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

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In summary, the conversation discusses finding the number of identical machines that can be added to a factory without exceeding the 90-dB limit, given that one machine produces a decibel rating of 80 dB. The solution involves calculating the intensity at both 80 dB and 90 dB and realizing that there is a ten-fold increase in intensity for a 10 dB increase in decibels. This leads to the conclusion that nine identical machines can be added to the factory without exceeding the limit.
  • #1
j.c
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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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  • #2
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).
 
  • #3
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
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:
 
  • #5
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
No worries. :smile: The only embarrassment is not to try. :biggrin:
 

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

1. What is the difference between sound and noise?

Sound refers to the vibrations that travel through the air and can be heard by the human ear. Noise, on the other hand, is any unwanted or unpleasant sound that can cause discomfort or harm.

2. How is sound measured?

Sound is measured in decibels (dB), which is a unit of measurement for the intensity of sound. A decibel meter is used to measure the sound pressure level (SPL) in a particular area.

3. What is the decibel scale?

The decibel scale is a logarithmic scale that measures sound intensity. It is based on the human perception of sound, where a 10 dB increase is perceived as a doubling of loudness.

4. How does sound decibel change affect the human ear?

Exposure to high levels of sound decibel can cause damage to the delicate structures in the inner ear, leading to temporary or permanent hearing loss. It is important to protect our ears from excessive noise levels to prevent hearing damage.

5. Can sound decibel changes be harmful to the environment?

Yes, sound decibel changes can have a negative impact on the environment. Loud and constant noise pollution can disrupt wildlife, causing stress and affecting their behavior. It can also have detrimental effects on the health and well-being of humans.

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