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.