Question

You place 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. use the difference in these two times to write an equation for the distance to the train.

Answer 1

To calculate the distance to the train from the difference in hearing the sound through steel and air, set up an equation based on the different sound speeds and solve for distance.

Step-by-step explanation:

To calculate the distance to the train using the difference in sound travel times through steel and air, we can set up two equations to represent the time it takes for the sound to travel those two paths. We'll use distance = speed × time for both equations.

Let the distance to the train be represented by d. The time it takes for sound to travel through steel to your ear is t_steel = d/vs and through the air t_air = d/va. According to the problem, hearing the sound through steel is δt = 2.6 seconds faster than through air, which gives us:

t_air - t_steel = δt

By substituting the expressions for t_air and t_steel and rearranging the equation, we get:

d/va - d/vs = δt

d(va - vs) = δt * va * vs

If we solve for d, we get the final distance to the train:

d = (δt × va × vs) / (va - vs)

Substituting known values:

d = (2.6 × 343 × 6100) / (6100 - 343)

Your final answer then is the calculated value of d.