DB(decibals) and sound Intensity

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SUMMARY

The discussion centers on calculating the intensity ratios of sound levels measured in decibels (dB). The key equation used is Value in dB = 10 log(P2/P1), where P1 is the reference power. Participants clarify that for every 10 dB increase, the power increases tenfold. The inquiry specifically addresses how to determine the intensity difference between 1 dB and higher levels such as 2 dB, 3 dB, and 4 dB, emphasizing the need to derive equations for these comparisons.

PREREQUISITES
  • Understanding of logarithmic functions
  • Familiarity with the concept of sound intensity
  • Knowledge of the decibel scale
  • Basic algebra for solving equations
NEXT STEPS
  • Study the relationship between sound intensity and decibels using the formula Value in dB = 10 log(P2/P1)
  • Explore how to calculate intensity ratios for various dB levels
  • Learn about sound intensity levels below 0 dB and their implications
  • Investigate real-world applications of sound intensity measurements in acoustics
USEFUL FOR

Students studying physics, audio engineers, and anyone interested in understanding sound intensity and decibel calculations.

Hellohi
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Homework Statement


How much greater than the intensity of a 1 dB sound is the intensity of a:
2dB sound?
3dB sound?
4dB sound?


Homework Equations


10pW/m^2 = 10 dB


The Attempt at a Solution


Hey guys, this question doesn't have an answer in my textbook i think you have multiply them all by 10 but I am not sure. Thanks for any help.
 
Last edited:
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Hellohi said:

Homework Statement


How much greater than the intensity of a 1 dB sound is the intensity of a:
2dB sound?
3dB sound?
4dB sound?


Homework Equations


10pW/m^2 = 10 dB


The Attempt at a Solution


Hey guys, this question doesn't have an answer in my textbook i think you have multiply them all by 10 but I am not sure. Thanks for any help.

Welcome to the PF.

I'm not sure what you mean by the equation 10pW/m^2 = 10 dB

But the key in this question is that they want to know the ratio of the intensities for each of those new levels.

The relevant equation for intensity (power) is this:

Value in dB = 10 log( P2/P1 ) (where P1 is typically the reference power)

That is, for each 10x increas in power, your value in dB goes up by 10. So

10dB = 10 log(10 P1/P1)

20dB = 10 log(100 P1/P1)

30dB = 10 log(1000 P1/P1)

And so on.

In your question above, they are asking about smaller increases in power. So you have a power P2 that compared to the reference power P1 is 1dB. Then you have a higher power P3, that compared to the reference power P1 is 2dB, and they are asking you to give the ratio of the powers P3/P2... Can you write the equations to be able to solve that part of the question?
 
I thank you very much for your help. I'm trying to understand it and I am sure I will soon.
 
Hi, thanks for the info, what about if they are lower than 10 dB? and um idk any other equations to solve it.
 
Hellohi said:
Hi, thanks for the info, what about if they are lower than 10 dB? and um idk any other equations to solve it.

Write the two equations:

1dB = ?

2dB = ?

In terms of the powers that I mentioned, P1, P2 and P3. Then look at those two equations to see if you can solve for the ratio of P3/P2...
 
Hellohi said:
Hi, thanks for the info, what about if they are lower than 10 dB? and um idk any other equations to solve it.

10 log(0.1 P1/P1)?
 
Ok, I think I get, thank you very much for your help. I am glad that I can use this site as I am a beginner in Physics.
 
Thank you too, root for your help.:approve:
 
rootX said:
10 log(0.1 P1/P1)?

That would be -10dB. Why did you ask that?
 

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