Change in sound intensity over distance

titans2206

1. The problem statement, all variables and given/known data
You are standing in between two sets of railroad tracks. On one set of tracks a train is initially 200 m away and approaching you with a constant speed of v0 = 11 m/s. On the other set of tracks second train is at the same distance and moving away from you at the same constant velocity. Both trains are blowing their horns. The output power of each horn is the same and the frequency of each horn is 440 Hz. Take the velocity of sound in air to be vair = 343 m/s.

Calculate the time it will take for the sound intensity from the approaching train at your position to increase by 2 dB?

Calculate the distance of the receding train from your position when its sound intensity has decreased by 6 dB?


2. Relevant equations
I=P/4πr²
dB=10log(I/I₀)

3. The attempt at a solution
Not really sure where to start, I do not know how to get dB into power so that I can use the first equation. Once I find the distance I know how to find the time, but I am having trouble relating distance to change in decibels.

Spinnor

Start with I(r) = P_o/4∏r^2

I0 = I_o = I(r_o) = P_o/4∏r_o^2

now use dB=10log(I/I0)

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