DB(decibals) and sound Intensity

In summary: Actually, I think you were trying to solve for P3 in terms of P2... But if you have learned how to use logs you can solve for P3/P2 that way.)In summary, the question is asking for the ratio of the intensity of a 2dB, 3dB, and 4dB sound to the intensity of a 1dB sound, and this can be found by using the equation 10 log(P2/P1) where P2 is the higher intensity and P1 is the reference intensity.
  • #1
Hellohi
42
0

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.
 
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  • #2
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?
 
  • #3
I thank you very much for your help. I'm trying to understand it and I am sure I will soon.
 
  • #4
Hi, thanks for the info, what about if they are lower than 10 dB? and um idk any other equations to solve it.
 
  • #5
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...
 
  • #6
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)?
 
  • #7
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.
 
  • #8
Thank you too, root for your help.:approve:
 
  • #9
rootX said:
10 log(0.1 P1/P1)?

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

1. What is the relationship between decibels and sound intensity?

The decibel scale measures the sound intensity or loudness of a sound. It is a logarithmic scale, meaning that a small change in decibel level corresponds to a large change in sound intensity. In general, the higher the decibel level, the louder the sound.

2. How is sound intensity measured in decibels?

Sound intensity is measured using a decibel meter. This device measures the pressure level of sound waves and converts it into a decibel reading. The decibel scale starts at 0, which is the threshold of human hearing, and can go up to 194 decibels, which is the threshold of pain.

3. What is the difference between sound intensity and sound pressure?

Sound intensity is the amount of energy per unit area that is being transmitted through sound waves. Sound pressure, on the other hand, is the force per unit area that is exerted by sound waves on a surface. While sound intensity is measured in watts per square meter, sound pressure is measured in pascals.

4. How do different decibel levels affect human hearing?

Exposure to high decibel levels can cause damage to our hearing. Prolonged exposure to sounds above 85 decibels can lead to noise-induced hearing loss. A sound at 85 decibels is equivalent to heavy city traffic, while a sound at 120 decibels is equivalent to a rock concert. It is important to protect our ears from loud noises to prevent hearing damage.

5. Can decibels be used to measure all types of sound?

While decibels are commonly used to measure sound intensity, they are not suitable for all types of sound. For example, decibels cannot accurately measure the sound of low frequency or infrasonic waves. This is because the decibel scale is based on the human perception of sound, which is not sensitive to very low frequencies.

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