How far back to sit for safe sound level at rock concert?

[cep]

Sound Intensity-- just need someone to check my work :)

Homework Statement

While enjoyable, rock concerts can damage people's hearing. In the front row at a rock concert, 5m from the speaker system, the sound intensity is 145 dB. How far back would you have to sit for the sound intensity to drop below the recommended safe level of 90 dB?

Homework Equations

$\Delta$B=10 log(I1/I2)

I1/I2=r2^2/r1^2, so $\Delta$B = 20 log (r2/r1)

The Attempt at a Solution

Plugging into the above equation yields (145-90) = 20 log (r2/5)

Rearranging, r2 = 5*10^[(145-90)/20] = 2812 m. I don't know where I could've made a mistake-- this is a pretty straightforward problem-- but that answer seems unreasonable.

Does it look alright to you?

Thanks!

 

[edgepflow]

This is correct under the simplifying (but not totally correct) assumption that all the sound power from the concert is a concentrated point source.

A better model would be a combination of point sources or a distributed line source.

 

[cep]

Thanks! The course I'm taking makes a LOT of simplifying assumptions haha.

 

[PeterO]

Thanks! The course I'm taking makes a LOT of simplifying assumptions haha.

You can get a rough estimate using the idea that if you double the distance from a sound source, you get a 6dB drop in level.

5m - 145 dB
10m - 139 dB
20m - 133 dB
40m - 127 dB
.
.
.
2560 - 91 dB

so you are after an answer a bit bigger than that, so you are correct.

The question is probably twisted tutor's attempt to tell you to stay away from rock concerts!