Sound Intensity Level

Question

The question is:

The noise from a vacuum cleaner is 85 dB while that from a television set is 78 dB. What is the intensity level of the two sounds together?

i can't find the right formula.

thanks.

Answer 1

Hint:

dBs are logarithmic and so can't be manipulated directly.

Express them on a linear scale, do the addition and then covert back to dB.

Answer 2

The formula is $$10\log(10^{[\text{dB of sound 1}]/10} + 10^{\text{[dB of sound2]}/10})$$ where Log(x) is the base-10 logarithm. Plugging in your numbers we get $85.790097$ dB