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.
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.
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.
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
Based on your explanation, it seems like you are on the right track, but there might be a mistake in your calculation. Let me walk you through the correct steps to find the distance at which the noise drops to 60.6 dB.
To solve this problem, you can use the inverse square law, which states that the intensity of sound decreases inversely with the square of the distance. Here's how you can do it:
1. Convert the dB values to intensities using the logarithmic equation you mentioned. Remember that the equation is: Intensity = 10^(dB/10). So, for the initial distance of 30m, the intensity is 10^(130/10) W/m^2, and for the unknown distance, you want to find the intensity that corresponds to 60.6 dB.
2. Calculate the ratio of the intensities using the formula: I2/I1 = (r1^2)/(r2^2), as you correctly mentioned. Let's call the unknown distance "d." So, the ratio becomes (30^2)/(d^2).
3. Set up the equation using the ratio calculated in the previous step and the intensities. It should look like: Intensity at 30m / Intensity at d = (30^2) / d^2.
4. Substitute the known values into the equation. The intensity at 30m is 10^(130/10) W/m^2, and the intensity at d is 10^(60.6/10) W/m^2.
5. Solve the equation for d. Cross multiply the equation and then take the square root of both sides to isolate d.
By following these steps correctly, you should obtain a reasonable value for the distance at which the noise drops to 60.6 dB. If you are still getting a very large value, double-check your calculations to ensure there are no errors in your arithmetic or the substitution of values.
I hope this helps! Let me know if you have any further questions.