Another question I'm having a hard time grasping; I followed a solution one of the tutors posted involving a similar question, but I have a feeling there is some mistake I am making.

Question

The question asks to find out what the distance should be from a source if you want the noise to drop in intensity to 60.6dB. The original distance was 30m where the intensity was 130dB.

I used the logarithmic equation that converts dB into W/m^2, and found out the ratio of the intensities at 30m and the unknown distance. Then I am using the following ratio, to find the distance:

I2/I1 = (r1^2 / (r2^2

The problem is I'm getting a REALLY large value for the distance >80000, which doesn't seem reasonable to me.

If someone can please confirm whether this is the correct way to do this question, or whether there IS a mistake that can be pointed out, it would be much appreciated. Thank you.

Answer 1

The approach is one way.

Consider this: 3db is 1/2 power loss. If you double the distance, power goes down then by 6db.

YOu want it about 70 db loss, so that is about 11.6 6 db losses, or approx

2^11.6=3100 as far (this is very approximate)
distance on order of 30*3100=93,000 meters, same order of magnitude you have.

I would go with your work.

If you want recheck your work.

Answer 2

I agree with you answer. To decrease sound level by 70 dB, which is a factor or 10^7 in power per area, the source has to be 10^3.5 = 3160 times farther away.

Using a db difference of 69.4 dB, I get a distance requirement of about 88,000 m