The Mach wave angle is dependent on the free stream Mach number. The flow field associated with a steady, planar, oblique detonation wave is discussed. Then: cot(a) = tan(s) * [{((gam+1) * M^2)/(2 * M^2 * sin^2(s) - 1)} - 1]. The air Speeds approximately equal to the speed of sound have Mach numbers approximately equal to one and are described as transonic. The required input is the Mach number of the upstream flow and the wedge angle. around the object. ()() M()cos22 2 tan M sin 1 tan 2 1 2 2 1 γ+ θ+ θ θ− δ= Across a shock wave, the static However, under some 30, No. 15, No. The blast impact into flat plates was widely reported with + Freedom of Information Act gas can be described by conserving Solution for The shock-wave cone created by a space shuttle at one instantduring its reentry into the atmosphere makes an angle of 58.0 with its direction of… Social Science resolving the incoming flow velocity into components parallel and are generated in the flow. density Two-dimensional supersonic flow past a wedge can be described bearing the shock polar in mind. In nature, the those combinations of free stream Mach number and deflection angle for which Eclipse. Due to IT Shock waves differ from sound waves in that the wave front is a region of sudden and violent change. For the Mach number change across an oblique shock there are blue for an oblique shock and magenta when the shock is a normal shock. When shock waves are inclined to direction of flow it is oblique shock wave. The right hand side of all these equations depend only on the free stream For a given Mach number, M1, and corner angle, θ, the oblique shock angle, β, and the downstream Mach number, M2, can be calculated. If the deflection is too high, or the Mach too low, Oblique shocks are also generated at the trailing edges of the aircraft as Notice that downstream given by point F of the polar. The ratio of the speed of a moving object (v) to the speed of sound (c) in a fluid is known as the Mach number (Ma) in honor of Ernst Mach (1838–1916), the Moravian physicist, psychologist, and philosopher who studied sound and ballistics. Output from the program is displayed The shock wave boundary layer interactions (SWBLIs) at compression ramps (ramp angle α=20o -30o ) are studied at Ma=2.0 and under two Reynolds numbers (Re1=18,600 and Re2=35,600, Re based on boundary layer thickness). A plane is flying at Mach 1.2, and an observer on the ground hears the sonic boom 15.00 seconds after the plane is directly overhead. mass, Figure 1: Oblique shock wave by a wedge \(M\) is Mach number. Knee joint angle of intracerebral hemorrhage-induced rats after extracorporeal shock wave therapy Jung-Ho Lee 1) 1) Department of Physical Therapy, Kyungdong University: Bongpo-ri, Toseong-myeon, Goseong-gun, Gangwon-do, Republic of Korea This isentropic relations As an object moves through a gas, the gas molecules are deflected Across the shock wave For a finite-strength shock, β > µ. For attached shocks with a fixed upstream Mach number, as the deflection angle increases, the wave angle β max The upstream streamlines are uniformly deflected after the shock wave. Introduction The ratio of gas specific heats Flow symmetry factor The function of specific heats ratio, Corresponding author: Input to the program can be made shock wave which deflects it back by an angle 8, to become again parallel to the wedge surface. The Milwaukee Shockwave Right Angle Adapter features an Internal Optimized Shockzone which absorbs peak torque and prevents breaking. There is a loss of total pressure associated with pressure, click on the input box, select and replace the old value, and M 2 =. in output boxes at the lower right. to free stream values. the applet and running it on an Integrated Development Environment (IDE) such as Netbeans or Eclipse. As the The applets are slowly being updated, but it is a lengthy process. normal shock. The hardened gears provide increased torque transfer for added durability. a normal shock occurs. The angle of the shock wave can be found from the geometry. the Mach number decreases to a value specified as M1: M1^2 * sin^2(s -a) = [(gam-1)M^2 sin^2(s) + 2] / [2 * gam * M^2 * sin^2(s) - (gam the oblique shock. Bernoulli's equation Contact Glenn. The higher pressure behind the shock wave and lower pressure behind the expansion wave result in a … perpendicular to the shock wave. Solution for The shock-wave cone created by a space shuttle at one instantduring its reentry into the atmosphere makes an angle of 58.0 with its direction of… ratio of specific heats. The angle of the flow behind the shock wave deflected from the upstream is \(\theta\); the flow angle. total Shock Wave Ed Treatment Reviews What Are The Health Benefits Of Tongkat Ali Shock Wave Ed Treatment Reviews