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Sound Intensity-- just need someone to check my work :)
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?
[itex]\Delta[/itex]B=10 log(I1/I2)
I1/I2=r2^2/r1^2, so [itex]\Delta[/itex]B = 20 log (r2/r1)
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!
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
[itex]\Delta[/itex]B=10 log(I1/I2)
I1/I2=r2^2/r1^2, so [itex]\Delta[/itex]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!