DB(decibals) and sound Intensity

[Hellohi]

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.

 

[berkeman]

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?

 

[Hellohi]

I thank you very much for your help. I'm trying to understand it and I am sure I will soon.

 

[Hellohi]

Hi, thanks for the info, what about if they are lower than 10 dB? and um idk any other equations to solve it.

 

[berkeman]

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...

 

[rootX]

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)?

 

[Hellohi]

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.

 

[Hellohi]

Thank you too, root for your help.

 

[berkeman]

10 log(0.1 P1/P1)?

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