When a wave's intensity doubles, the relative change is ______.

When a wave's intensity doubles, the relative change is ______.

• A. +9dB
• B. +6dB
• C. +3dB
• D. 0dB

Answer: (C)

The key idea is how decibels relate to intensity on a logarithmic scale. The decibel level changes by ΔL = 10 log10(I2/I1). If the intensity doubles, I2/I1 = 2, so ΔL = 10 log10(2) ≈ 3.01 dB. So the relative change is about +3 dB. Note the distinction: doubling amplitude would give +6 dB because intensity ∝ amplitude^2. Doubling intensity, as in the question, yields about +3 dB. 0 dB would mean no change, and +9 dB would correspond to a much larger increase in intensity (a factor of about 8).

The key idea is how decibels relate to intensity on a logarithmic scale. The decibel level changes by ΔL = 10 log10(I2/I1). If the intensity doubles, I2/I1 = 2, so ΔL = 10 log10(2) ≈ 3.01 dB. So the relative change is about +3 dB.

Note the distinction: doubling amplitude would give +6 dB because intensity ∝ amplitude^2. Doubling intensity, as in the question, yields about +3 dB. 0 dB would mean no change, and +9 dB would correspond to a much larger increase in intensity (a factor of about 8).