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 (v) in an ideal gas is determined by the formula:
v = √(γRT/M)
where γ is the adiabatic index, R is the universal gas constant, T is the absolute temperature, and M is the molar mass of the gas.

From this formula, it is evident that the speed of sound depends only on the absolute temperature and the nature of the gas. While the speed of sound can also be expressed as v = √(γP/ρ), according to the ideal gas law (PV = nRT), at a constant temperature, the ratio of pressure (P) to density (ρ) remains constant. Therefore, if the pressure is doubled while the temperature is kept constant, the density also doubles, leaving the speed of sound unchanged.

Since the temperature is constant, the initial speed x is equal to the final speed y. Thus, the ratio x/y is 1.