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Multiple choice intensity and loudness waves physics

The threshold of hearing for the human ear $ 10^{-12} Wm^{-2} $. This is taken as the standard level. The intensity of sound is $ 1Wm^{-2} $. It has intensity (in $db$)

  1. $10^{12} db $
  2. $12\ db$
  3. $240\ db$
  4. $120\ db$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Intensity in $dB$:
$I _{dB} = 10 \log _{10}(\dfrac{I}{I _0})=10 \log _{10}(\dfrac{1}{10^{-12}})=10\times 12 \log _{10}10=120$ $dB$

Multiple choice intensity and loudness waves physics

The threshold of sound is $ 10^{-12} Wm^{-2} $.What is the intensity level of sound whose intensity is $10^{-8} Wm^{-2} $?

  1. 40 db

  2. 8db

  3. 12 db

  4. 20 db
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Intensity in decibels is expressed as $I(dB)=10log(\dfrac{I}{I _0})$

where $I _0$ is the threshold intensity of sound.
Thus $I(dB)=10log(\dfrac{10^{-8}}{10^{-12}})=40$

Multiple choice intensity and loudness waves physics

A key of a mechanical piano is struck gently and then struck again but much harder this time. In the second case

  1. both loudness and pitch will remain unaffected

  2. sound will be louder and pitch will also be higher

  3. sound will be louder but pitch will be lower

  4. sound will be louder but pitch will not be different
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

When the key of a mechanical piano struck harder, the vibrations caused are more resulting in larger amplitude of the wave that propagates from the key.
Loudness depends on the square of the amplitude of the wave. 
That is, $loudness\propto { \left( amplitude \right)  }^{ 2 }$
Amplitude is the size of the vibration, and this determines how loud the sound is.  Larger vibrations make a louder sound.
Pitch of the sound depends on the frequency of the wave which is not change when the key is struck harder.

Multiple choice intensity and loudness waves physics

How many times more intense is 90 dB sound than 40 dB sound :

  1. 5

  2. 50

  3. 500
  4. $ 10^5 $
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Let $I$ represents the intensity of sound.
Loudness of sound          $L = 10  log _{10} \frac{I}{I _o}$
$\implies  L _2 - L _1   = 10   log _{10} \frac{I _2}{I _1}$
$90 - 40  = 10  \log _{10} \dfrac{I _2}{I _1}$
$5= log _{10} \dfrac{I _2}{I _1}              \implies  \dfrac{I _2}{I _1} = 10^5$
Multiple choice intensity and loudness waves physics

A person is talking in a small room and the sound intensity level is 60 dB everywhere in the room. If there are eight people talking simultaneously in the room, what is the sound intensity level?

  1. 60 dB

  2. 69 dB

  3. 74 dB

  4. 81 dB
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let $I$ be the  intensity due to a person. For 8 persons, the  intensity, $I^{'}=8I$


Given, the sound intensity level, $B _1$ inside the room is 60 dB. We have to find out the sound intensity level when  eight people talking simultaneously in the room. Let it be $B _2$

We have the equation,

$\triangle B= 10 \, log \, (\frac{I^{'}}{I})$

$B _2-B _1=10 \, log \, (\frac{I{'}}{I})$


$B _2-60=10 \, log \, (\frac{8I}{I})$


$B _2-60=10 \, log \,8$

$B _2-60=10 \, log \,2^3$

$B _2=9=69\,dB$

Hence the sound intensity level is $69\,dB$.

Multiple choice intensity and loudness waves physics

A sound absorber attenuates the sound level by $20 dB$. The intensity decreases by a factor of

  1. $100$
  2. $200$
  3. $10000$
  4. $10$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

We have, $\displaystyle L _1=10log \left ( \frac {I _1}{I _0}\right)$

$\displaystyle L _2=10log \left ( \frac {I _2}{I _0}\right)$

$\displaystyle \therefore L _1 - L _2=10log \left ( \frac {I _1}{I _0}\right) - 10log \left ( \frac {I _2}{I _0}\right)$

or, $\displaystyle \Delta L = 10log \left ( \frac {I _1}{I _0} \times \frac {I _0}{I _2}\right)$

or, $\displaystyle \Delta L = 10log \left ( \frac {I _1}{I _2}\right)$

or, $\displaystyle 20 = 10log \left ( \frac {I _1}{I _2}\right)$

or, $\displaystyle 2 = log \left ( \frac {I _1}{I _2}\right)$

or, $\displaystyle \frac {I _1}{I _2}=10^2$

or, $\displaystyle I _2 = \frac {I _1}{100}$

$\Rightarrow $ Intensity decreases by a factor $100$

Multiple choice intensity and loudness waves physics

How many times more intense is a $60 \ dB$ sound than a $30 \ dB$ sound?

  1. $1000$
  2. $2$
  3. $100$
  4. $4$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Loudness of two sounds are given as  $L _2 = 60 \ dB$ and $L _1 = 30 \ dB$

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  $60 - 30  = 10\log _{10}\dfrac{I _2}{I _1}$

Or  $\log _{10}\dfrac{I _2}{I _1} = 3$
Or  $\dfrac{I _2}{I _1} = 10^3 = 1000$
Thus $60dB$ sound is $1000$ times more intense than $30dB$ sound.

Multiple choice intensity and loudness waves physics

How many times more intense is a $ 90\, dB$ sound than a $ 40\, dB$ sound ?

  1. $2.5$
  2. $ 5 $
  3. $ 50$
  4. $ 10^{5}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$90=10 log _{10}(\dfrac{I _1}{I _0})$
$\Rightarrow    \dfrac{I _1}{I _0}=10^9$......(i)
Again, $40=10 log _{10}(\dfrac{I _2}{I _0})$
$\Rightarrow    \dfrac{I _2}{I _0}=10^4$......(ii)
From Eqs.(i) and (ii), we get 
$\dfrac{I _1}{I _2}=10^5$

Multiple choice intensity and loudness waves physics

$90dB$ sound is $'x'$ times more intense than $40dB$ sound, then $x$ is

  1. $5$
  2. $50$
  3. $10^{5}$
  4. $500$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For every 10dB, intensity rises by 10 times, so for 50 dB intensity will rise by $10^5$

Multiple choice intensity and loudness waves physics

A hearing test is conducted on an aged person. It is found that her threshold of hearing is $20$ decibels at $1$ kHz and it rises linearly with frequency to $60$ decibels at $9$ kHz. The minimum intensity of sound that the person can hear at $5$ kHz is?

  1. $10$ times than that at $1$ kHz
  2. $100$ times than that at $1$ kHz
  3. $0.5$ times than that at $9$ kHz
  4. $0.05$ times than that at $9$ kHz
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The threshold rises from 20 dB at 1 kHz to 60 dB at 9 kHz. The slope is (60-20)/(9-1) = 5 dB/kHz. At 5 kHz, the threshold is 20 + (5 * 4) = 40 dB. The difference between 40 dB and 20 dB is 20 dB, which corresponds to a factor of 10^(20/10) = 100.