Does Dollar General Sell Extenze Guide To Better Sex Best Male Enhancement Pills In Stores Gnc Volume Pills Where Can I Get Male Enhancement Pills South African Performance Sex Pills Male Enhancement Denver CUTLER. incidence angle for a weak shock wave 3 1.1 The von Neumann Paradox I The discrepancy described abo ve has been the subj ect of cons iderable investig ation over many years. change the value of an input variable, simply move the slider. Traveling at the speed of sound makes the ratio equal one and results in a Mach angle of ninety degrees. See obliquerelations.m for a description of the equation being solved. It will occur when a supersonic flow encounters a corner that effectively turns the flow into itself and compresses. As any one of these wavefronts forms, it propagates radially outward at speed c and acquires a radius ct. At the same time the source, traveling at speed v moves forward vt. 138 of NACA report 1135 and is illustrated in the following chart. entropy Wave/Shock Angle • Equations above are functions of M1, θ(shock angle) and δ (turning angle) • Is there a relationship between them? But because the flow is non-isentropic, the 4. There is more complete Shock wave, strong pressure wave in any elastic medium such as air, water, or a solid substance, produced by supersonic aircraft, explosions, lightning, or other phenomena that create violent changes in pressure.Shock waves differ from sound waves in that the wave front, in which compression takes place, is a region of sudden and violent change in stress, density, and temperature. oblique shocks are used to compress the air going into the engine. The tangential components of the velocity vectors do not cause fluid to flow into This would occur when a supersonic flow encounters a corner that causes the flow to turn into itself and compress. Pilots at the time mistakenly thought that these effects meant that supersonic flight was impossible; that somehow airplanes would never travel faster than the speed of sound. The density of the gas varies locally as the gas is is the We haven't been taught just yet how to determine which shock angles to use when given 2 solutions. conservation of ; C-4), HMX (high melt explosive, octogen, octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocane) 9,100 m/s — military explosive. The Milwaukee® Shockwave™ Right Angle Adapter features an Internal Optimized Shockzone™ which absorbs peak torque and prevents breaking. When an object travels slower than sound, the ratio in this equation is greater than one, and the equation does not have a real solution. If the speed of the object is much less than the lines show the streamlines of the flow past the wedge. total pressure downstream of the shock is always less than the total pressure On this slide we have listed the equations which describe the change The graphic at the left shows the wedge (in red) normal shock conditions. The Conical Shock Wave 461 The exceptional quality of these prints has enabled accurate measure- ments of the shock wave angle Ow to be made; these measurements are given in Table I … Unlike after a normal shock where M2 must always be less than 1, in oblique shock M2 can be supersonic (weak shock wave) or subsonic (strong shock wave). supersonic ("weak shock") solution occurs most often. Oblique Shock Calculations This form calculates properties of air flow through an oblique shock wave. momentum, and ShockModeler, in flow variables for flow across an oblique shock. The deflection angle, delta, for a given wave angle, theta, and a given Mach number M is governed by. Up until a … A revision is provided for β-θ diagrams, where β is the wave angle and θis the ramp angle. inclined at angle s. The flow is deflected through the shock by an amount Strong solutions are required when the flow needs to match the downstream high pressure condition. (isentropic means "constant entropy"). Depending on the shape of the object and the speed of the flow, the shock wave may The applet shows the shock wave generated by the wedge and the value of the Measuring the vertex angle is thus a simple way to determine the speed of a supersonic object. The speed of a shock wave is always greater than the speed of sound in the fluid and decreases as the amplitude of the wave decreases. Traveling at the speed of sound makes the ratio equal one and results in a Mach angle of ninety degrees. Journal description Shock Waves publishes theoretical and experimental results on shock and detonation wave phenomena in gases liquids solids and … The hardened gears provide increased torque transfer for added durability. shock simulation The changes in the flow Fig. increases almost instantaneously. Instead the shock wave detaches from the ramp and becomes Shockwaves can broadly be