Tag: waves

Questions Related to waves

The intensity level due to two waves of the same frequency in a given medium are 1 dB and 4 dB. The ratio of their amplitude is

intensity and loudness waves physics

  1. $1 : 10^4$

  2. $1 : 4$

  3. $1 : 2$

  4. $1 : 10^{0.15}$

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Correct Option: D
Explanation:

Loudness of the sound       $L = 10  log _{10} \dfrac{I}{I _o}$


$L _2 -L _1 = 10  log _{10} \dfrac{I _2}{I _1}$

As  intensity of the wave is directly proportional to the square of the 
amplitude,    i.e       $I   \propto    A^2$

$\implies  $ $L _2 -L _1 = 20  log _{10} \dfrac{A _2}{A _1}$

$4 -  1 = 20  \log _{10} \dfrac{A _2}{A _1}$

Thus   $\dfrac{A _2}{A _1} =   10^{0.15}$

Most of the human ears cannot hear sound of intensity less than :

intensity and loudness waves physics

  1. $\displaystyle 10^{-12} Wm^{-2}$

  2. $\displaystyle 10^{-6} Wm^{-2}$

  3. $\displaystyle 10^{-3} Wm^{-2}$

  4. $\displaystyle 1 Wm^{-2}$

Show answer
Correct Option: A
Explanation:

A human ear can hear a sound of minimum intensity $10^{-12} W/m^2$. This intensity sound corresponds to loudness $0 \ dB$. So, we say that a human ear cannot hear a sound of loudness $0 \ dB$.
A human ear can hear a sound of maximum intensity $1 \ W/m^2.$

The power of a loud speaker is increased from 20 W to 400 W. What is the intensity increase as compared to the original value?

intensity and loudness waves physics

  1. 13 dB

  2. 7 dB

  3. 4 dB

  4. 2 dB

Show answer
Correct Option: A
Explanation:
As intensity of wave is directly proportional to power, i.e $I  \propto   P$
Loudness of sound, $L =  10  log _{10} \dfrac{I}{I _o}$
$\implies    L _2 - L _1 = 10   log _{10} \dfrac{I _2}{I _1}$    
Thus, $  L _2 - L _1 = 10   log _{10} \dfrac{P _2}{P _1}$  
$  L _2 - L _1 = 10   log _{10} \dfrac{400}{20}$  

$  L _2 - L _1 = 10   log _{10} 20        $             $(log _{10} 20 = 1.3 )$ 

$\implies  L _2 - L _1 = 13    dB$

At what sound level headache begins?

intensity and loudness waves physics

  1. 120-125 dB

  2. 100-105 dB

  3. 80-85 dB

  4. 60-65 dB

Show answer
Correct Option: C
Explanation:

headache starts at 80 dB sound for a normal person.

The power , or loudness, of sound is measured on a scale of increased by a factor of 100$(=10^2$), the sound is called twice as loud and when it increases 10,000 $(=10^4)$ times it is called four times as loud. The exponent of ten is called a bel and one decible is one tenth of a bel. Zero decible is chosen as the intensity of the slowest sound which is just audible or is on the threshold of hearing whereas the intensity of loudest sound is about 170 decibel. A sound of 60 decibel is ......... times more intense than a sound of 40 decibel :

intensity and loudness waves physics

  1. 20

  2. 100

  3. $\displaystyle 10^{20}$

  4. none of these

Show answer
Correct Option: B
Explanation:

Loudness of two sounds are given as  $L _2 = 60 \ dB$ and $L _1 = 40 \ dB$

Loudness of sound  $L = 10 \log _{10}\dfrac{I}{I _o}$
$\implies$  $L _2 - L _1 = 10\log _{10}\dfrac{I _2}{I _1}$

Or  $60 - 40  = 10\log _{10}\dfrac{I _2}{I _1}$

Or  $\log _{10}\dfrac{I _2}{I _1} = 2$
Or  $\dfrac{I _2}{I _1} = 10^2 = 100$
Thus $60dB$ sound is $100$ times more intense than $40dB$ sound.

The power , or loudness, of sound is measured on a scale of increased by a factor of 100$(=10^2$), the sound is called twice as loud and when it increases 10,000 $(=10^4)$ times it is called four times as loud. The exponent of ten is called a bel and one decible is one tenth of a bel. Zero decible is chosen as the intensity of the slowest sound which is just audible or is on the threshold of hearing whereas the intensity of loudest sound is about 170 decibel. Sound intensities above a level of nearly descibels produce a feeling of pain :

intensity and loudness waves physics

  1. 60

  2. 120

  3. 140

  4. 170

Show answer
Correct Option: B
Explanation:

A human ear can hear a sound of maximum loudness of $120 \ dB$. Sound intensities above nearly $120 \ dB$ produce pain in the human ear.

The intensity of ordinary conversation is rated as nearly 

intensity and loudness waves physics

  1. 10 decibel

  2. 50 decibel

  3. 40 decibel

  4. 60 decibel

Show answer
Correct Option: D
Explanation:

Human ear can hear sound from 0dB to 140dB. Intensity of ordinary conversation is rated as nearly 60dB.

Two waves of the same pitch have amplitude in the ratio 1 : 3. What will be the ratio of their loudness:

intensity and loudness waves physics

  1. 1:3

  2. 3:1

  3. 1:9

  4. 9:1

Show answer
Correct Option: C
Explanation:

Loudness depends on the square of the amplitude of the wave. 


That is, $loudness\propto { \left( amplitude \right)  }^{ 2 }$

Thus, when the ratio of amplitudes of the wave is 1:3, the loudness becomes 1:9.

In expressing sound intensity, we take $ 10^{-12} Wm^{-2} $ as the reference level. For ordinary conversion, the intensity level is about $ 10^{-6} Wm^{-2} $. Expressed in decibel, this is :

intensity and loudness waves physics

  1. $ 10^6$

  2. $ 6$

  3. $ 60 $

  4. $ log _e(10^6) $

Show answer
Correct Option: C
Explanation:

Intensity of reference level  $I _o = 10^{-12} Wm^{-2}$

Measured intensity  $I = 10^{-6} W m^{-2}$
Using  $L = 10\log _{10}\dfrac{I}{I _o}$  decibels
$\therefore  $  $L = 10\log _{10}\dfrac{10^{-6}}{10^{-12}}$   decibels
Or  $L = 10 \ log _{10} 10^{6} = 10\times 6 = 60$  decibels

Decibel (dB) is a unit of loudness of sound. It is defined in a manner such that when amplitude of sound is multiplied by a factor of $\sqrt{10}$, the decibel level increase by 10 units. Loud music of 70 dB is being played at a function. To reduce the loudness to a level of 30 dB, the amplitude of the instrument playing music to be reduced by a factor of

intensity and loudness waves physics

  1. $0$

  2. $10\sqrt{10}$

  3. $100$

  4. $100\sqrt{100}$

Show answer
Correct Option: C
Explanation:

We know that Loudness of Sound is given by equation,
$\beta  = 10\log \left ( \frac{1}{I _{0}} \right ) dB$
where $I _{0} = 10^{-12} Wm^{-2} $ is the reference unit.
Intensity $ I \propto a^{2} $
where $a$ = amplitude.
Solving we get, the amplitude of the instrument playing music to be reduced by a factor of $100$.