Question

which change will decrease the speed of a sound wave traveling through a gaseous matter?
replacing the gaseous matter with a liquid
replacing the gaseous matter with a solid
decreasing the temperature of the matter
increasing the temperature of the matter

Explanation:

The speed of sound in a gas is affected by temperature. The formula for the speed of sound in an ideal gas is \(v = \sqrt{\frac{\gamma RT}{M}}\), where \(v\) is the speed of sound, \(\gamma\) is the adiabatic index, \(R\) is the gas constant, \(T\) is the absolute temperature, and \(M\) is the molar mass of the gas. As \(T\) (temperature) decreases, \(v\) (speed of sound) decreases.

Sound travels faster in solids and liquids than in gases. So, replacing gas with liquid (A) or solid (B) would increase the speed of sound. Increasing the temperature (D) would increase the speed of sound in a gas (from the formula \(v=\sqrt{\frac{\gamma RT}{M}}\), as \(T\) increases, \(v\) increases). Only decreasing the temperature (C) will decrease the speed of a sound wave traveling through a gaseous matter.

Answer:

C. decreasing the temperature of the matter