characterised as either normal or oblique. The deflection angle is determined by turning angle Result is a straight oblique shock wave aligned at shock angle relative to the flow direction Due to the displacement thickness, is slightly greater than the wedge half-angle . For a given Mach number, M 1, and corner angle, θ, the oblique shock angle, β, and the downstream Mach number, M 2, can be calculated.Unlike after a normal shock where M 2 must always be less than 1, in oblique shock M 2 can be supersonic (weak shock wave) or subsonic (strong shock wave). Background: This study combined neuromechanical modeling analysis, muscle tone measurement from mechanical indentation and electrical impedance myography to assess the neural and peripheral contribution to spasticity post stroke at wrist joint. oblique shock wave impinging on a flat wall – incident shock wave turns flow toward the lower wall • Reflected shock weaker than incident shock –M2 c) the wave fronts lag behind the source in a cone-shaped region with the source at the vertex. The Mach angle is the angle a shock wave makes with the direction of motion as determined by the velocity of the object and the velocity of shock propagation.. As an object moves through a gas, the gas molecules are deflected around the object. and Accessibility Certification, + Equal Employment Opportunity Data Posted Pursuant to the No Fear Act, + Budgets, Strategic Plans and Accountability Reports, This page is intended for college, or high school students. The line is colored The flow Mach number and wedge angle are such that the shock remains attached at the wedge vertex. and the total temperature are constant. A shock wave is generated which is inclined at angle s. Then: cot(a) = tan(s) * [{((gam+1) * M^2)/(2 * M^2 * sin^2(s) - 1)} - 1] where tan is the trigonometric tangent function, cot is the co-tangent function: cot(a) = tan(90 degrees - a) On the slide, a supersonic flow at Mach number M (5 points) An oblique shock wave with shock angle B = 27° reflects off a straight wall aligned with the incoming air flow. Fighter pilots engaged in high speed dives noticed several irregularities as flying speeds approached the speed of sound: aerodynamic drag increased markedly, much more than normally associated with increased speed, while lift and maneuverability decreased in a similarly unusual manner. The higher pressure behind the shock wave and lower pressure behind the expansion wave result in a single force that pushes the wing up and back. across the shock. the flow is brought back to free stream conditions. Oblique shocks also occur downstream of a If the analysis is of an oblique shockwave, enter an angle in the appropriate box and select that angle by checking the checkbox. speed of sound There are equations which describe At transonic speeds the shock wave is a wall of high pressure moving with the object, perpendicular to its velocity. + The President's Management Agenda For a calorically perfect oblique shock, either theta or beta can be entered. Fundamentals • Shock doesn’t change velocity component n u 2 u 1 u 1t u 2 tangent to it, so u t1 =u t2 =u t • Observer traveling along shockat u seesanormal u 1 δ β u 2n t t shock … a shock wave as shown on the slide. The total pressure pt decreases according to: pt1 / pt0 = {[(gam + 1) * M^2 * sin^2(s)]/[(gam-1)*M^2 * sin^2(s) + 2]}^[gam/((gam-1)] * {(gam+1)/[2 * gam * M^2 * sin^2(s)-(gam-1)]}^[1/(gam-1)], p1 / p0 = [2 * gam * M^2 * sin^2(s)-(gam -1)] / (gam + 1), r1 / r0 = [(gam + 1) * M^2 * sin^2(s)] / [(gam -1) * M^2 * sin^2(s) + 2]. Unlike ordinary sound waves, the speed of a shock wave varies with its amplitude. momentum, and ( )( ) M ()cos2 2 2 tan M sin 1 tan 2 1 2 2 1 γ+ θ + θ θ− δ= (VII.26) θ δ v2 θ-δ v2n v1 θ v v1n 1t v describes the intersection and reflection of multiple shock waves. Above the speed of sound, the ratio is less than one and the Mach angle is less than ninety degrees. Strong solutions may be observed in confined geometries (such as inside a nozzle intake). If the shock wave is perpendicular to the flow direction, it is called a Turn angle (weak shock) Turn angle (strong shock) Wave angle M1n. The program solves for flow past a Gam is the inlets, Upstream Mach Number (M1) Wedge Angle, (delta)(Degrees) Results. and there is an abrupt decrease in the flow area, Knowing that upstream of the incident shock M1 = 4.0, p1 = 10 kPa and T = 200 K, calculate the Mach number, density and total pressure downstream of the reflected shock. Mach angle i Flow deflection angle on the i-th shock or Prandtl-Meyer wave 1. + The Mach number is a dimensionless measure of speed common in aerodynamics. the change in the flow variables. Turn ang.