# Intensities at different distances

1. May 10, 2015

### Ethan_Tab

1. The problem statement, all variables and given/known data
Person A, who is 1.5 meters away from me is speaking to me at a decibel level of 25dB. How loud does person B, who is 15 meters away from me need to speak in decibels to submit me to the same intensity of sound?

2. Relevant equations
Ia/Ib=rb^2/ra^2
∆dB=10log(Ia/Ib)

3. The attempt at a solution
I figured I should start by figuring out the intensity of sound I would be experiencing if someone way 1.5m away from me and speaking at 25dB however, I can't seem to find a way to acount for the distance between me and person A. Any Ideas on how to start? Thanks.

2. May 10, 2015

### Staff: Mentor

Using your first equation, what is the ratio Ia/Ib for this problem? And using your 2nd equation, what is the ∆dB number? And given that the closer speaker is speaking at 25dB, what level does your result imply that the more distant speaker has to speak at?

3. May 10, 2015

### Ethan_Tab

So since the ratio Ia/Ib is 100 we can figure out the ∆dB level:

∆dB=10log(100)
=20

And since person B is farther away then person A is, he will have to speak louder then person A by a factor of 20 decibels.

Do I just add the two decibels now 20+25=45dB? Or do I have to convert both decibel levels to W/m^2, add them and then convert them back into dB which would give me a decibel level of 26.193dB.

4. May 10, 2015

Correct!