Question

The power, or loudness, of sound is measured on a scale of increased by a factor of $100\left( { = {{10}^2}} \right)$, the sound is called twice as loud and when it increases $10,000\left( { = {{10}^4}} \right)$ times it is called four times as loud. The exponent of ten is called a bel and one decibel is one-tenth of a bel. Zero decibels is chosen as the intensity of the slowest sound which is just audible or is on the threshold of hearing whereas the intensity of the loudest sound is about 170 decibels. A sound of 60 decibels is ___ times more intense than a sound of 40 decibels:
A. 20
B. 100
C. ${10^{20}}$
D. None of these

Answer 1

Hint: A sound is a wave, which is made up of vibrations in the air. The loudness of a sound refers to how loud or soft a sound seems to a listener. The loudness of sound is determined, by the intensity, or amount of energy, in the sound waves. The unit of intensity is the decibel (dB). As decibel levels get higher, sound waves have greater intensity and sound gets louder.
Formula Used:
$L = 10{\log _{10}}\dfrac{I}{{{I_ \circ }}}$

Complete step-by-step solution
Let us assume the loudness of the two sounds to be given as
${L_1} = 40dB$ and ${L_2} = 60dB$
The loudness of sound ‘L’ is given as,
$L = 10{\log _{10}}\dfrac{I}{{{I_ \circ }}}$
$ \Rightarrow {L_2} - {L_1} = 10{\log _{10}}\dfrac{{{I_2}}}{{{I_1}}}$
$ \Rightarrow 60 - 40 = 10{\log _{10}}\dfrac{{{I_2}}}{{{I_1}}}$
$ \Rightarrow {\log _{10}}\dfrac{{{I_2}}}{{{I_1}}} = 2$
$\therefore \dfrac{{{I_2}}}{{{I_1}}} = {10^2} = 100$
Hence, a sound of 60 decibels is 100 times more intense than a sound of 40 decibels.

Additional Information:
The sound which we hear around us is known to be the energy generated by the vibration that moves through the air or any other medium. There are three characteristics of sound:
1) Pitch: It is a feature of sound with the help of which we can distinguish whether a sound is ‘higher’ or ‘lower’.
2) Quality: It is also known as the ‘timbre’, it allows the ear to distinguish sounds, which have the same pitch and loudness.
3) Loudness

Note: The phenomenon of a sound depending upon the amplitude of the sound wave is known as the loudness of the sound. When the amplitude of the sound wave is large, then the sound is said to be loud. The loudness of a sound is said to be directly proportional to the square of the amplitude of the vibration. When the amplitude of the sound wave is doubled, then the loudness of the sound gets quadrupled. It is expressed in decibel (dB). Sounds above 80 dB become noisy to the human ears.