A very large container consists of an ideal gas. The speed of sound in the gas is x. When the pressure of the gas is doubled while keeping the temperature constant, the speed of sound now becomes y. What is the ratio of x to y?

The speed of sound in an ideal gas is v = √(γRT/M), which depends only on the temperature, the adiabatic index γ, and the molar mass M — not on the pressure. Equivalently, v = √(γP/ρ); when pressure is doubled at constant temperature, density also doubles (since PV = nRT means ρ ∝ P at constant T), so the ratio P/ρ stays the same. Therefore the speed of sound is unchanged, and x : y = 1 : 1.