# The front row of a concert has a sound level of 120 dB and an IPod produces 100 dB. How many IPods would be needed to produce the same intensity as the front row of the concert?

Apr 13, 2015

Since the $\mathrm{dB}$-scale is logarithmic, it turns multiplying into adding.

Originally it was the $B e l l$-scale, purely logarithmic, where "times 10" is translated into "plus 1" (just like normal logs). But then the steps became too big so they divided the $B e l l$ in 10 parts, the $\mathrm{de} c i B e l l$.
The levels above could well have been called $10 B$ and $12 B$.

So now, ten times the sound means adding $10$ to the $\mathrm{dB}$'s, and vice versa.

Going from 100 to 120 equals 2 steps of ten.
These are equivalent to 2 times multiplying by 10.

Answer : you will need $10 \cdot 10 = 100$ iPods