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+ <h2>Solutions of Savchenko Physics Textbook</h2>
+ <p class="author">
+ Aliaksandr Melnichenka <br/>
+ October 2023
+ </p>
+ </header>
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+ <h3 id="back-link"><a href="../">$\leftarrow$Back</a></h3>
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+ <h3> Statement </h3>
+ <p>
+ $1.1.11^*.$ A supersonic airplane is flying horizontally. Two microphones on the same vertical at a distance $l$ from each other register the arrival of sound from an airplane flying over the microphones with a time lag $\Delta t$. The speed of sound in air is $c$. What is the speed of the plane?
+ </p>
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+ <h3>Solution</h3>
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+ <p>
+ 1. The more the aircraft exceeds the speed of sound, the smaller the value of $AD$, T.e. $v \sim 1/AD$.
+ </p>
+ <p>
+ 2. If the aeroplane is travelling at sonic speed $v = s$, then $AD = AB = L$, in which case triangle
+$ADB$ is equilateral, or
+</p>
+ <p style="text-align: center;">
+ $$v = c \frac{AB}{AD} = c \frac{L}{AD} \; (1)$$
+ </p>
+ <p>
+ 3. Let's define the elements of the triangle $ADB$
+ </p>
+ <p style="text-align: center;">
+ $$DB = c \cdot \Delta t\text{; }AD = \sqrt{L^2 - DB^2} \; (2)$$
+ </p>
+ <p>
+ 4. Substituting $(2)$ into equation $(1)$, we obtain
+ </p>
+ <p style="text-align: center;">
+ $${v}=\frac{{cL}}{\sqrt{{L}^{2}-{c}^{2}\Delta{t}^{2}}}.$$
+ </p>
+
+ <p>
+ <i>NO: This problem is related to the Mach wave phenomenon. This phenomenon was written about in the journal ‘Quantum’. <a href="http://kvant.mccme.ru/pdf/2010/2010-03.pdf" target="_blank">2010-03.pdf</a> </i>(42 стр.)
+ </p>
+ </p>
+
+ <h4>Answer</h4>
+ <p>
+ $$v = cl/\sqrt{l^{2}-{c}^{2}{∆t}^{2}}$$
+
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