Which statement with respect to the speed of sound is correct?

• A. It varies with the square of the absolute temperature.
• B. It varies with air density.
• C. It varies with the square root of the absolute temperature.
• D. It is independent of temperature.

Answer: (C)

In gases, the speed of sound is governed by how stiff the medium is to compression compared with how much inertia the molecules have. For an ideal gas like air, the speed is a = sqrt(gamma * R * T), where gamma is the specific-heat ratio, R is the specific gas constant for air, and T is the absolute temperature. This shows the speed increases with the square root of temperature.

The reason density isn’t the controlling factor is that if you start from a = sqrt(gamma * p / rho) and substitute p = rho * R * T (the ideal gas law), the rho cancels out and you’re left with a = sqrt(gamma * R * T). So the key variable is temperature, not density, for a given gas composition.

For context, dry air at sea level gives roughly 331 m/s at 0°C and about 343 m/s at 20°C, illustrating how the speed rises with temperature.

Therefore the statement that the speed of sound varies with the square root of the absolute temperature is the correct description. The other options either overstate the dependence on temperature (square of T), tie it to density, or claim independence from temperature.