Question

Two friends whisper at a volume of 20 decibels. Later, they converse at a volume of 40 decibels.

How much greater is the energy intensity of the conversation compared to the whisper?
A.20 times
B.10 times
C.1,000 times
D.100 times

Answer 1

40 dB is 20 dB more power than 20 dB is. 20 dB more means 100 times as much.

Answer 2

Step-by-step explanation:

The sound intensity is given by:

I (dB) = 10 log(I/Io)

Where I is the intensity in W/m²

Io = 1.0 × 10⁻¹² W/m²

`40 dB = 10 log(I_2)/(I_o) \Rightarrow I_2 = 10^4 * 1.0 * 10^(-12)W/m^2 = 10^(-8)W/m^2`

`20 dB = 10 log(I_1)/(I_o) \Rightarrow I_1 = 10^2 * 1.0 * 10^(-12)W/m^2 = 10^(-10)W/m^2`

`(I_2)/(I_1) = (10^(-8)W/m^2)/(10^(-10)W/m^2)=100`

Thus, the conversation would have 100 times greater than the whisper.