Question 6: Explain the speed of sound in a gas and give all factors which affect the speed of sound in the air.

Sound waves are compressional mechanical waves propagating in gas or air obeying Boyle’s Law under adiabatic conditions (PVγ = Constant). Here γ is a constant depending on the nature of the gas/air. Hence if P and V are the initial pressure and P + ΔPand V – ΔV are the final, then,

Expanding by using Binomial Formula and neglecting the very small terms,

Neglect the last term on RHS being very small and cancel P on both sides and re-arrange,

## Factors affecting speed of sound

• Density: Since speed of sound is inversely proportional to the square root of the density of the gas, therefore, smaller the density of the gas, greater will be the speed of the sound through it and vice versa.
• Moisture: Moisture reduces the density of the gas. When the humidity increases, the number of water molecules increases in the air. Air generally consists of Oxygen, Nitrogen and Carbon dioxide. Water molecules are less heavy than these air molecules. Therefore, the density of air decreases with moisture. Applying equation (A), the speed of sound will increase. In damp air sound will travel faster than dry air.
• Pressure: For one mole of an ideal gas of volume V, pressure P and temperature T,

Wind: If the sound carrying air is moving itself,the speed of sound increases or decreases accordingly. If the sound and air are moving in the same direction, then velocities are added. The resultant velocity is v + vw. It will be v – vw if both move in opposite directions.