Sound intensity level, decibels

[jehan4141]

A student typing in a computer cluster generates a sound level of 55 dB. What will the dB level the night before essays are due when there are 30 equally noisy students working in the cluster?

dB_o = 55
I_hearing = 1E-12 W/m²

B_o = 10log(I/I_hearing)
55 = 10log(I/I_hearing)
55 = 10log(I/1.0E-12)
I = 3.16227766E-7 W/m²

If there are 30 other individuals, this makes a total of 31 individuals.

I_total = 31 x I = 31 x 3.16227766E-7
I_total = 9.80E-6 W/m²
B_total = 10log(I_total/I_hearing) = 10log(9.80E-6/1E-12)
B_total = 69.91 dB ?

The answer says that it is 63.8 dB. Please can somebody help me find where in my logic I have failed? Thank you so very much everyone!

 

[Pythagorean]

looks like a matter of significant figures to me. You are being more numerically accurate than the book. Try rounding your answers to only two or three significant figures and see how it compares.

 

[jehan4141]

It is definitely not a matter of significant figures. Even when I tried your suggestion I still get very close to my original answer. Can anybody else please confirm if this thought process is at least correct? Thank you again.