Speed of Sound Downstream of Sound Wave Solution

STEP 0: Pre-Calculation Summary
Formula Used
Sound Speed Downstream = sqrt((Specific Heat Ratio-1)*((Flow Velocity Upstream of Sound^2-Flow Velocity Downstream of Sound^2)/2+Sound Speed Upstream^2/(Specific Heat Ratio-1)))
a2 = sqrt((γ-1)*((u1^2-u2^2)/2+a1^2/(γ-1)))
This formula uses 1 Functions, 5 Variables
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Sound Speed Downstream - (Measured in Meter per Second) - Sound Speed Downstream refers to the speed of sound in a medium after passing through a sound wave or disturbance.
Specific Heat Ratio - The Specific Heat Ratio is the ratio of the heat capacity at constant pressure to heat capacity at constant volume of the flowing fluid for non-viscous and compressible flow.
Flow Velocity Upstream of Sound - (Measured in Meter per Second) - Flow Velocity Upstream of Sound represents the velocity of a fluid flow or airflow before being influenced by a sound wave.
Flow Velocity Downstream of Sound - (Measured in Meter per Second) - Flow Velocity Downstream of Sound represents the velocity of a fluid flow or airflow after being influenced by a sound wave.
Sound Speed Upstream - (Measured in Meter per Second) - Sound Speed Upstream refers to the speed of sound in a medium before passing through a sound wave.
STEP 1: Convert Input(s) to Base Unit
Specific Heat Ratio: 1.4 --> No Conversion Required
Flow Velocity Upstream of Sound: 80 Meter per Second --> 80 Meter per Second No Conversion Required
Flow Velocity Downstream of Sound: 45 Meter per Second --> 45 Meter per Second No Conversion Required
Sound Speed Upstream: 12 Meter per Second --> 12 Meter per Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
a2 = sqrt((γ-1)*((u1^2-u2^2)/2+a1^2/(γ-1))) --> sqrt((1.4-1)*((80^2-45^2)/2+12^2/(1.4-1)))
Evaluating ... ...
a2 = 31.9217793990247
STEP 3: Convert Result to Output's Unit
31.9217793990247 Meter per Second --> No Conversion Required
FINAL ANSWER
31.9217793990247 31.92178 Meter per Second <-- Sound Speed Downstream
(Calculation completed in 00.020 seconds)

Credits

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Shri Govindram Seksaria Institute of Technology and Science (SGSITS), Indore
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18 Governing Equations and Sound Wave Calculators

Speed of Sound Downstream of Sound Wave
Go Sound Speed Downstream = sqrt((Specific Heat Ratio-1)*((Flow Velocity Upstream of Sound^2-Flow Velocity Downstream of Sound^2)/2+Sound Speed Upstream^2/(Specific Heat Ratio-1)))
Speed of Sound Upstream of Sound Wave
Go Sound Speed Upstream = sqrt((Specific Heat Ratio-1)*((Flow Velocity Downstream of Sound^2-Flow Velocity Upstream of Sound^2)/2+Sound Speed Downstream^2/(Specific Heat Ratio-1)))
Flow Velocity Downstream of Sound Wave
Go Flow Velocity Downstream of Sound = sqrt(2*((Sound Speed Upstream^2-Sound Speed Downstream^2)/(Specific Heat Ratio-1)+Flow Velocity Upstream of Sound^2/2))
Flow Velocity Upstream of Sound Wave
Go Flow Velocity Upstream of Sound = sqrt(2*((Sound Speed Downstream^2-Sound Speed Upstream^2)/(Specific Heat Ratio-1)+Flow Velocity Downstream of Sound^2/2))
Ratio of Stagnation and Static Pressure
Go Stagnation to Static Pressure = (1+((Specific Heat Ratio-1)/2)*Mach Number^2)^(Specific Heat Ratio/(Specific Heat Ratio-1))
Critical Pressure
Go Critical Pressure = (2/(Specific Heat Ratio+1))^(Specific Heat Ratio/(Specific Heat Ratio-1))*Stagnation Pressure
Stagnation Temperature
Go Stagnation Temperature = Static Temperature+(Flow Velocity Downstream of Sound^2)/(2*Specific Heat Capacity at Constant Pressure)
Speed of Sound
Go Speed of Sound = sqrt(Specific Heat Ratio*[R-Dry-Air]*Static Temperature)
Ratio of Stagnation and Static Density
Go Stagnation to Static Density = (1+((Specific Heat Ratio-1)/2)*Mach Number^2)^(1/(Specific Heat Ratio-1))
Critical Density
Go Critical Density = Stagnation Density*(2/(Specific Heat Ratio+1))^(1/(Specific Heat Ratio-1))
Mayer's Formula
Go Specific Gas Constant = Specific Heat Capacity at Constant Pressure-Specific Heat Capacity at Constant Volume
Ratio of Stagnation and Static Temperature
Go Stagnation to Static Temperature = 1+((Specific Heat Ratio-1)/2)*Mach Number^2
Critical Temperature
Go Critical Temperature = (2*Stagnation Temperature)/(Specific Heat Ratio+1)
Isentropic Compressibility for given Density and Speed of Sound
Go Isentropic Compressibility = 1/(Density*Speed of Sound^2)
Mach Number
Go Mach Number = Speed of Object/Speed of Sound
Speed of Sound given Isentropic Change
Go Speed of Sound = sqrt(Isentropic Change)
Mach Angle
Go Mach Angle = asin(1/Mach Number)
Isentropic Change across Sound Wave
Go Isentropic Change = Speed of Sound^2

