If the intensity doubles, by approximately how many decibels does Beta increase?

If the intensity doubles, by approximately how many decibels does Beta increase?

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

Answer: (B)

The key idea here is that decibels measure changes in intensity on a logarithmic scale. The decibel change when one intensity level becomes another is given by ΔL = 10 log10(I2/I1). If the intensity doubles, I2/I1 = 2. So ΔL = 10 log10(2) ≈ 10 × 0.3010 ≈ 3.01 dB. So the increase is about 3 dB. This makes sense on the broader scale: increasing intensity by a factor of 10 adds 10 dB, while a factor of 2 adds only a little over 3 dB. (If we were talking about amplitude instead of intensity, doubling amplitude would correspond to about 6 dB because power scales with amplitude squared.)

The key idea here is that decibels measure changes in intensity on a logarithmic scale. The decibel change when one intensity level becomes another is given by ΔL = 10 log10(I2/I1).

If the intensity doubles, I2/I1 = 2. So ΔL = 10 log10(2) ≈ 10 × 0.3010 ≈ 3.01 dB. So the increase is about 3 dB.

This makes sense on the broader scale: increasing intensity by a factor of 10 adds 10 dB, while a factor of 2 adds only a little over 3 dB. (If we were talking about amplitude instead of intensity, doubling amplitude would correspond to about 6 dB because power scales with amplitude squared.)