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

odigranogi5

odigranogi5

Answered question

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

Beginner2023-01-02Added 13 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.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?