P18_021 - 21. (a) Let I1 be the original intensity and I2...

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Unformatted text preview: 21. (a) Let I1 be the original intensity and I2 be the final intensity. The original sound level is β1 = (10 dB) log(I1 /I0 ) and the final sound level is β2 = (10 dB) log(I2 /I0 ), where I0 is the reference intensity. Since β2 = β1 + 30 dB, (10 dB) log(I2 /I0 ) = (10 dB) log(I1 /I0 ) + 30 dB, or (10 dB) log(I2 /I0 ) − (10 dB) log(I1 /I0 ) = 30 dB. Divide by 10 dB and use log(I2 /I0 ) − log(I1 /I0 ) = log(I2 /I1 ) to obtain log(I2 /I1 ) = 3. Now use each side as an exponent of 10 and recognize that 10log(I2 /I1 ) = I2 /I1 . The result is I2 /I1 = 103 . The intensity is increased by a factor of 1000. (b) The pressure amplitude is proportional to the square root of the intensity so it is increased by a √ factor of 1000 = 32. ...
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