To solve this problem, we need to consider the relationship between the speed of sound and the molecular weight of gases. The speed of sound through a gas is given by the formula:

v = √(γRT/M)

Where:
- v is the speed of sound
- γ is the adiabatic index (for monatomic gases, it is 5/3)
- R is the gas constant
- T is the temperature
- M is the molar mass of the gas

Now, let's consider the speed of sound through helium and the mixture.

1. Speed of sound through helium:
The molar mass of helium (He) is 4 g/mol. Substituting this value into the formula, we have:

v1 = √(γRT/M1)
= √(5/3 * R * T/4)

2. Speed of sound through the mixture:
In the mixture, we have equal volumes of helium and argon. Let's assume the volume of each gas is V. The total volume of the mixture is then 2V. Since the ratio of the volumes is 1:1, the mole fraction of helium (XHe) is 0.5 and the mole fraction of argon (XAr) is also 0.5.

The molar mass of argon (Ar) is given as 40 g/mol. The molar mass of the mixture (MMix) can be calculated using the mole fractions:

MMix = XHe * MHe + XAr * MAr
= 0.5 * 4 + 0.5 * 40
= 2 + 20
= 22 g/mol

Substituting this value into the formula for the speed of sound, we have:

v2 = √(γRT/MMix)
= √(5/3 * R * T/22)

3. Ratio of the speeds of sound:
Dividing v1 by v2, we get:

v1/v2 = (√(5/3 * R * T/4)) / (√(5/3 * R * T/22))
= √(22/4)
= √(11/2)

Therefore, the ratio of the speed of sound through helium to the speed of sound through the mixture is √(11/2). Hence, the correct answer is option (d) √(11/2).