Sound Intensity

[wambam]

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I don't really understand this question - can someone explain? 🙂

Sound emanating from a particular source travels in all directions. This sound is measured at 20 dB by an observer standing 40 m away. In order to decrease the intensity level to 10 dB, approximately how far from teh source must the observer be?

a. 80 m
b. 126 m
c. 160 m
d. 400 m


I thought that since we need to reduce intensity to the 4th then radius has to double... so that would mean that the answer would be 80m but that's not the case. I don't get it. Can someone explain how and why the answer is 126m? Thank yoou!
BTW this is from EK 1001 Question 660!

 

[cloak25]

I don't really understand this question - can someone explain? 🙂

Sound emanating from a particular source travels in all directions. This sound is measured at 20 dB by an observer standing 40 m away. In order to decrease the intensity level to 10 dB, approximately how far from teh source must the observer be?

a. 80 m
b. 126 m
c. 160 m
d. 400 m


I thought that since we need to reduce intensity to the 4th then radius has to double... so that would mean that the answer would be 80m but that's not the case. I don't get it. Can someone explain how and why the answer is 126m? Thank yoou!
BTW this is from EK 1001 Question 660!

I = P/A (power/unit area)
Intensity = 1/r^2
from 20dB to 10dB intensity decreased by a factor of 10 so r has to increase by sqrt10. sqrt 10 * 40 = 126

 

[kasho11]

Well you need to increase intensity by a factor of 10 right? Well I = P / A, Area = pi r^2. By tripling r^2, that would result in an increase in area of 10, so P / 10A would result in a decrease by a factor of 10.

Haha you jerk beat me to it

 

[chiddler]

yeah my numbers were wrong. cloak25 has it correct, it seems.

 

[wambam]

Thanks! 🙂