Sound Question

[Mr. Study]

Hey guys,

I'm just curious as to how someone would work out this question. (From Heinemann 2 Physics)

The sound from a pneumatic drill is 1.0mW m^-2 at a distance of 1.0m. Assume that the sound spreads out equally in all directions.

a) Calculate the intensity, at a distance of 10m.

B) What is the sound level, at a distance of 10m?

The worked solutions are confusing. :S

Thanks!

[Lasercookie]

The sound from a pneumatic drill is 1.0mW m^-2 at a distance of 1.0m. Assume that the sound spreads out equally in all directions.

Watts per sq. metre is the units for intensity.

So the inverse square law:

So if we have and
and

We know that
and

We can easily get this expression for the ratio between and from that



Sub in and solve for I_2








So the sound intensity level refers to the decibel scale. We know the sound intensity at 10m, so it's just a matter of subbing in.



is the intensity of the source, is the intensity of the reference source.

For the decibel scale, the reference intensity is . Note that if you want to compare the difference between two sound levels, you can sub in I_1 as one intensity, and I_0 as another sound intensity. I'd recommend playing around with the logs laws / subbing in stuff and see what you can get out (you should be able to show what happens for those increase by a factor of 10 etc.)

Anyway: