# Find the loudness of a moving object at a certain distance

1. May 20, 2014

### ichivictus

1. The problem statement, all variables and given/known data
An object emitting a sound with a 400hz frequency is thrown 10m away and passes right next to you. At 10m away, you can barely hear the object and you have average hearing. When the object passes you, you observe a sound with a frequency of 435hz.

Find the loudness in dB when the object was 2 meters away. Assume the object was headed straight towards you.

2. Relevant equations
L = 10 log(I/Io) = 20 log(P/Po)
Io = 10-12 W/m2
I = Pav/A = 1/2 Po2/ρv

Doppler's Effect:
fs (v/(v-vo)) = fr
v = speed of sound ≈ 343 m/s

3. The attempt at a solution
So to solve for this I need to solve for I with little information. To solve I believe I will need to solve for the initial velocity of this object.

Solving for vo

vo = v - fsv/fr = 343m/s - 400hz/435hz * 343 m/s = 27.6 m/s

Would Po be the amplitude of the sound wave? I'm really not sure how to tackle this problem. I think that since you can barely hear it at 10m away means something too. That means that initially the loudness is 0dB.

λ = v/f = 343m/s / 400hz = .8575m

Really not sure what I am doing. Any help would be appreciated!

2. May 20, 2014

### haruspex

"When the object passes" is a bit vague. Seems like it should mean when it is level with you, but then there would be no Doppler effect, so you should hear it as 400Hz, no? So I guess it means when it is just about to reach you.
But in that case I don't understand why the 400Hz or the object's speed are of interest. Wouldn't the perceived pitch be the same at all distances? Maybe all that information is just to confuse.
So all that seems relevant are the two distances. If it's 0dB at 10m what is it at 2m?