Question

The threshold of hearing for the human ear ${10^{ - 12}}W{m^{ - 2}}$. This is taken as the standard level. The intensity of sound is $1W{m^{ - 2}}$. It has intensity (in db.)
(A) ${10^{12}}db$
(B) $12db$
(C) $240db$
(D) $120db$

Answer 1

Hint: To answer this question we need to apply the formula of intensity. Once we write the formula we have to put the values from the question into the formula. After the expression is formed we have to evaluate to get the value of ${I_{dB}}$. This will give us the answer to the required question.

Complete step by step answer:
We should know that the intensity in dB is given by:
${I_{dB}} = 10{\log _{10}}\left( {\dfrac{I}{{{I_0}}}} \right)$
Now we have to put the values in the above expression to get:
$
  {I_{dB}} = 10{\log _{10}}\left( {\dfrac{1}{{{{10}^{ - 2}}}}} \right) \\
   \Rightarrow {I_{dB}} = 10 \times 12{\log _{10}}10 \\
   \Rightarrow {I_{dB}} = 120dB \\
 $
Hence we can say that the intensity is 120 dB.

So the correct answer is Option D.

Note: We should know that the hearing threshold is defined as the sound level below the human ear will not be able to detect any sound. In the case of adults the reference level of threshold hearing is 0 dB.
We should also have an idea that a threshold shift is defined as the increase in the hearing threshold with the respect to a particular frequency of sound. The normal hearing for any human being is marked between -10 dB and 15 dB.
The application of hearing thresholds is found in audiometry for studying the hearing behaviour of human beings and mammals.
The symbol used in the answer is dB which is known as decibel. It is the relative unit which is used for the measurement for the corresponding one tenth of a bel. It is expressed as the ratio between one value of the power or we can also say the field quantity with respect to the logarithmic quantity.