A boy stands between two vertical wall and fires a rifle. Under what condition will he hear a single echo from both walls? Calculate the distance between the walls if the single echo is heard six seconds later
when he stands between the walls at a point equidistance from them
when he stands between the walls at a point equidistant from them.
x=vt
330*6=1980
To understand the conditions for hearing a single echo from both walls, we need to consider the speed of sound and the distances involved.
1. Speed of sound: The speed of sound in air is approximately 343 meters per second at room temperature.
2. Time for the echo: The time it takes for an echo to reach the boy depends on the distance between the walls. We are given that the single echo is heard six seconds later.
Now, let's break down the scenario:
When the boy fires the rifle, he will hear the direct sound (the original sound from the rifle) first, and then the sound waves will bounce off the two walls and return to him as an echo. For the boy to hear a single echo from both walls, two conditions must be met simultaneously:
1. The time it takes for the sound waves to travel from the rifle to each wall and back must be the same. This means that the distance from the boy to each wall must be the same (or equal when considering any time delay caused by the sound).
2. The time it takes for the sound waves to travel from the boy to each wall and back must be the same. This means that the distance between the two walls must be effectively twice the distance from the boy to either wall.
Let's calculate the distance between the walls:
Since the single echo is heard six seconds after firing the rifle, it means that the total time for the sound waves to travel from the boy to one wall and back, and then from the boy to the other wall and back is six seconds.
Let's denote the distance between the boy and each wall as "d" and the distance between the walls as "D."
From our conditions above, we can set up the following equation:
2d + 2d = D
Simplifying the equation, we get:
4d = D
Now, we know that the total time for the sound waves' round trip is six seconds. The time it takes for sound to travel a certain distance can be calculated by dividing the distance by the speed of sound.
So, the equation becomes:
2d/343 + 2d/343 = 6 seconds
Simplifying this equation, we get:
4d/343 = 6 seconds
Now, we can solve for "d" by multiplying both sides by 343/4:
d = (6 seconds) * (343/4)
Calculating this, we find:
d = 514.5 meters
Since the distance between the boy and each wall is "d," the distance between the walls is twice that value:
D = 2 * d = 2 * 514.5 meters = 1029 meters
Therefore, the distance between the walls is 1029 meters for the boy to hear a single echo from both walls, and the single echo is heard six seconds later.