<meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
<meta name="description" content="Three microphones located on the same straight line at points A, B, C recorded successively at the moments t_A > t_B > t_C the sound of an explosion that occurred at point O, which lies on the segment AC. Find the length of the segment AO if AB = BC = L. At what point in time did the explosion occur? For problem 1.1.4">
<meta property="og:title" content="Three microphones located on the same straight line at points A, B, C recorded successively at the moments t_A > t_B > t_C the sound of an explosion that occurred at point O, which lies on the segment AC. Find the length of the segment AO if AB = BC = L. At what point in time did the explosion occur? For problem 1.1.4">
<meta property="og:image" content="img/logo.png">
@@ -15,9 +15,9 @@
<meta property="og:description" content="Three microphones located on the same straight line at points A, B, C recorded successively at the moments t_A > t_B > t_C the sound of an explosion that occurred at point O, which lies on the segment AC. Find the length of the segment AO if AB = BC = L. At what point in time did the explosion occur? For problem 1.1.4">
<title>Three microphones located on the same straight line at points A, B, C recorded successively at the moments t_A > t_B > t_C the sound of an explosion that occurred at point O, which lies on the segment AC. Find the length of the segment AO if AB = BC = L. At what point in time did the explosion occur? For problem 1.1.4</title>
$1.1.4.$ Three microphones located on the same straight line at points $A$, $B$, $C$ recorded successively at the moments $t_A > t_B > t_C$ the sound of an explosion that occurred at point $O$, which lies on the segment $AC$. Find the length of the segment $AO$ if $AB = BC = L$. At what point in time did the explosion occur?
<center>
<figure>
<img src="statement.png"
loading="lazy" width="230" />
<figcaption>
For problem 1.1.4
</figcaption>
</figure>
</center>
</p>
<h3>Solution</h3>
<p>
<p>
1. Let us introduce the following variables
</p>
<p>
$$x_B=L-x$$
</p>
<p>
$$t_A=t_B+\Delta t$$
</p>
<p>
2. Time of flight of $\gamma$-quantum to counters
</p>
<p>
$$t_B+\Delta t=\frac{x}{c}$$
</p>
<p>
$$t_B=\frac{L-x}{c}$$
</p>
<p>
3. Solving the equations together, we obtain
</p>
<p>
$$\frac{L-x}{c} + \Delta t = \frac{x}{c}$$
</p>
<p>
$$x= \frac{L+c\Delta t}{2}=1.15\,м$$
</p>
</p>
<h4>Answer</h4>
<p>
At a distance $1.15\, \text{m}$ from the microphone $A$
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> astrosander01@gmail.com <br></small>
<meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
<meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
<meta name="description" content="Three microphones located on the same straight line at points A, B, C recorded successively at the moments t_A > t_B > t_C the sound of an explosion that occurred at point O, which lies on the segment AC. Find the length of the segment AO if AB = BC = L. At what point in time did the explosion occur? For problem 1.1.4">
<meta name="description" content="Three microphones located on the same straight line at points A, B, C recorded successively at the moments t_A > t_B > t_C the sound of an explosion that occurred at point O, which lies on the segment AC. Find the length of the segment AO if AB = BC = L. At what point in time did the explosion occur? For problem 1.1.4">
<meta property="og:title" content="Three microphones located on the same straight line at points A, B, C recorded successively at the moments t_A > t_B > t_C the sound of an explosion that occurred at point O, which lies on the segment AC. Find the length of the segment AO if AB = BC = L. At what point in time did the explosion occur? For problem 1.1.4">
