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<meta name="description" content="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?">
<meta property="og:title" content="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?">
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<meta property="og:description" content="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?">
<title>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?</title>
$1.1.11^*.$ 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>
<h3>Solution</h3>
<p>
<center>
<figure>
<img src="1.1.11.png"
loading="lazy" alt="1.1.11" width="250" />
</figure>
</center>
<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 $ADB$
<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.)
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> alex@savchenkosolutions.com <br></small>
<meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
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<meta name="description" content="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?">
<meta name="description" content="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?">
<meta property="og:title" content="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?">
<meta property="og:title" content="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?">
<meta property="og:image" content="img/logo.png">
<meta property="og:image" content="img/logo.png">
@@ -14,9 +14,9 @@
<meta property="og:description" content="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?">
<meta property="og:description" content="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?">
<title>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?</title>
<title>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?</title>
$1.1.11^*.$ 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?
$1.1.11^*.$ 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>
</p>
<h3>Solution</h3>
<h3>Solution</h3>
<p>
<p>
<center>
<center>
<figure>
<figure>
<img src="1.1.11.png"
<img src="1.1.11.png"
loading="lazy" alt="1.1.11" width="250" />
loading="lazy" alt="1.1.11" width="250" />
</figure>
</figure>
</center>
</center>
<p>
<p>
1. The more the aircraft exceeds the speed of sound, the smaller the value of $AD$, T.e. $v \sim 1/AD$.
1. The more the aircraft exceeds the speed of sound, the smaller the value of $AD$, T.e. $v \sim 1/AD$.
</p>
</p>
<p>
<p>
2. If the aeroplane is travelling at sonic speed $v = s$, then $AD = AB = L$, in which case triangle
2. If the aeroplane is travelling at sonic speed $v = s$, then $AD = AB = L$, in which case triangle
$ADB$ is equilateral, or
$ADB$ is equilateral, or
</p>
</p>
<p style="text-align: center;">
<p style="text-align: center;">
$$v = c \frac{AB}{AD} = c \frac{L}{AD} \; (1)$$
$$v = c \frac{AB}{AD} = c \frac{L}{AD} \; (1)$$
</p>
</p>
<p>
<p>
3. Let's define the elements of the triangle $ADB$
3. Let's define the elements of the triangle $ADB$
<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.)
<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.)
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> alex@savchenkosolutions.com <br></small>
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> alex@savchenkosolutions.com <br></small>
