A small speaker delivers 2W of audio output. At what distance from the speaker will one detect 120 DB intensity sound?

 [Given reference intensity of sound as 10^{-12}W/m^{2}]

  • Option 1)

    40 cm

  • Option 2)

    20 cm

  • Option 3)

    10 cm

  • Option 4)

    30 cm

 

Answers (1)

 

Sound level in decibels -

\beta = \: \: 10 \log_{10}\left ( I/I_{0} \right ),\\for \: \: I=I_{0}\\ \beta =0

- wherein

Where I is the intensity of the sound and I_{0}  is a constant reference intensity = 10-12 W/m2

 

 

I_{o}=10^{-12}w/m^{2}

dB=10\log \left ( \frac{I}{I_{o}} \right )= loudness

120=10\log \left ( \frac{I}{I_{o}} \right )

\frac{I}{I_{o}}=10^{12}

I=1 w/m^{2}

And we know

I=\frac{P}{A}=\frac{P}{4\pi r^{2}}=\frac{2}{4\pi r^{2}}

so r^{2}=\frac{2}{4\pi }

r= 40 cm


Option 1)

40 cm

Option 2)

20 cm

Option 3)

10 cm

Option 4)

30 cm

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