What is the intensity of sound at the pain level of 120 dB?

[needhelp83]

What is the intensity of sound at the pain level of 120 dB? Compare this to that of a whisper at 20 dB?

b=10 log (I/ I0)
120 dB=10 log (I/1)
10^12=(I/ 1)
I= 10^12 W/m^2


b=10 log (I/I0)
20 dB=10 log (I/1)
10^2=(I/1)
I=10^2 W/m^2


The intensity of 120 dB would be 10^12 W/m^2 compared to the whisper with the intensity at 10^2 W/m^2 which equals 10^10 more intense.

Sound good?

 

[OlderDan]

How did I0 become 1? Where did you get that from?

 

[needhelp83]

This is the pain threshold

 

[needhelp83]

This should look better:

SL=10 log(Sl/10)
I=Io10^(sl/10) = (1.0*10-12 W/m^2) = 1 W/m^2


SL=10 log(Sl/10)
I=Io10^(sl/10) = (1.0*10-12 W/m^2) = 1.0*10^-10 W/m^2

 

[OlderDan]

This should look better:

SL=10 log(Sl/10)
I=Io10^(sl/10) = (1.0*10-12 W/m^2) = 1 W/m^2


SL=10 log(Sl/10)
I=Io10^(sl/10) = (1.0*10-12 W/m^2) = 1.0*10^-10 W/m^2

It sounds to me like you are trying to use the answer to find the answer. The things I highlighted in red in your quote are not equalities. I think your first equation was OK, but I_o is not the pain threshold; it is the threshoold of hearing, the 1.0*10-12 W/m^2. If you had used that instead of 1 in your original equation, you would have found the correct value for I. The value you got initially would knock your head off.

http://hyperphysics.phy-astr.gsu.edu/hbase/sound/intens.html