Speed of Sound Downstream of Sound Wave Formula

Sound Speed Downstream = sqrt((Specific Heat Ratio-1)*((Flow Velocity Upstream of Sound^2-Flow Velocity Downstream of Sound^2)/2+Sound Speed Upstream^2/(Specific Heat Ratio-1)))
a2 = sqrt((γ-1)*((u1^2-u2^2)/2+a1^2/(γ-1)))

On what factors does the speed of sound depends?

The speed of sound in a medium is determined by a combination of the medium's rigidity (or compressibility in gases) and its density. The more rigid (or less compressible) the medium, the faster the speed of sound. The greater the density of a medium, the slower the speed of sound.

How to Calculate Speed of Sound Downstream of Sound Wave?

Speed of Sound Downstream of Sound Wave calculator uses Sound Speed Downstream = sqrt((Specific Heat Ratio-1)*((Flow Velocity Upstream of Sound^2-Flow Velocity Downstream of Sound^2)/2+Sound Speed Upstream^2/(Specific Heat Ratio-1))) to calculate the Sound Speed Downstream, The Speed of sound downstream of sound wave formula calculates the speed of sound behind the sound wave by using the relation between the adiabatic flow velocity and the speed of the sound wave. Sound Speed Downstream is denoted by a2 symbol.

How to calculate Speed of Sound Downstream of Sound Wave using this online calculator? To use this online calculator for Speed of Sound Downstream of Sound Wave, enter Specific Heat Ratio (γ), Flow Velocity Upstream of Sound (u1), Flow Velocity Downstream of Sound (u2) & Sound Speed Upstream (a1) and hit the calculate button. Here is how the Speed of Sound Downstream of Sound Wave calculation can be explained with given input values -> 31.92178 = sqrt((1.4-1)*((80^2-45^2)/2+12^2/(1.4-1))).

FAQ

What is Speed of Sound Downstream of Sound Wave?
The Speed of sound downstream of sound wave formula calculates the speed of sound behind the sound wave by using the relation between the adiabatic flow velocity and the speed of the sound wave and is represented as a2 = sqrt((γ-1)*((u1^2-u2^2)/2+a1^2/(γ-1))) or Sound Speed Downstream = sqrt((Specific Heat Ratio-1)*((Flow Velocity Upstream of Sound^2-Flow Velocity Downstream of Sound^2)/2+Sound Speed Upstream^2/(Specific Heat Ratio-1))). The Specific Heat Ratio is the ratio of the heat capacity at constant pressure to heat capacity at constant volume of the flowing fluid for non-viscous and compressible flow, Flow Velocity Upstream of Sound represents the velocity of a fluid flow or airflow before being influenced by a sound wave, Flow Velocity Downstream of Sound represents the velocity of a fluid flow or airflow after being influenced by a sound wave & Sound Speed Upstream refers to the speed of sound in a medium before passing through a sound wave.
How to calculate Speed of Sound Downstream of Sound Wave?
The Speed of sound downstream of sound wave formula calculates the speed of sound behind the sound wave by using the relation between the adiabatic flow velocity and the speed of the sound wave is calculated using Sound Speed Downstream = sqrt((Specific Heat Ratio-1)*((Flow Velocity Upstream of Sound^2-Flow Velocity Downstream of Sound^2)/2+Sound Speed Upstream^2/(Specific Heat Ratio-1))). To calculate Speed of Sound Downstream of Sound Wave, you need Specific Heat Ratio (γ), Flow Velocity Upstream of Sound (u1), Flow Velocity Downstream of Sound (u2) & Sound Speed Upstream (a1). With our tool, you need to enter the respective value for Specific Heat Ratio, Flow Velocity Upstream of Sound, Flow Velocity Downstream of Sound & Sound Speed Upstream and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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