How Do You Calculate Sound Intensity from a Decibel Level?

AI Thread Summary
To calculate sound intensity from a decibel level, the equation IL = 10 log(I/I0) is used, where I0 is the reference intensity of 10^-12 W/m^2. A sound level of 45 dB corresponds to an intensity calculation that yields 3.16 x 10^-8 W/m^2. However, the correct intensity should be 31.6 W/m^2, indicating a potential unit conversion error. The discrepancy may arise from mixing up units, suggesting that the correct solution could be in nanowatts per meter squared. Understanding the correct application of the formula and unit conversions is crucial for accurate calculations.
alkhan22
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Homework Statement



A sound-level meter placed 150 mm from a small sound source records a reading of 45dB. What is the intensity at that point.

Homework Equations



I m using this equation IL = 10 log(I/I.) where I. is the lowest intensity i think which should be 10^-12 W/m^2.

The Attempt at a Solution



I have used the above equation to find the intensity but i get different answer which is 3.16 x 10^-8. but the correct answer given is 31.6 w/m square.

I will be very thankful if some body can hel as this is my 1t question in this forum. please let me know if i have missed something.
 
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can you show how you arrived at your answer?
 
this is how i got my answer.

45= 10[logI - Log10^-12]
4.5= LogI +12
-7.5 = log I

BECAUSE THE BAS WAS 10 SO

10^-7.5 = 3.1622 X 10^-8
 
that looks correct. it seems that the problem is one of mixing up units. the correct solution you have may be in units of nanowatts per meter squared.
 
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