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A sound absorber attenuates the sound level by 20 dB. The intensity decreases by a factor of 100 or 10 ?

sudhanshu , 11 Years ago
Grade 12
anser 2 Answers
Saurabh Koranglekar

Last Activity: 5 Years ago

We need to determine by what factor the intensity of sound decreases when the sound level is attenuated by 20 dB.

Step 1: Understanding the Decibel Formula
The relationship between sound intensity level (in decibels) and intensity is given by the formula:

L = 10 log(I/I₀)

where:

L is the sound level in decibels (dB),

I is the final intensity,

I₀ is the initial intensity,

log is the base-10 logarithm.

Step 2: Applying the Given Attenuation
The problem states that the sound level decreases by 20 dB. This means:

ΔL = -20 dB
Thus, we write:

-20 = 10 log(I/I₀)

Step 3: Solving for the Intensity Ratio
Dividing both sides by 10:

-2 = log(I/I₀)

Now, converting from logarithmic to exponential form:

I/I₀ = 10^(-2)
I/I₀ = 1/100

Step 4: Conclusion
The intensity decreases by a factor of 100.

Thus, the correct answer is 100, not 10.

Vikas TU

Last Activity: 5 Years ago

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Dear student 
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