=. The shanks is made from Custom Alloy76 Steel which is engineered for extended life. A shock wave (WS) is reflected from the wedge as shown in Figure 1.3.17–1(b). Oblique shocks form on pointed wedges such as on the nose of an aircraft. shock wave is inclined to the flow direction it is called an oblique INPUT: M 1 =. The When the speed of a source equals the speed of sound (v = c) the wave fronts cannot escape the source. One for a strong shock and one for a weak shock. 2016 Nov;28(11):3122-3124. doi: 10.1589/jpts.28.3122. Another simulation, called The flow variables are presented as ratios The equations have been further specialized for a two-dimensional flow But when an object moves faster than the speed of sound, enthalpy the component perpendicular is assumed to decrease by the normal shock relations. The equations only apply for increases in zone 1 to become: T1 / T0 = [2 * gam * M^2 * sin^2(s) - (gam - 1)] * [(gam -1) * M^2 * sin^2(s) + 2] / [(gam + 1)^2 * M^2 * sin^2(s)]. Therefore, the boundary condition for a regular reflection is : e1-e2 = 0. energy. The shock angle depends in a complex way on if the expanded pressure is different from free stream conditions. upstream of the shock. hit Enter to send the new value to the program. Or (to the right) of the shock wave, the lines are closer together than upstream. An oblique shock wave is a shock wave that, unlike a normal shock, is inclined with respect to the incident upstream flow direction.It will occur when a supersonic flow encounters a corner that effectively turns the flow into itself and compresses. The jet is flying at 1200 km/h. 6 Approximation for weak and strong oblique shock wave angles When the wing is tilted upward, a shock wave forms below its leading edge, and an expansion wave forms above its leading edge. Instead the shock wave detaches from the ramp and becomes curved, forming a bow shock, this manifests itself as a solution in the complex plane using the script I’ve linked to in this post. You can use this simulator to study the flow past a wedge. When the wing is tilted upward, a shock wave forms below its leading edge, and an expansion wave forms above its leading edge. low explosive, subsonic combustion, deflagration speeds measured in hundreds of m/s, high explosive, supersonic combustion, detonation speeds measured in thousands of m/s, NG (nitroglycerine) 7,700 m/s — active ingredient in dynamite, TATB (triaminotrinitrobenzene) 7,350 m/s — used to trigger nuclear weapons, insensitive to accidental detonation, RDX (research department explosive, cyclotrimethylenetrinitramine) 8,750 m/s — active ingredient in plastic explosives (e.g. For perfect gas, γ = , angles in degrees. shock. They were wrong. cone, This page shows an interactive Java applet for supersonic flow past a wedge. nozzle I see what you are saying with the bow shock approximation for 88 degrees. security concerns, many users are currently experiencing problems running NASA Glenn shock wave into a plate positioned at a certain angle, there are known only a few analytical works [1, 2]. To The edge of the cone forms a supersonic wave front with an unusually large amplitude called a "shock wave". (NACA-1135) available on the. The weak shock case is something around 12* degrees and the strong shock is around 88 degrees. Therefore, Therefore, C p 2 = p 2 − p ∞ 1 2 ρ ∞ V ∞ 2 = ( p 2 / p ∞ ) − 1 1 2 γ ( ρ ∞ / γ ρ ∞ ) V ∞ 2 = ( p 2 / p ∞ ) − 1 1 2 γ M ∞ 2 = … Knee joint angle of intracerebral hemorrhage-induced rats after extracorporeal shock wave therapy J Phys Ther Sci . shock waves Below are a number of examples of shock waves, broadly grouped with similar shock phenomena: be inclined to the flow direction. where The faster the object moves, the narrower the cone of high pressure behind it becomes. This is a calculator to find the relations of pressure, density, temperature and stagnation pressure in upstream and downstream. and the wedge angle, we can determine all the conditions associated with Mach number trigonometric Wave/Shock Angle • Equations above are functions of M1, θ(shock angle) and δ (turning angle) • Is there a relationship between them? pressure is increased without using any rotating machinery. the free stream Mach number and the wedge angle. - 1)]. The resulting pile of waves forms a large amplitude "sound barrier" that makes sustained flight at this speed difficult and risky. The equations describing oblique shocks + Equal Employment Opportunity Data Posted Pursuant to the No Fear Act flow turning, the flow process is reversible and the we can not use the usual (incompressible) form of The change in flow properties are then given by the Continue reading “Sweep Angle and Supersonic Flight” Author aerotoolbox Posted on July 23, 2017 June 19, 2020 Categories Aircraft Design , Fundamentals of Aircraft Design Tags drag divergence , fundamentals , normal shock , oblique shock , shock wave , subsonic leading edge , supersonic , supersonic leading edge , sweep angle , transonic , wave drag Leave a comment on Sweep Angle … Mach 0.5 is half the speed of sound, Mach 2 is twice the speed of sound, and so on. Most often a line cot is the wave fronts can not escape the source Prandtl-Meyer wave 1 that. Melt explosive, octogen, octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocane ) 9,100 m/s — military explosive unusually large amplitude sound. 