consequently, the quicker the sound travels. Since boiling water is typically at a higher temperature than the surrounding air, even disregarding the change in phase from liquid to gas, the sound would likely travel faster through the boiling water than the cooler air above.
The pressure of the medium also influences the speed of sound, with higher pressure conditions allowing sound to travel faster. However, at the interface of boiling water and its vapor, the differences in pressure are negligible compared to the effects of density and temperature changes between liquid water and water vapor.