Question

How many times louder is the intensity of sound at a rock concert in comparison with that of a whisper, if the two intensity levels are  110dB and  3dB, respectively?​

Answer 1

5 × 10¹⁰ or 5 billion times louder is the intensity of sound at a rock concert in comparison with that of a whisper

Step-by-step explanation:

Given that at a rock concert;

the intensity of sound is 110 dB compared to a whisper of 3 dB

Now; how many times louder will that of the whisper be compared to the sound of the rock concert

Using the formula for calculating decibels (dB);

For 110 dB

dB = 10log₁₀(W)

110 dB =
`10^((110/10))`

110 dB = 10¹¹

For 3dB

dB = 10log₁₀(W)

3 dB =
`10^((3/10))`

3 dB = 2

Now:

(110/3)dB = 10¹¹/2

(110/3)dB = 5 × 10¹⁰ or 5 billion times louder is the intensity of sound at a rock concert in comparison with that of a whisper