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<p>In <a href="Fluid_dynamics" title="Fluid dynamics">fluid dynamics</a>, a <b>Mach wave</b>, also known as a <b>weak discontinuity</b>,<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> is a pressure wave traveling with the <a href="Speed_of_sound" title="Speed of sound">speed of sound</a> caused by a slight change of <a href="Pressure" title="Pressure">pressure</a> added to a <a href="Compressible_flow" title="Compressible flow">compressible flow</a>. These weak waves can combine in supersonic flow to become a <a href="Shock_wave" title="Shock wave">shock wave</a> if sufficient Mach waves are present at any location. Such a shock wave is called a <b>Mach stem</b> or <b>Mach front</b>. Thus, it is possible to have shockless compression or expansion in a supersonic flow by having the production of Mach waves sufficiently spaced (<i>cf.</i> <a href="Isentropic_process" title="Isentropic process">isentropic</a> compression in supersonic flows). A Mach wave is the weak limit of an <a href="Oblique_shock" title="Oblique shock">oblique shock</a> wave where time averages of flow quantities don't change (a normal shock is the other limit). If the size of the object moving at the speed of sound is near 0, then this domain of influence of the wave is called a <b>Mach cone</b>.<sup id="cite_ref-sasoh_3-0" class="reference"><a href="#cite_note-sasoh-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading2"><h2 id="Mach_angle">Mach angle</h2></div>

<p>A Mach wave propagates across the flow at the <b>Mach angle</b> <i>μ</i>, which is the angle formed between the Mach wave <a href="Wavefront" title="Wavefront">wavefront</a> and a vector that points opposite to the vector of motion.<sup id="cite_ref-sasoh_3-1" class="reference"><a href="#cite_note-sasoh-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> It is given by

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<mi>arcsin</mi>

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<annotation encoding="application/x-tex">{\displaystyle \mu =\arcsin \left({\frac {1}{M}}\right),}</annotation>

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</math></span><img src="./ad1d64f23ea5ede189f8fb2915613a4ef1ded93f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:17.809ex; height:6.176ex;" alt="{\displaystyle \mu =\arcsin \left({\frac {1}{M}}\right),}" loading="lazy"></span></dd></dl>

<p>where <i>M</i> is the <a href="Mach_number" title="Mach number">Mach number</a>.

</p><p>Mach waves can be used in <a href="Schlieren_photography" title="Schlieren photography">schlieren</a> or shadowgraph observations to determine the local Mach number of the flow. Early observations by <a href="Ernst_Mach" title="Ernst Mach">Ernst Mach</a> used grooves in the wall of a duct to produce Mach waves in a duct, which were then photographed by the schlieren method, to obtain data about the flow in nozzles and ducts. Mach angles may also occasionally be visualized out of their condensation in air, for example <a href="Vapor_cone" title="Vapor cone">vapor cones</a> around aircraft during <a href="Transonic" title="Transonic">transonic</a> flight.

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<ul><li><a href="Compressible_flow" title="Compressible flow">Compressible flow</a></li>

<li><a href="Prandtl%E2%80%93Meyer_expansion_fan" title="Prandtl–Meyer expansion fan">Prandtl–Meyer expansion fan</a></li>

<li><a href="Shadowgraph" title="Shadowgraph">Shadowgraph technique</a></li>

<li><a href="Schlieren_photography" title="Schlieren photography">Schlieren photography</a></li>

<li><a href="Shock_wave" title="Shock wave">Shock wave</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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<li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text">Landau, Lev Davidovich, and Evgenii Mikhailovich Lifshitz. Fluid mechanics: Landau And Lifshitz: course of theoretical physics, Volume 6. Vol. 6. Elsevier, 2013.</span>

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<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">Zelʹdovich, I︠A︡kov Borisovich, Yurii Petrovich Raizer, and Wallace D. Hayes. Physics of shock waves and high-temperature hydrodynamic phenomena. Vol. 1. New York: Academic Press, 1966.</span>

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</style><cite id="CITEREFSasoh2020" class="citation book cs1">Sasoh, Akihiro (2020-01-02). "4.3 Oblique Shock Wave". <i>Compressible Fluid Dynamics and Shock Waves</i>. Nagoya, Japan: <a href="Springer_Nature" title="Springer Nature">Springer Nature</a> Singapore. pp. <span class="nowrap">80–</span>82. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-981-15-0504-1">10.1007/978-981-15-0504-1</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-981-15-0504-1</bdi>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:213248761">213248761</a>.</cite></span>

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<li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><cite id="CITEREFE._CarscallenPatrick2013" class="citation book cs1">E. Carscallen, William; Patrick, H. Oosthuizen (2013-07-12). <i>Introduction to Compressible Fluid Flow</i> (2 ed.). <a href="CRC_Press" title="CRC Press">CRC Press</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-4398-7792-0</bdi>.</cite></span>

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<li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://www.grc.nasa.gov/WWW/K-12/airplane/machang.html">Mach angle</a> at NASA.</span>

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<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

<ul><li><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=iNBZBChS2YI">Supersonic wind tunnel test demonstration (Mach 2.5) with flat plate and wedge creating an oblique shock along with numerous Mach waves(Video)</a></li></ul></div><div><div class="zim-footer">

This article is issued from <a class="external text" title="Last edited on 2025-07-03" href="https://en.wikipedia.org/wiki/?title=Mach_wave&oldid=1298635498">Wikipedia</a>. The text is available under <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-Share Alike 4.0</a> unless otherwise noted. Additional terms may apply for the media files.

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