A 30 dB increase in noise pollution level represents:
2023
A 30 dB increase in noise pollution level represents:
Answer: C. 1000-fold increase in sound intensity — ConceptThe decibel scale for sound intensity is logarithmic. For two intensities I2 and I1, the level difference is ΔL = 10 log10(I2/I1), so the intensity…
- A.
30-fold increase in sound intensity
- B.
100-fold increase in sound intensity
- C.
1000-fold increase in sound intensity
- D.
15-fold increase in sound intensity
Show answer & explanation
Correct answer: C
Concept
The decibel scale for sound intensity is logarithmic. For two intensities I2 and I1, the level difference is ΔL = 10 log10(I2/I1), so the intensity ratio is I2/I1 = 10ΔL/10.
Application
Set the level increase as ΔL = 30 dB.
Substitute into the ratio formula: I2/I1 = 1030/10 = 103.
Evaluate 103 = 1000, so the intensity becomes 1000 times the original intensity.
Cross-check
Putting the ratio 1000 back into the definition gives 10 log10(1000) = 10 × 3 = 30 dB, which reproduces the stated increase.