Question

Name the unit in which the loudness of sound is expressed.

Answer 1

Hint: The loudness of sound is determined by the function of intensity of the sound wave. Loudness of a sound relates the intensity of the sound wave of any given sound to the intensity of sound wave at the threshold of hearing. We will find the expression relating loudness and intensity of sound waves.

Complete step by step answer:
Loudness of Sound means how loud or soft a sound seems to a listener. The loudness of sound is determined by the help of intensity of the sound waves. Intensity of a sound wave is a measure of the amount of energy associated with a sound wave.
Intensity of a sound wave is determined by two factors: the amplitude of the sound wave and how far the wave has travelled from the source of the sound.
Amplitude is a measure of the size of a sound wave. Its value depends on the energy that originated the wave. Greater amplitude waves have more energy associated with them and greater intensity, so they sound louder.
As sound waves travel more distance farther from the source, the energy associated with them becomes more spread out. As distance from the origin or source increases, the area covered by the wave increases and the same amount of energy is spread over a larger area. The intensity and loudness of the sound becomes less. This is the reason; even loud sound fades away as we move farther from its source.
We measure sound intensity, also called the power of sound waves, in units called Decibels. Decibels (dB) are different from other measuring scales. While many standard measuring devices and scales are linear, decibel scale is logarithmic. Using the logarithmic decibel scale, if a sound is 80 decibels and we add another 10 decibels, the sound will be 10 times more intense and we will hear the sound twice as loud as before.
Loudness and intensity are related to each other by the relation:
\[\begin{align}
  & \text{L (in dB)}\propto \text{log}\left( \text{I} \right) \\
 & \text{L (in dB)}=\text{Klog}\left( \text{I} \right) \\
\end{align}\]
Where,
$\text{L}$ is the loudness in decibels
$\text{I}$ is the intensity
$\text{K}$ is a constant
Expression for loudness of Sound:
$\text{L = 10log}\left( \dfrac{\text{I}}{{{\text{I}}_{\text{o}}}} \right)$
Where,
$\text{L}$ is the loudness in decibels
$\text{I}$ is the intensity of sound wave at a specific point
${{\text{I}}_{\text{o}}}$ is the intensity of sound wave at reference point
The loudness of sound is measured in a unit called Decibels.

Note:
Loudness is the subjective perception of sound pressure. The sensation of loudness of sound is not proportional to the energy intensity, but rather a logarithmic function. A decibel unit expresses the relative intensity of sounds on a scale ranging from zero to about 100 decibels, which is near the level that most people find uncomfortably loud to hear.