Question

The intensity level of sound having intensity I is defined in term\[{{I}_{0}}\]. The threshold intensity of hearing is
\[\begin{align}
  & \text{A}\text{. Intensity level=}\dfrac{I}{{{I}_{0}}}decibels \\
 & \text{B}\text{. Intensity level=}I\times {{I}_{0}}decibels \\
 & \text{C}\text{. Intensity level=}\dfrac{I}{{{I}_{0}}}decibels \\
 & \text{D}\text{. Intensity level=10lo}{{\text{g}}_{\text{10}}}\left( \dfrac{I}{{{I}_{0}}} \right)decibels \\
\end{align}\]

Answer 1

Hint: Sound intensity level is a logarithmic equation of sound intensity relative to some reference intensity. Here we have given the sound intensity relative to \[{{I}_{0}}\] which is our reference intensity. We have found the threshold intensity of hearing in terms of the sound intensity level and for that we will discuss sound intensity and the sound intensity level to get the answer.

Complete step by step answer:
Sound intensity gives us the power which is carried by sound waves per unit area and its direction is perpendicular to the area whereas its level that is sound intensity level is given by logarithmic expression of sound intensity and the reference intensity.
Reference intensity as the name suggests is the intensity relative to which sound intensity is measured.
The unit of sound intensity level is decibels (dB)
The expression for level of sound intensity (or sound intensity level) is given as
\[\text{Intensity level=10lo}{{\text{g}}_{\text{10}}}\left( \dfrac{I}{{{I}_{0}}} \right)decibels\]
The threshold intensity of hearing is the sound level below which humans cannot hear anything that is the level which is not audible to the human ear.
The threshold intensity of hearing is given by the same expression as the sound intensity level.
Hence, the correct answer is D.

Note:
The threshold intensity of hearing is zero as in this case the sound intensity is the same as the reference intensity giving the ratio 1. The logarithm of 1 for base 10 gives us zero value. Therefore below 0 dB for the human ear the sound is inaudible and they cannot hear it.
Sound intensity is also known as acoustic intensity.