Question

Youplace your ear onto a steel railroad track and hear the sound of a distant train through the rails Δt=2.6 seconds faster than you do through the air. The speed of sound in steel is Vs =6100 m/s while in air the speed of sound is Va =343 m/s. Write an equation for the time it takes the sound to reach you through the air if the distance to the train is represented by D.

Answer 1

To calculate the time it takes for the sound to reach you through the air, we need to consider the difference in the speed of sound in steel and air.

Step-by-step explanation:

To calculate the time it takes for the sound to reach you through the air, we need to consider the difference in the speed of sound in steel and air. The time difference, Δt, is given as 2.6 seconds. The speed of sound in steel is Vs =6100 m/s and in air it is Va =343 m/s.

We can use the formula: Distance = Speed × Time. Let the distance to the train be represented by D. The time it takes for the sound to reach you through the air is D/Va and through the steel rails is D/Vs. The difference in time is given as Δt=2.6 seconds.

Using the given information, we can write the equation:

D/Va - D/Vs = Δt

Answer 2

To calculate the time it takes for the sound to reach you through the air, use the equation D / 6100 = D / 343 + 2.6. Solve for D and you get D ≈ 0.154 meters.

Step-by-step explanation:

To calculate the time it takes for the sound to reach you through the air, we need to consider the difference in speeds between sound in steel and sound in air. Let's call the time it takes for the sound to reach you through the steel rails tsteel and the time it takes through the air tair.

Given that tsteel = tair + 2.6 seconds and the speed of sound in steel Vs = 6100 m/s while in air Va = 343 m/s, we can write the equation:

tsteel = D / Vs

tair + 2.6 = D / Va

Substituting the values:

D / 6100 = D / 343 + 2.6

Now, we can solve for D:

343D = 6100D + 343 * 2.6

5757D = 343 * 2.6

D = (343 * 2.6) / 5757

D ≈ 0.154 meters