<meta property="og:title" content="Three microphones located on the same straight line at points A, B, C recorded successively at the moments t_A > t_B > t_C the sound of an explosion that occurred at point O, which lies on the segment AC. Find the length of the segment AO if AB = BC = L. At what point in time did the explosion occur? For problem 1.1.4">
<meta property="og:image" content="img/logo.png">
<meta property="og:image" content="img/logo.png">
@@ -15,9 +15,9 @@
<meta property="og:description" content="Three microphones located on the same straight line at points A, B, C recorded successively at the moments t_A > t_B > t_C the sound of an explosion that occurred at point O, which lies on the segment AC. Find the length of the segment AO if AB = BC = L. At what point in time did the explosion occur? For problem 1.1.4">
<meta property="og:description" content="Three microphones located on the same straight line at points A, B, C recorded successively at the moments t_A > t_B > t_C the sound of an explosion that occurred at point O, which lies on the segment AC. Find the length of the segment AO if AB = BC = L. At what point in time did the explosion occur? For problem 1.1.4">
<title>Three microphones located on the same straight line at points A, B, C recorded successively at the moments t_A > t_B > t_C the sound of an explosion that occurred at point O, which lies on the segment AC. Find the length of the segment AO if AB = BC = L. At what point in time did the explosion occur? For problem 1.1.4</title>
<title>Three microphones located on the same straight line at points A, B, C recorded successively at the moments t_A > t_B > t_C the sound of an explosion that occurred at point O, which lies on the segment AC. Find the length of the segment AO if AB = BC = L. At what point in time did the explosion occur? For problem 1.1.4</title>
$1.1.4.$ Three microphones located on the same straight line at points $A$, $B$, $C$ recorded successively at the moments $t_A > t_B > t_C$ the sound of an explosion that occurred at point $O$, which lies on the segment $AC$. Find the length of the segment $AO$ if $AB = BC = L$. At what point in time did the explosion occur?
$1.1.4.$ Three microphones located on the same straight line at points $A$, $B$, $C$ recorded successively at the moments $t_A > t_B > t_C$ the sound of an explosion that occurred at point $O$, which lies on the segment $AC$. Find the length of the segment $AO$ if $AB = BC = L$. At what point in time did the explosion occur?
<center>
<center>
<figure>
<figure>
<img src="statement.png"
<img src="statement.png"
loading="lazy" width="230" />
loading="lazy" width="230" />
<figcaption>
<figcaption>
For problem 1.1.4
For problem 1.1.4
</figcaption>
</figcaption>
</figure>
</figure>
</center>
</center>
</p>
</p>
<h3>Solution</h3>
<h3>Solution</h3>
<p>
<p>
<p>
<p>
1. Let us introduce the following variables
1. Let us introduce the following variables
</p>
</p>
<p>
<p>
$$x_B=L-x$$
$$x_B=L-x$$
</p>
</p>
<p>
<p>
$$t_A=t_B+\Delta t$$
$$t_A=t_B+\Delta t$$
</p>
</p>
<p>
<p>
2. Time of flight of $\gamma$-quantum to counters
2. Time of flight of $\gamma$-quantum to counters
</p>
</p>
<p>
<p>
$$t_B+\Delta t=\frac{x}{c}$$
$$t_B+\Delta t=\frac{x}{c}$$
</p>
</p>
<p>
<p>
$$t_B=\frac{L-x}{c}$$
$$t_B=\frac{L-x}{c}$$
</p>
</p>
<p>
<p>
3. Solving the equations together, we obtain
3. Solving the equations together, we obtain
</p>
</p>
<p>
<p>
$$\frac{L-x}{c} + \Delta t = \frac{x}{c}$$
$$\frac{L-x}{c} + \Delta t = \frac{x}{c}$$
</p>
</p>
<p>
<p>
$$x= \frac{L+c\Delta t}{2}=1.15\,м$$
$$x= \frac{L+c\Delta t}{2}=1.15\,м$$
</p>
</p>
</p>
</p>
<h4>Answer</h4>
<h4>Answer</h4>
<p>
<p>
At a distance $1.15\, \text{m}$ from the microphone $A$
At a distance $1.15\, \text{m}$ from the microphone $A$
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> astrosander01@gmail.com <br></small>
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> astrosander01@gmail.com <br></small>
