Decibel question, not sure where I went wrong.

[TheKShaugh]

Homework Statement

At a rock concert the fans in the front row are bombarded with 113 dB of sound. How many rock bands playing simultaneously at this level would be required to reach or exceed the pain threshold (120 dB)?
The answer has to be an integer. (Fractional rock bands don't exist ...)

Homework Equations

Db = 10log(I/I_ref)

The Attempt at a Solution

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I started by finding the intensity (in W/m^2) of the band using I_ref of 1E-12 W/m^2. That number was 0.1995 Then I found the intensity that would be needed to produce 120 decibels, which was 5 times greater, but that answer was marked wrong. It makes sense to me though, and when I check how many decibels 5x.01995 W/m^2 would produce, I get 120. Where did I go wrong on this one?

Thanks!

 

[jbriggs444]

First, there is no need to convert to W/m² and then back to decibels. There is an easier way.

Second, the question hints that the answer will need to be converted to an integer. Does 120 decibels involve exactly 5 times the power of 113 decibels?

 

[TheKShaugh]

First, there is no need to convert to W/m² and then back to decibels. There is an easier way.

Second, the question hints that the answer will need to be converted to an integer. Does 120 decibels involve exactly 5 times the power of 113 decibels?

It doesn't involve exactly 5, no, it's actually 5.01 and when I put in 6 as the answer I was told it's correct. You say there's a better way, I guess you mean by taking the 113 decibels as the reference and just having 10^(7/10)? I don't really know the ins and outs of the equation, would you be able to explain it?

 

[jbriggs444]

Yes, that is exactly what I had in mind. 120 decibels is $10^\frac{7}{10}$ times the power of 113 decibels.