Question

How much more intense is a 20-dB whisper than the threshold of human hearing?

Answer 1

Hint: Decibel is the unit of measuring the intensity of sound.
The threshold of human hearing is assigned as 0 (zero) Decibels
The decibel scale follows the logarithmic expansion of values

Complete answer:
As discussed in the hint the decibel scale of sound measurement follows the logarithmic function of base 10.
The logarithmic scale of base 10 simply means the increase in 1 point just doubles the intensity or we can say that a 10-point increase raises the intensity 10 times. The threshold of human hearing is given the value of 0dB, and the decibel scale is a logarithmic one, such that an increase of 10 dB increases the intensity 10 times i.e. new intensity is 10x of the previous.
Now in this question, the given value is 20 dB and we know that 10-point increase raises the intensity by 10 times so here we are having 20dB which means the intensity is increased twice by 10.
So, the increased intensity will be \[\left( {10 \times 10} \right)x = 100x\]
So, the new intensity will be 100 times more powerful than the original.
So, the 20-dB whisper will be 100 times more than the threshold of human hearing (0dB).

Note:
A logarithmic scale is used when there is a large range of quantities. It is based on orders of magnitude, rather than a standard linear scale, so each mark on the decibel scale is the previous mark multiplied by a value.
Any sound above 85 dB can cause hearing loss.
Each 10dB increase in sound increases its intensity by 10 times so, a 20dB increase will be $10 \times 10 = 100$times