Speed of Sound Upstream of Sound Wave Calculator

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Compressible Flow

Fundamentals of Inviscid and Incompressible Flow

Three-Dimensional Incompressible Flow

Two-Dimensional Incompressible Flow

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Governing Equations and Sound Wave

Normal Shock Wave

Oblique Shock and Expansion Waves

✖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.ⓘ Specific Heat Ratio [γ]			+10% -10%
✖Flow Velocity Downstream of Sound represents the velocity of a fluid flow or airflow after being influenced by a sound wave.ⓘ Flow Velocity Downstream of Sound [u₂]			+10% -10%
✖Flow Velocity Upstream of Sound represents the velocity of a fluid flow or airflow before being influenced by a sound wave.ⓘ Flow Velocity Upstream of Sound [u₁]			+10% -10%
✖Sound Speed Downstream refers to the speed of sound in a medium after passing through a sound wave or disturbance.ⓘ Sound Speed Downstream [a₂]			+10% -10%

✖Sound Speed Upstream refers to the speed of sound in a medium before passing through a sound wave.ⓘ Speed of Sound Upstream of Sound Wave [a₁]

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Formula

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Speed of Sound Upstream of Sound Wave

Formula

`"a"_{"1"} = sqrt(("γ"-1)*(("u"_{"2"}^2-"u"_{"1"}^2)/2+"a"_{"2"}^2/("γ"-1)))`

Example

`"11.94194m/s"=sqrt(("1.4"-1)*((("45m/s")^2-("80m/s")^2)/2+("31.90m/s")^2/("1.4"-1)))`

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Download Governing Equations and Sound Wave Formulas PDF

Speed of Sound Upstream of Sound Wave Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
a₁ = sqrt((γ-1)*((u₂^2-u₁^2)/2+a₂^2/(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 Upstream - (Measured in Meter per Second) - Sound Speed Upstream refers to the speed of sound in a medium before passing through a sound wave.
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 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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Specific Heat Ratio: 1.4 --> No Conversion Required
Flow Velocity Downstream of Sound: 45 Meter per Second --> 45 Meter per Second No Conversion Required
Flow Velocity Upstream of Sound: 80 Meter per Second --> 80 Meter per Second No Conversion Required
Sound Speed Downstream: 31.9 Meter per Second --> 31.9 Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

a₁ = sqrt((γ-1)*((u₂^2-u₁^2)/2+a₂^2/(γ-1))) --> sqrt((1.4-1)*((45^2-80^2)/2+31.9^2/(1.4-1)))

Evaluating ... ...

a₁ = 11.9419428905015

STEP 3: Convert Result to Output's Unit

11.9419428905015 Meter per Second --> No Conversion Required

FINAL ANSWER

11.9419428905015 ≈ 11.94194 Meter per Second <-- Sound Speed Upstream

(Calculation completed in 00.004 seconds)

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Created by Ravi Khiyani

Shri Govindram Seksaria Institute of Technology and Science (SGSITS), Indore

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National Institute Of Technology (NIT), Hamirpur

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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 Upstream of Sound Wave Formula

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 Upstream of Sound Wave?

Speed of Sound Upstream of Sound Wave calculator uses 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))) to calculate the Sound Speed Upstream, The Speed of Sound Upstream of Sound Wave can be determined by considering the properties of the medium and the flow conditions ahead of the sound wave. In an isentropic flow, the speed of sound is related to the Mach number and the flow velocity upstream of the sound wave. Sound Speed Upstream is denoted by a₁ symbol.

How to calculate Speed of Sound Upstream of Sound Wave using this online calculator? To use this online calculator for Speed of Sound Upstream of Sound Wave, enter Specific Heat Ratio (γ), Flow Velocity Downstream of Sound (u₂), Flow Velocity Upstream of Sound (u₁) & Sound Speed Downstream (a₂) and hit the calculate button. Here is how the Speed of Sound Upstream of Sound Wave calculation can be explained with given input values -> 5 = sqrt((1.4-1)*((45^2-80^2)/2+31.9^2/(1.4-1))).

FAQ

What is Speed of Sound Upstream of Sound Wave?

The Speed of Sound Upstream of Sound Wave can be determined by considering the properties of the medium and the flow conditions ahead of the sound wave. In an isentropic flow, the speed of sound is related to the Mach number and the flow velocity upstream of the sound wave and is represented as a₁ = sqrt((γ-1)*((u₂^2-u₁^2)/2+a₂^2/(γ-1))) or 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))). 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 Downstream of Sound represents the velocity of a fluid flow or airflow after being influenced by a sound wave, Flow Velocity Upstream of Sound represents the velocity of a fluid flow or airflow before being influenced by a sound wave & Sound Speed Downstream refers to the speed of sound in a medium after passing through a sound wave or disturbance.

How to calculate Speed of Sound Upstream of Sound Wave?

The Speed of Sound Upstream of Sound Wave can be determined by considering the properties of the medium and the flow conditions ahead of the sound wave. In an isentropic flow, the speed of sound is related to the Mach number and the flow velocity upstream of the sound wave is calculated using 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))). To calculate Speed of Sound Upstream of Sound Wave, you need Specific Heat Ratio (γ), Flow Velocity Downstream of Sound (u₂), Flow Velocity Upstream of Sound (u₁) & Sound Speed Downstream (a₂). With our tool, you need to enter the respective value for Specific Heat Ratio, Flow Velocity Downstream of Sound, Flow Velocity Upstream of Sound & Sound Speed Downstream 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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