A person, with his ear to the ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 2.7s apart. speed of sound in air is 343 m/s and concrete is 3000 m/s
To solve this problem, we can use the formula:
time = distance / speed
Let's break down the information given in the question:
1. The time difference between the two sounds is 2.7 seconds.
2. The speed of sound in the air is 343 m/s.
3. The speed of sound in concrete is 3000 m/s.
First, let's find the distance traveled by the sound in the air and in the concrete:
Let's assume that 'd' represents the distance traveled by the sound in the air, and 'D' represents the distance traveled by the sound in the concrete.
In the air:
time = d / speed of sound in air
2.7 = d / 343
In the concrete:
time = D / speed of sound in concrete
2.7 = D / 3000
Now we have a system of two equations with two unknowns.
We can solve these equations simultaneously to find the values of 'd' and 'D':
From the first equation:
2.7 = d / 343
Multiply both sides by 343:
2.7 * 343 = d
d = 926.1 meters
From the second equation:
2.7 = D / 3000
Multiply both sides by 3000:
2.7 * 3000 = D
D = 8100 meters
Therefore, the sound traveled a distance of 926.1 meters in the air and 8100 meters in the concrete.