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 1.7 s apart. How far away did the impact occur?
You did not give me the speed of sound in air and in concrete
call air va and concrete vc
d = va t
d = vc (t-1.7)
so
va t = vc t - 1.7 vc
t (vc-va) = 1.7 vc
solve for t
then
d = va t
To determine the distance at which the impact occurred, we can use the speed of sound in air and the speed of sound in concrete.
Let's start by finding the time it takes for sound to travel through air and concrete separately. We know that the time difference between the two sounds is 1.7 seconds.
Let's assume the speed of sound in air is approximately 343 meters per second (this value may vary slightly depending on various factors like temperature and humidity). Therefore, the sound that traveled through the air covered a distance of 1.7 x 343 = 582.1 meters.
Now, we need to calculate the speed of sound through concrete. The speed of sound in concrete is generally higher than in air. Let's take an approximate value of 5000 meters per second for the speed of sound in concrete.
Since the two sounds originated from the same impact, the time taken by the sound traveling through the concrete should be equal to the time difference of 1.7 seconds. Using this information, we can calculate the distance:
Distance = Speed × Time
Distance = 5000 × 1.7 = 8500 meters
Therefore, the impact occurred approximately 8500 meters away.