# Sound and decibel changes

1. Jan 26, 2012

### j.c

1. The problem statement, all variables and given/known data
a noisy machine in a factory produces a decibel rating of 80 dB. how manyidentical machines could you add to the factory without exceeding the 90-dB limit?

2. Relevant equations
I=P/A and B+10log(I/I(sub)0) ... (I think)

3. The attempt at a solution I tried to find the intensity at 80 decibels and the intensity at 90 decibels by solving for I using B=10log(I/I0) and the inverse log equation and got 1 x 10^-4 and 1 x 10 ^-3 respectively. I had no idea where to go from here though.

2. Jan 26, 2012

### Curious3141

OK, you've calculated the intensities, so by what factor is the intensity corresponding to 90dB higher than that corresponding to 80dB?

This question can actually be solved more simply by observing that 90dB - 80dB = 10dB = a ___ fold increase. (I left that blank for you to think about).

3. Jan 26, 2012

### j.c

so then... an increase of 10 dB means that the intensity of the sound is multiplied by a factor of ten right?

but i'm still confused about how to get the number of machines that can be added

4. Jan 26, 2012

### Curious3141

Great! That's correct.

OK, so you can squeeze ten machines there (and still meet the limit), but you only have one. The number of machines you could *add* is ____.

5. Jan 26, 2012

### j.c

oh ok. thank you!! I came to the conclusion of nine after your first post but that seemed almost too simple and i didnt want to embarass myself with a wrong answer haha. :)

6. Jan 26, 2012

### Curious3141

No worries. The only embarrassment is not to try.