Find the speed of sound (in m/s) at -35°C at 1 atm pressure in dry air.
What was wrong with my previous response to this?
To find the speed of sound in dry air at a given temperature and pressure, we can use the following formula:
v = sqrt((γ * R * T) / M)
where:
v = speed of sound
γ = adiabatic index of air (approximately 1.4)
R = gas constant for dry air (approximately 287.1 J/(kg·K))
T = temperature in Kelvin (converted from Celsius)
M = molar mass of dry air (approximately 0.029 kg/mol)
Now let's calculate the speed of sound at -35°C (in Kelvin -35 + 273.15 = 238.15K) at 1 atm pressure.
Substituting the values into the formula:
v = sqrt((1.4 * 287.1 * 238.15) / 0.029)
Now let's calculate it step by step:
1.4 * 287.1 = 401.94
401.94 * 238.15 = 95679.231
95679.231 / 0.029 = 3295600.724
Taking the square root of 3295600.724, we get approximately 1813.85 m/s.
Therefore, the speed of sound at -35°C at 1 atm pressure in dry air is approximately 1813.85 m/s.