Question

The intensity of a sound wave gets reduced by $20$percent on passing through a slab. The reduction in intensity on passing through two such consecutive slabs is-
(A)$20$%
(B)$36\%$
(C)$30\%$
(D)$50\%$

Answer 1

Take initial intensity and then according to the question firstly find reduction in intensity for one slab. Now consider this one as initial for the second case and calculate the reduction in intensity.

Complete step by step answer:
Consider the initial intensity is I and I’ is the new intensity after the passing of the sound wave.
Now, according to the question, $I' = I - \dfrac{{20}}{{100}}I$
$I' = \dfrac{{80}}{{100}}I$
Now, if two consecutive slabs are here, then the intensity is $I''$ which can be calculated by-
$I'' = I' - \dfrac{{20}}{{100}}I'$
$= \dfrac{{80}}{{100}}I\left( {1 - \dfrac{{20}}{{100}}} \right)$
$= \dfrac{{64}}{{100}}I$
$\therefore$ $I'' = 0.64I$
So, percentage reduction intensity on passage through two such consecutive slabs=$\dfrac{{I - 0.64I}}{I}$ %
=$36\%$
So, intensity reduces by $36\%$.

So, the correct answer is “Option B”.

Additional Information:
Additionally we can say that sound is a longitudinal wave which consists of compressions and refractions travelling through a medium. A sound wave can be described by its five characteristics- Wavelength, frequency, amplitude, time-period, velocity or speed. When a sound wave travels from one medium to another medium then the wavelength and velocity of the sound wave decreases whereas frequency remains the same.

Note:
The sensation felt by our ears is known as Sound. Basically it is a form of energy which makes us hear and it travels in the form of waves.
A wave is a disturbance in a medium which carries energy from one point to another without being in direct contact between two points.