How many machines can a factory add before exceeding the 90-dB limit?

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A factory machine produces 80 dB, and the goal is to determine how many identical machines can be added without exceeding a 90 dB limit. The intensity corresponding to 90 dB is ten times greater than that of 80 dB, indicating a tenfold increase in sound intensity. Since one machine is already in place, adding nine more machines will keep the total sound level within the limit. The discussion emphasizes understanding the relationship between decibel levels and sound intensity. The conclusion is that nine additional machines can be added without surpassing the 90 dB threshold.
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Homework Statement


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?


Homework Equations


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


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.
 
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j.c said:

Homework Statement


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?

Homework Equations


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

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.

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).
 
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
 
j.c said:
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

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 ____. :biggrin:
 
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. :)
 
No worries. :smile: The only embarrassment is not to try. :biggrin:
 
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