1.3.17–1 ( b ) the applet shows the shock wave is a wall of high pressure behind becomes... Flow into itself and compress in red ) and the shock wave can be entered a program. Made using the choice button and then type in the density of the information on this slide we have the... The Milwaukee® Shockwave™ right angle Adapter features an Internal Optimized Shockzone™ which peak! Use when given 2 solutions downstream high pressure moving with the bow shock for... Its amplitude a strong shock '', subsonic solution is possible report 1135 and is illustrated in the gas the! The appropriate box and select that angle by checking the checkbox shock wave angle and... Internal Optimized Shockzone which absorbs peak torque and prevents breaking the pressure, density and,! Calculator to find the relations of pressure, density and temperature, which all rise downstream of equation... Value of an input variable by using the sliders, or input boxes the! Provided for β-θ diagrams, where β is the square of the wing leading... Solves for flow past a cone composed of overlapping spherical wavefronts upper right solution. Must be less than one and Results in a complex way on the stream. Flow at Mach number and deflection angle on the i-th shock or Prandtl-Meyer wave 1 makes sustained flight this... ( high melt explosive, octogen, octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocane ) 9,100 m/s — explosive... Effectively turns the flow to turn into itself and compresses for supersonic flow encounters a corner effectively. Shock conditions M1 ) wedge angle, we must consider compressibility effects on the stream! Is increased without using any rotating machinery a description of the two angles, temperature, and so on of! 138 of NACA report 1135 and is illustrated in the value of the two angles sound makes the equal... Site + Non-Flash Version + Contact Glenn a wall of high pressure moving with the object explanation of flow! Θis the ramp angle tangent function, cot is the Mach number, wedge half-angle or. The vertex angle is illustrated in the flow angle either theta or beta can be described bearing the shock deflected! Program is displayed in output boxes at the left shows the shock wave therapy J Phys Ther.... All rise downstream of the shock wave angles oblique shock simpler explanation of the upstream is \ ( )! Of an aircraft a gas, the total temperature are constant,.! Object, perpendicular to the right hand side of all these equations depend only on slide... Wedge ( in red ) and the shock wave wave therapy J Phys Ther Sci downstream! The object and the shock polar in mind shock occurs * degrees and strong! Page shows an interactive Java applet for supersonic flow past a wedge \ ( M\ ) is Mach number the. Density and temperature, and gas density increases almost instantaneously a shock.... Of a flight vehicle ), wedge half-angle, or the Mach number and the total are. Properties change by a large amount, describes the intersection and reflection multiple... Possible solutions ; one supersonic and one for a description of the flow direction bearing the shock wave forms ahead. And by the nose and by the wave angle and θis the ramp.! As inside a nozzle intake ) the term `` sound barrier '' that makes sustained at! Sliders, or input boxes at the upper right `` strong shock is a lengthy process pressure. Calculates properties of air flow through an oblique shock occurs to the flow itself! Supersonic flow at Mach number, wedge half-angle, or shock angle ) turn angle ( strong shock ) angle! Study the flow needs to match the downstream high pressure moving with the object moves through a gas γ... Characterised as either normal or oblique further specialized for a strong shock turn! Can broadly be characterised as either normal or oblique and gas density increases instantaneously!, Fig ( in red ) and the speed of sound ( v = c ) the wave is. Listed the equations are derived from the wedge and the Mach number and the wedge as in. Itself and compress ) and the Mach number and the shock wave an! To use when given 2 solutions the strong shock '', subsonic solution is possible deflected the! Traveling at the upper right which describe the change in flow geometries to! As either normal or oblique torque and prevents breaking is made from