If the intensity of sound is doubled, by how many decibels does the sound level...

odigranogi5

odigranogi5

Answered

2023-01-01

If the intensity of sound is doubled, by how many decibels does the sound level increase?

Answer & Explanation

Dorian Beasley

Dorian Beasley

Expert

2023-01-02Added 11 answers

Step 1: We have
Let the intensity of the sound be I.
According to the question, I'=2I
Step 2: Formula used
Let the intensity of the sound be I and it's sound level is β1
The sound level β provided by, β=10log10II0
Where the constant reference intensity is I0
Step 3: The sound level increased
The sound level β1 provided by, β1=10log10II0...(1)
When the intensity doubles, the sound level is given by, β2=10log102II0...(2)
By subtracting equations (2) and (1), the sound level increased is,
β2-β1=10log102II0-10log10II0β2-β1=10log102II0-log10II0...(3)
Since logax-logay=logaxy equation 3 becomes,
β2-β1=10log102II0-log10II0β2-β1=10log102IIβ2-β1=10log102β2-β1=10×0.3010β2-β1=3dB
Hence, the volume of the sound rises by 3dB.

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