Sound Wave Speed
Sound waves propagate in a room filled with a monatomic ideal gas. Suppose more gas is flooded into the room, so that the new density of gas in the room is twice what it was previously. The room is climate-controlled so that the temperature stays fixed. By what factor does the speed of the sound waves change?
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1 solution
The velocity of sound waves is given by: v = ρ γ p where γ is the adiabatic index of the gas medium, p is the pressure of the gas, and ρ is the gas density. Here, γ remains unchanged, while the density ρ increases by a factor of two. Now consider the ideal gas law: p V = n R T By doubling the density of gas in a fixed volume, the number of moles of gas must have doubled. Since the temperature and volume are fixed, the pressure has doubled as well. Therefore the sound wave speed remains unchanged.