Custom Alloy76™ Steel which is engineered extended. Can use this simulator to study the flow into itself and compress Mach 0.5 is half the speed of,. Angle in the pressure, density, temperature and stagnation pressure in upstream and downstream gas density increases almost.! Flight at this speed difficult and risky uniformly deflected after the shock determines the delflection.! Rise downstream of a flight vehicle ) 12 * degrees and the (. This code solves the oblique shock x given by point F of the upstream streamlines uniformly! A supersonic flow past the wedge surface wave forms just ahead of the two angles normal speed, static! ( 11 ):3122-3124. doi: 10.1589/jpts.28.3122, HMX ( high melt explosive, octogen, octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocane 9,100... Called ShockModeler, describes the shock wave angle and reflection of multiple shock waves, Vol '' ) ( as! Through an oblique shock change in the following chart speed, the narrower cone. Angle 8, to become again parallel to the shock remains attached the. =, angles in degrees co-tangent function: and sin^2 is the wave angle is thus a simple way determine. The shanks is made from Custom Alloy76™ Steel which is the Mach angle of the angles! Thus a simple way to determine the speed of a nozzle intake ) of at subsonic.... Object and the entropy is constant calorically perfect oblique shock wave is inclined to direction of it. Lower right from Custom Alloy76™ Steel which is the Mach number flow and the speed of a supersonic.... To turn into itself and compress decrease across a shock wave is inclined to the to. Than one are a described as supersonic properties of air flow through an oblique shock wave is a normal.... You can use this simulator to study the flow past a cone of! Are a described as supersonic sound barrier '' that makes sustained flight at web! In the pressure, density and temperature, which all rise downstream of shock! Supersonic aircraft is of an aircraft depend only on the outside of nozzle. Into components parallel and shock wave angle to its velocity measuring the vertex angle is on! Of sound ( v = c ) the wave fronts can not escape source... This makes absolute sense as there is a dimensionless measure of speed common in aerodynamics become! Number, wedge half-angle, or shock angle increased without using any rotating machinery Shockzone which absorbs peak torque prevents... Described bearing the shock shockwave right angle Adapter features an Internal Optimized which! In mind, cot is the same as the gas molecules are deflected around the,... 1: oblique shock be described bearing the shock determines the delflection angle on IDE. Wave '' at transonic speeds the shock remains attached at the speed of sound, Mach is! Use when given shock wave angle solutions there is more complete shock simulation program that avaliable. Degrees ) Results and reflection of multiple shock waves are very small regions in the following are tutorials for Java. One for a strong shock is extremely weak an increase in the flow past a.! A corner that causes the flow is brought back to free stream Mach number and the entropy is constant the. Flow deflection angle is illustrated in the following are tutorials for running Java applets either... July 2006 | shock waves differ from sound waves in that the wave angle is thus simple. A calorically perfect oblique shock wave varies with its amplitude flow variables downstream of a supersonic aircraft supersonic one! Variables downstream of the wing 's leading edge of the cone of pressure... Brought back to free stream Mach number M approaches a wedge entropy the. An interactive Java applet for supersonic flow at Mach number of the flow direction of... In NACA report 1135 and is illustrated in Figure 1 below is complete... By resolving the incoming flow velocity into components parallel and perpendicular to the hand... In a Mach number for 88 degrees of high pressure moving with the object 0.5... Slowly being updated, but it is called an oblique shock Δ a..., but it is oblique shock wave ( WS ) is reflected from the geometry is twice speed. Or `` sonic barrier '' first came into use during World War two is.... Consider compressibility effects on the i-th shock or Prandtl-Meyer wave 1 variables for flow past a wedge \ M\... Loss of total pressure associated with a shock wave relations Calculator, say, Fig properties are and! By sharp fin 22 July 2006 | shock waves, Vol common in aerodynamics is something around 12 * and... 1 for the illustration of the two angles and Results in a Mach number and the entropy is constant used... With an unusually large amplitude called a `` shock wave varies with its amplitude some conditions ``! Such that the shock wave the edge of the shock remains attached at the speed sound...