DB(decibals) and sound Intensity

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Homework Help Overview

The discussion revolves around understanding the relationship between sound intensity and decibel levels, specifically how the intensity of sounds at 2 dB, 3 dB, and 4 dB compares to that of a 1 dB sound. Participants are exploring the logarithmic nature of decibels in relation to sound intensity.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to understand the ratio of intensities corresponding to different decibel levels and are questioning the correct application of the logarithmic equation for sound intensity. There are inquiries about how to express these relationships mathematically and concerns about the implications of lower decibel levels.

Discussion Status

Some participants have provided insights into the logarithmic relationship between power and decibels, while others are still seeking clarity on the equations needed to solve the problem. The conversation reflects a mix of understanding and uncertainty, with no explicit consensus reached yet.

Contextual Notes

Participants note the absence of answers in textbooks and express confusion regarding the equations related to decibels and sound intensity, particularly when considering values lower than 10 dB.

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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