Flow Physics - Speed of Sound
Sounds are all around us; birds chirping, mowers growling, cars rumbling, and whistles blowing. Sound shapes our world in important ways and allows humans to interact with their environment quickly and with great precision. For many people, sound is an innate quality of life that they never fully understand. But what exactly is sound and why is it important for fluid flow and nozzle design?
What humans hear is actually pressure pulses through air that reverberate the eardrum into signals that the brain can interpret into thoughts and ideas. The sound our ears pick up has traveled from the source of the disturbance through a medium (normally air) into our ear drums and the frequency of the pulses is what our eardrums actually encounter. But as is the case with any wave formation, the energy from the disturbance does not travel instantly to a destination.
Instead, the energy from the disturbance travels along the wave at the speed of sound. In air at sea level (one atmosphere of pressure), the speed of sound is about 340 meters per second. For many things in our life, this may seem instantaneous, but anyone who has been in a thunderstorm has encountered the phenomena of seeing a lightning strike and then hearing it up to 10 seconds or more later. This is because the sound wave takes time to travel from the position of the lightning strike to our ears!
The speed of sound depends on many factors including the material or medium the pressure wave is traveling through, the temperature, and the specific heat ratio of the medium. Because nozzle flow is usually restricted to compressible fluids (gases), we will concentrate on speeds of sounds through gases. The propagation rate of any infinitesimally small pressure wave can be solved for by taking the square root of the partial derivative of the pressure of the gas in terms of the density of the gas. This can be simplified to the square root of the multiplication of the ratio of the specific heats, K, the gas constant, R, and the temperature in Kelvin.
These two equations can be seen below. The speed of sound is represented by the variable a. The ratio of specific heats is found by dividing the specific heat at a constant pressure by the specific the heat at a constant volume (Cp/Cv) and has a value of approximately 1.4 for most calculations in air.
Instead, the energy from the disturbance travels along the wave at the speed of sound. In air at sea level (one atmosphere of pressure), the speed of sound is about 340 meters per second. For many things in our life, this may seem instantaneous, but anyone who has been in a thunderstorm has encountered the phenomena of seeing a lightning strike and then hearing it up to 10 seconds or more later. This is because the sound wave takes time to travel from the position of the lightning strike to our ears!
The speed of sound depends on many factors including the material or medium the pressure wave is traveling through, the temperature, and the specific heat ratio of the medium. Because nozzle flow is usually restricted to compressible fluids (gases), we will concentrate on speeds of sounds through gases. The propagation rate of any infinitesimally small pressure wave can be solved for by taking the square root of the partial derivative of the pressure of the gas in terms of the density of the gas. This can be simplified to the square root of the multiplication of the ratio of the specific heats, K, the gas constant, R, and the temperature in Kelvin.
These two equations can be seen below. The speed of sound is represented by the variable a. The ratio of specific heats is found by dividing the specific heat at a constant pressure by the specific the heat at a constant volume (Cp/Cv) and has a value of approximately 1.4 for most calculations in air.
\[a = \sqrt {kRT} = \sqrt {\frac{{{\partial ^2}P}}{{\partial {\rho ^2}}}} \]
JL