Quadrupling the power output from a speaker emitting a single frequency will result in what increase in loudness (in units of dB)

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Quadrupling the power output from a speaker emitting a single frequency will result in what increase in loudness (in units of dB)

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Cherry 5 years 2021-08-17T06:52:43+00:00 1 Answers 133 views 0

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  1. taiduc
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    2021-08-17T06:54:09+00:00
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    Answer:

    6.02 dB increase  

    Explanation:

    Let us take the initial power from the speaker P’ = P Watt

    then, the final power P = 4P Watt

    for a given unit area, initial intensity (power per unit area) will be

    I’ = P Watt/m^2

    and the final quadrupled sound will produce a sound intensity of

    I = 4P Watt/m^2

    Increase in loudness is gotten from the relation

    ΔL =  10log_{10} \frac{I}{I'}

    where

    I = final sound intensity

    I’ = initial sound intensity

    imputing values of the intensity into the equation, we have

    ==>  10log_{10} \frac{4P}{P} =  10log_{10} 4 = 6.02 dB increase  

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