Re: Are there traffic noise pollution equations?

The Question:
Are there traffic noise pollution equations?
I am studying Noise Pollution, and am highly interested in any equations that 
may relate the type of vehicle, acceleration, velocity, and/or distance from 
source to sink to the external noise produced by the vehicle.  The quantity 
must be measured in dB(A).

The answer:

Definitely, this is a very good question. It was even a good question for me 
because I was forced to open the textbooks about sounds I used to read before, 
and remember these equations.

First of all, sound is a mechanical wave, that propagates through a medium; 
this medium may be air, where the speed of sound reaches 340 m/s, or may be 
water (V=1480 m/s), and solids (V=5200 m/s). when waves propagate, they cause 
disturbance in air pressure, this is termed as compression and rarefaction. The 
main equations that govern this part are:
V=(Elasticity  modulus of the medium / Density )^(1/2) -> (1)
V= frequency X wave length.           -> (2)

Thus as you see, the frequency, which is the number of complete wave lengths 
that happen in one second, is a key factor in determining the speed of the 
sound in the medium. 

Let’s shift to the other side, with some definitions. The first definition is 
Intensity of the wave (I), which is the power per unit area. 
I= Power / Area   -> (3)
Thus it is the rate at which sound flows through a unit area A perpendicular to 
the direction of the wave propagation. There is another equation that says:
P = (pi)(density X velocity X (frequency X Amplitude )^2)   -> (3)
(pi = 22 / 7) 
Then the power is equal to that above mentioned equation; from which we can get 
an equation for the intensity. 
The second part is to link the previous equation with the Decibels level.
The equation says:

dB = 10 log (I/I0) ->(4)
where I0 is called the threshold of hearing, which is the minimum sound 
intensity that that human ear can distinguish. This value I0 = 10 E-12  
Watt/m^2. 

Finally, let us transfer to the final point; after which we will link all these 
equations together. The final part is a famous concept called: Doppler effect. 
Its definition is:
"Doppler effect is experienced whenever there is a relative motion between the 
source and the observer. When the source and observer are moving towards each 
other, the frequency heard by the observer is higher than the frequency of the 
source. When the source and the observer move away from each other, the 
observer hears a frequency which is lower than the source frequency". (Serway: 
464)

you can feel Doppler effect with ambulances and police cars, when they approach 
towards you, or go away. You will note the change in their frequency and hence 
their noise level. 
Doppler’s equation says:
1-If we have a stationary source and observer moving away from it:
relative frequency = original frequency X ( 1 - (relative speed between the 
observer and the source / sound velocity ) )
The negative sign turns to be positive when the observer is moving towards the 
source .
2-If the observer is stationary, while the source is in motion:
relative frequency = original frequency/ (1 -  (relative speed between the 
observer and the source / sound velocity ))
The negative sign turns to be positive when the source is moving towards the 
observer.
3-Both are moving toward each other:

f’ = f ( (V +Vo)/(V-Vs))
f’ is the relative velocity
V= speed of sound
Vo= Observer speed
Vs= Source speed

Signs will be reversed in case they are moving in opposite directions.

From all this dilemma, what do we get?
First know the speed of the source and the observer, and second determine the 
frequency. Then calculate the power and followed by the intensity. Usually the 
area is taken to be your ear drum area !!! Then calculate the dB level due to 
the moving object. 

There more points I want to add; however they are not closely relevent to your 
question but to sound in general. Anyway, I am ready to receive your questions 
ins the future.

Looking forward to your reply,

Moataz Attallah
Undergraduate, Mechanical Engineering Junior
The American University in Cairo
mizoa@aucegypt.edu
References:

Abbott, A.F. Ordinary Level Physics. Heinemann Educational Books, London. 
Fourth edition 1984.

Serway, Raymond. Physics for Scientists and Engineers. Saunders Collage 
publishing, USA. Third updated edition 1990.