Mach wave

<h2 id="mach-angle">Mach angle</h2>

<p>A Mach wave propagates across the flow at the Mach angle <i>μ</i>, which is the angle formed between the Mach wave <a href="/facts/Wavefront/5XVoVtDQ">wavefront</a> and a vector that points opposite to the vector of motion.<a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a><a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a> It is given by
</p>

μ
        =
        arcsin
        ⁡
        
          (
          
            
              1
              M
            
          
          )
        
        ,
      
    
    {\displaystyle \mu =\arcsin \left({\frac {1}{M}}\right),}

<p>where <i>M</i> is the <a href="/facts/Mach_number/Ee01MIgw">Mach number</a>.
</p><p>Mach waves can be used in <a href="/facts/Schlieren_photography/3AosIAbb">schlieren</a> or shadowgraph observations to determine the local Mach number of the flow. Early observations by <a href="/facts/Ernst_Mach/gfSFynYK">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="/facts/Vapor_cone/sTKcJ4Bo">vapor cones</a> around aircraft during <a href="/facts/Transonic/F7SV9hrt">transonic</a> flight.
</p>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Compressible_flow/SUX6gw9D">Compressible flow</a></li>
<li><a href="/facts/Prandtl%25E2%2580%2593Meyer_expansion_fan/bftUtQjj">Prandtl–Meyer expansion fan</a></li>
<li><a href="/facts/Shadowgraph/SvbncIPM">Shadowgraph technique</a></li>
<li><a href="/facts/Schlieren_photography/3AosIAbb">Schlieren photography</a></li>
<li><a href="/facts/Shock_wave/CqrG1Xm5">Shock wave</a></li></ul>

<h2 id="external-links">External links</h2>
<ul><li><a 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>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>Landau, Lev Davidovich, and Evgenii Mikhailovich Lifshitz. Fluid mechanics: Landau And Lifshitz: course of theoretical physics, Volume 6. Vol. 6. Elsevier, 2013. <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>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. <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>Sasoh, Akihiro (2020-01-02). "4.3 Oblique Shock Wave". Compressible Fluid Dynamics and Shock Waves. Nagoya, Japan: Springer Nature Singapore. pp. 80–82. doi:10.1007/978-981-15-0504-1. ISBN 978-981-15-0504-1. S2CID 213248761. <a href="978-981-15-0504-1" target="_blank">978-981-15-0504-1</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
<li id="fn:4"><p>E. Carscallen, William; Patrick, H. Oosthuizen (2013-07-12). Introduction to Compressible Fluid Flow (2 ed.). CRC Press. ISBN 978-1-4398-7792-0. <a href="978-1-4398-7792-0" target="_blank">978-1-4398-7792-0</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li>
<li id="fn:5"><p>Sasoh, Akihiro (2020-01-02). "4.3 Oblique Shock Wave". Compressible Fluid Dynamics and Shock Waves. Nagoya, Japan: Springer Nature Singapore. pp. 80–82. doi:10.1007/978-981-15-0504-1. ISBN 978-981-15-0504-1. S2CID 213248761. <a href="978-981-15-0504-1" target="_blank">978-981-15-0504-1</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li>
<li id="fn:6"><p>Mach angle at NASA. <a href="https://www.grc.nasa.gov/WWW/K-12/airplane/machang.html" target="_blank">https://www.grc.nasa.gov/WWW/K-12/airplane/machang.html</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li>
</ol>

Mach wave open-in-new

Mach wave