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

Answer:

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

$40 dB = 10 log\frac{I_2}{I_o} \Rightarrow I_2 = 10^4 \times 1.0 \times 10^{-12}W/m^2 = 10^{-8}W/m^2$

$20 dB = 10 log\frac{I_1}{I_o} \Rightarrow I_1 = 10^2 \times 1.0 \times 10^{-12}W/m^2 = 10^{-10}W/m^2$

$\frac{I_2}{I_1} = \frac{10^{-8}W/m^2}{10^{-10}W/m^2}=100$

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