Sonic Velocity Calculator:
Enter the values of adiabatic constant, y, absolute temperature, T(K) and molar mass, M(kg/mol) to determine the value of sonic velocity, Vs(m/s).
Sonic Velocity Formula:
Sonic velocity, often referred to as the speed of sound, is the velocity at which sound waves propagate through a medium. In the context of gases, the sonic velocity is crucial in various applications such as aerodynamics, thermodynamics, and fluid dynamics.
This value is particularly important in engineering fields like aerospace, where understanding the flow of gases at high speeds near or beyond the speed of sound is necessary.
Sonic velocity, Vs(m/s) in metres per seconds is calculated by the square root of product of adiabatic constant, y, universal gas constant, R(J/mol.kg) (8.314J/mol.kg) in joules per mole kilograms, absolute temperature, T(K) in Kelvin and then divided by molar mass, M(kg/mol) in kilograms per mole.
Sonic velocity, Vs(m/s) = √( y * R(J/mol.kg) * T(K) / M(kg/mol))
Vs(m/s) = sonic velocity in metres per seconds, m/s.
y = adiabatic constant.
R(J/mol.kg) = universal gas constant in joules per mole kilograms, J/mol.kg.
T(K) = absolute temperature in kelvin, K.
M(kg/mol) = molar mass in kilogram per mole, kg/mol.
Sonic Velocity Calculation:
1.Calculate the sonic velocity of air at room temperature (298 K). Assume airhas an adiabatic index of 1.4 and an approximate molar mass of 0.029kg/mol.
Given: y = 1.4, R(J/mol.kg) = 8.314J/mol.kg, T(K) = 298K, M(kg/mol) = 0.029kg.mol.
Sonic velocity, Vs(m/s) = √( y * R(J/mol.kg) * T(K) / M(kg/mol))
Vs(m/s) = √( 1.4 * 8.314 * 298 / 0.029)
Vs(m/s) = √( 3468.6008/ 0.029)
Vs(m/s) =√119606.9
Vs(m/s) = 345.8m/s.
2.Determine the molar mass of helium at 273 K, with adiabatic constant of 1.66 and sonic velocity 3064m/s.
Given: y = 1.66, R(J/mol.kg) = 8.314J/mol.kg, T(K) = 273K, Vs(m/s) = 3064m/s.
Sonic velocity, Vs(m/s) = √( y * R(J/mol.kg) * T(K) / M(kg/mol))
M(kg/mol) = y * R(J/mol.kg) * T(K) / V2s(m/s)
M(kg/mol) = 1.66 * 8.314 * 273 / 30642
M(kg/mol) = 37569.3462 / 9388096
M(kg/mol) = 0.004kg/mol.
Applications and Considerations:
- Aerodynamic Design: Engineers use sonic velocity to design aircraft and rockets that can safely operate at or above the speed of sound.
- Acoustic Studies: Understanding sonic velocity aids in the design of better acoustic environments, from concert halls to noise control in urban settings.
- Meteorology: Sonic velocity is used in atmospheric studies to understand phenomena like thunder and the propagation of other acoustic signals.
- Safety: In industrial settings, knowing the sonic velocity can help in designing safer systems for handling high-speed gases.
- Educational and Research Applications: Sonic velocity calculations are fundamental in physics and engineering education and research, enhancing understanding of fluid dynamics and thermodynamics.