Question

Quest: A window whose area is 2 m^2 opens on a street where the street noise results in a sound level 60 dB at window. If an acoustic absorber is fitted at the window which absorbs all the acoustic power entering in the window, find the total energy collected by the absorber in 5 hours.

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Answer 1

We know that -

$\sf{ Intensity = 10 log_{10}( \dfrac{ i }{ i_{0} } ) }$

Here ,

i_{0} is taken as the standard intensity , which has a value of 10^ { - 12 }

We know that the unit of intensity is always Watt per metre square i.e, Bels or Decibels

The dimension of Intensity is always ML^ { -3 } .

Coming back to the question -

Here , in this question , the following information is given -

A window whose area is 2 m^2 opens on a street where the street noise results in a sound level 60 dB at window.

an acoustic absorber is fitted at the window which absorbs all the acoustic power entering in the window.

time = 5 hrs.

We have to calculate the amount of energy absorbed by the acoustic absorber .

So , I = 60 dB

Now ,

Substuting this into the formula given -

$\sf{ 60 dB = 10 log_{10} ( \dfrac{ i }{ 10^ { -12 } } ) }$

Now ,

Solving this -

$\sf{ 6 = log ( \dfrac{ i }{ 10^ { -12 } } ) } \\ \\ \sf{ \dfrac{ I }{ 10^ { -12 } } = antilog ( 6 ) } \\ \\ \sf{ \dfrac{ I }{ 10^ { -12 } } = { 10 } ^ 6 } \\ \\ \sf{ I = 10^ 6 \times 10^ { -12 } } \\ \\ \sf{ \implies { I = 10^ { -6} dB }}$

The intensity value of 10^ { -6 } dB is quite moderate and can be considered as possible.

Now ,

We also know that -

Intensity = [ Power / Area ]

Here , we have had provided the value of Area in the beginning of the question as -

" A window whose area is 2 m^2 .... "

So , the area of the window is 2 m^2

$\sf{ \implies { 10^ { -6 } = \dfrac{ Power }{ 2 } } } \\ \\ \sf{ \implies { Power = 2 \times 10^ { -6 } Watt } }$

Hence , the power of the sound waves generated by the street is $2 \times 10 ^ { -6 } Watt$ , which means that the street is quite busy and polluted xD

Coming back to the question -

Energy = Power × Time

Time = 5 hrs

1 hr = 3600 Seconds

So ,

5 hrs = 18000 seconds

=> Energy = $2 \times 10^ { -6 } \times 18 \times { 10 } ^ { 3 } \\ \\ => => 36 \times10^ { -3 } Joules$

Hence , the required energy absorbed by the acoustic absorber is 36 × 10^ { -3 } Joules .

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