Sound travels faster on a hot day than on a cold day.
Explanation
Sound is a longitudinal mechanical wave that propagates through the vibration of particles in a medium. The speed at which sound travels is governed by the properties of the medium, primarily its elasticity (stiffness) and density, as well as environmental factors such as temperature and humidity.- Sound travels faster on a hot day than on a cold day. is Correct: The speed of sound in a gas is directly proportional to the square root of its absolute temperature ($v \propto \sqrt{T}$). As the temperature increases, the kinetic energy of the gas molecules increases, allowing them to transmit the vibratory energy more rapidly. Therefore, sound travels faster on a hot day than on a cold day.
- Sound travels faster in air than in water. is Incorrect: Sound travels significantly faster in liquids than in gases. Although liquids are denser than gases (which would theoretically lower speed), they are much less compressible (higher modulus of elasticity). The factor of elasticity dominates, resulting in a higher speed of sound in water (~1480 m/s) compared to air (~343 m/s).
- Sound travels at the same speed in all gaseous media. is Incorrect: The speed of sound is not constant across all gases. It depends on the density and molecular mass of the gas ($v \propto \frac{1}{\sqrt{M}}$). For instance, sound travels faster in lighter gases like helium or hydrogen compared to heavier gases like nitrogen or oxygen at the same temperature.
- Sound speed is independent of the medium's temperature. is Incorrect: As explained in Sound travels faster on a hot day than on a cold day., the speed of sound is dependent on the temperature of the medium. It increases by approximately 0.61 m/s for every 1°C rise in temperature in air.
Key Takeaway: The speed of sound follows the general order: Solids > Liquids > Gases. In air, the speed of sound increases with a rise in temperature and humidity, but is independent of pressure changes (provided temperature remains constant).