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Speed of Sound

The speed of sound is different depending on the type of fluid that is being observed. It is based off of how fast a disturbance can travel through a fluid due to the relationship between pressure and density. Refer to equation 1.

(Eq 1) $c=\sqrt{\frac{dP}{dρ}}

c = Speed of Sound

dP = Pressure Differential

dρ = Density Differential

Since there is a relationship between pressure and density a pressure wave builds up has an object approaches the speed of sound. Because of this pressure wave, it is impossible for an object to travel exactly at the speed of sound. The reason why is because as the object flies at the speed of sound the pressure wave will continue to build until it destroys the object. This is why jets have after burners. The after burners are used to get the jet past this building pressure wave and essentially break the sound barrier causing the plane to out run its pressure wave which is referred to as the sonic boom. To relate an objects speed to the speed of sound, the Mach number would be used, which is a unit less number. Refer to equation 2.

(Eq 2) $Mach~Number=\frac{v}{c}$

v = Velocity

Finally, the ideal gas law can also be used to calculate the speed of sound. It will be assumed that an isentropic process will occur. Refer to equation 3.

(Eq 3) $c=\sqrt{kRT}$

k = Specific Heat Ratio

R = Ideal Gas Constant

T = Temperature

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