Question

What is the intensity of a sound which has a sound level of $35$ dB?

Answer 1

Hint: The sound intensity is the quantity of energy per unit time transported by sound waves in sound wave propagation through a unit area perpendicular to this direction. In different words, sound intensity is the time at which sound energy transfers through the unit area. Its unit is the power per square meter.

Complete answer:
Given: $I (dB) = 35$
$I (dB) = 10 log\dfrac{I}{I_{o}}$
Where, $I_{o}$ represents the intensity which is just audible.
I (dB) represent the sound intensity level.
I is the sound intensity in $Wm^{-2}$ .
$I_{o} = 10^{-12} Wm^{-2}$
Put I (dB) and $I_{o}$ in the above formula. We get,
$35= 10 log\dfrac{I}{10^{-12}}$
$I = 10^{3.5} \times 10^{-12} = 3.16 \times 10^{-9} Wm^{-2}$
$3.16 \times 10^{-9} Wm^{-2}$ is the intensity of a sound which has a sound level of 35 dB.

Additional Information:
Our ears perceive sound intensity as loudness, in the same fashion as our ears perceive a sound's frequency as its pitch. The threshold value of human hearing is $I_{o} = 10^{-12} Wm^{-2}$ . It means that in order for us to "listen to" a sound, not just must it be within our limit of hearing, but it needs sufficient intensity.

Note:
To calculate the sound intensity, it is essential to utilize at least two microphones set close together. The two microphones can be set in a measuring probe side-by-side, face-to-face, back-to-back. The image measuring the sound intensity using a sound intensity probe in two face-to-face measurement microphones was placed together in a support structure.