In an ideal gas, the speed of sound is given by a = sqrt(gamma R T / M). Which of the following is the correct expression for a?

In an ideal gas, the speed of sound is given by a = sqrt(gamma R T / M). Which of the following is the correct expression for a?

• A. a = sqrt(gamma R T / M)
• B. a = gamma R T / M
• C. a = RT/M
• D. a = sqrt(R T / M)

Answer: (A)

The speed of sound in an ideal gas comes from the relation a^2 = gamma p / rho, where gamma is Cp/Cv. For an ideal gas, p = rho R_specific T with R_specific = R / M (M is the molar mass). Substituting p/ρ = R_specific T gives a^2 = gamma R_specific T = gamma (R/M) T. Taking the square root yields a = sqrt(gamma R T / M). This shows how the adiabatic index, temperature, and molar mass determine the sound speed. The other forms either miss the square root or miss the M in the denominator, leading to incorrect units or dependence.

The speed of sound in an ideal gas comes from the relation a^2 = gamma p / rho, where gamma is Cp/Cv. For an ideal gas, p = rho R_specific T with R_specific = R / M (M is the molar mass). Substituting p/ρ = R_specific T gives a^2 = gamma R_specific T = gamma (R/M) T. Taking the square root yields a = sqrt(gamma R T / M). This shows how the adiabatic index, temperature, and molar mass determine the sound speed. The other forms either miss the square root or miss the M in the denominator, leading to incorrect units or dependence.