Find Pressure amplitude from given decibels

In summary, the conversation discussed finding the pressure amplitude of a sound wave with an intensity level of 49 dB. The correct answer is 0.0056 Pa, with the possibility of online homework sites requiring a specific number of significant digits.
  • #1
Angie_Agnes
23
0

Homework Statement


A sound wave has an intensity level of 49 dB. What is the pressure amplitude of this wave?

Po= 2x10^-5

Homework Equations



β=10log(I/I0)
I≈P^2

The Attempt at a Solution


I can't figure out why I'm getting this problem wrong. So I set it up, 49=10log(I/I0)
-> 4.9=log(I/I0) -> 10^4.9=(I/I0) From there, I replaced the intensity for pressure amp (equation 2) -> p=(2*10^-5)√(10^4.9)
Pamp=.0056Pa

??
 
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  • #2
Hi Angie_Agnes! :smile:

You calculation looks good.
Any reason to doubt your result?
 
  • #3
yes, it's online homework and says it's wrong :(
 
  • #4
Well, I think you have to tweak your result a bit then.
I believe it is numerically correct, but these online homework sites can be a bit difficult with the exact phrasing.
Btw, I'm assuming you did not make a typo in the problem statement...
 
  • #5
I copied and pasted the question, so no typo... I typed it in as .005 Pa and .006Pa and both came up wrong. Frustrating!
 
  • #6
With 2 significant digits in 49 dB, it should be 0.0056 Pa or 5.6 mPa.
I can't make anything else from it.
 
  • #7
THANK YOU! got it right as .0056Pa. Awesome!
 
  • #8
Huh? But that is your original answer from your opening post! :confused:
 
  • #9
I looked back at my past answers, I had entered it .005 and .006 at first, before entering it finally as .0056.
 
  • #10
All is well that ends well! :wink:
 

What is the relationship between decibels and pressure amplitude?

The relationship between decibels (dB) and pressure amplitude is logarithmic. This means that for every increase of 10 dB, the pressure amplitude increases by a factor of 10. In other words, a sound with a decibel level of 80 dB has a pressure amplitude 10 times greater than a sound with a decibel level of 70 dB.

What is the formula for converting decibels to pressure amplitude?

The formula for converting decibels to pressure amplitude is:
PA (in Pascals) = 10^(dB/20)
Where dB is the decibel level.

Can pressure amplitude be negative?

No, pressure amplitude cannot be negative. It is a measure of the magnitude of pressure, and negative pressure does not exist in the physical world. However, the decibel scale can have negative values as it is a relative measure of sound intensity.

Is there a standard reference value for pressure amplitude in decibels?

Yes, the standard reference value for pressure amplitude in decibels is 20 micropascals (µPa). This is equivalent to the threshold of human hearing. Any sound with a pressure amplitude of 20 µPa will have a decibel level of 0 dB.

Can decibels be used to measure pressure amplitude for all types of sounds?

No, decibels are only suitable for measuring pressure amplitude of sounds that are audible to the human ear. For sounds that are below or above the audible range, different units of measurement are used, such as bels or neper. Additionally, decibels are not an accurate measure for measuring pressure amplitude of non-sound waves, such as seismic waves or electromagnetic waves.

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