The speed of sound in an ideal gas is given by

where:
is the ratio of specific heats,
is the pressure, and
is the density.
Since the problem states that is the same for all the gases, the speed of sound in each gas is determined solely by the factor .

Let's determine the appropriate for each gas:

Helium (He):
Helium is a monatomic gas.
For a monatomic gas, .
Therefore, .
Methane ( ):
Methane is a polyatomic gas (a tetrahedral molecule with three rotational degrees of freedom).

For nonlinear polyatomic gases, is typically taken as .

Thus, .
Carbon Dioxide ( ):
Carbon dioxide is a linear molecule.
For linear molecules, .

Hence, .
Therefore, the ratio of the speeds of sound in the gases is:

Comparing this expression with the given options, we see that it matches Option C.