# Question dd2a2

Mar 28, 2017

Let us first of all understand what is meant by Loudness of sound.

Loudness of sound is a subjective term which describes the strength of perception of ear of a sound signal. In other words it is psycho-physiological correlation of amplitude of the sound by ear-brain combination.

Though loudness is related to sound intensity but it can not be considered identical to intensity of sound being heard, as the relationship is not linear. The magnitude of loudness sensation is known to be proportional to the logarithm of the physical stimulus which produced it.

Unit of loudness of sound is decibel, dB. A decibel expresses the relative intensity of sound on a scale from zero, (average least perceptible sound) to around 100 dB, (the level most people find uncomfortably loud). Normal speech is around 50 to 60 dB.
Mathematically Loudness or Acoustic intensity level $L$ is given as
$L = 10 \log \left(\frac{I}{I} _ 0\right) \text{dB}$
${I}_{0}$ is taken as $1 {\text{ pWm}}^{-} 2$ as reference.

It can also be stated in terms of Sound pressure Level $p$ as

$L = 20 \log \left(\frac{p}{p} _ 0\right) \text{dB}$
${p}_{0}$ in air is taken as $= 2 \times {10}^{-} 5 \text{ Pa" = 20 µ"Pa}$ as threshold of hearing.

Given is atmospheric pressure $= {10}^{5} \text{ pa}$, density of air is $1.3 {\text{ kgm}}^{-} 3$ and speed of sound is $340 {\text{ ms}}^{-} 1$

We know that
Intensity of Sound I= 2π²n²A²ρv
where, $n$ is frequency of sound, $A$ is the amplitude of sound wave, $v$ is velocity of sound, and ρ# is density of medium in which sound is traveling.

In the absence of either sound pressure generated or Amplitude of the sound wave, Loudness can not be calculated.