Question

You purchased a new set noise-cancelling headphones to wear on your plane ride to Hawaii last month. The intensity of the background noise on the plane (prior to wearing the headphones) was 4 x 10-2 w/m2. When wearing the headphones, the intensity of the noise was reduced to 2 x 10-3 w/m2. How much noise reduction (in dB) did the headphones provide?

Answer 1

Answer:

$gain_{db}=-10_{db}$

Explanation:

Let's analyze the gain of the noise when wearing the headphones, in this case the gain has to be under 1.

$gain=\frac{N_{after}}{N_{before}}\\\\gain=\frac{2*10^{-3}W/m^2}{4*10^{-2}W/m^2}}\\\\gain=0.1$

In order to convert it to decibels we need to apply the next formula:

$Gain_{db}=10log(gain)\\gain=-10_{db}$