When the intensity is increased by a factor of 10, the relative change is:

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Multiple Choice

When the intensity is increased by a factor of 10, the relative change is:

Explanation:
Decibels express how big a change in intensity is on a logarithmic scale. The formula is ΔdB = 10 log10(I2/I1). If the intensity increases by a factor of 10, the ratio I2/I1 is 10, so ΔdB = 10 log10(10) = 10 × 1 = 10 dB. Therefore the relative change is +10 dB. For context, 3 dB corresponds to about a factor of 2 in intensity, 20 dB to a factor of 100, and -10 dB would be a tenfold decrease.

Decibels express how big a change in intensity is on a logarithmic scale. The formula is ΔdB = 10 log10(I2/I1). If the intensity increases by a factor of 10, the ratio I2/I1 is 10, so ΔdB = 10 log10(10) = 10 × 1 = 10 dB. Therefore the relative change is +10 dB.

For context, 3 dB corresponds to about a factor of 2 in intensity, 20 dB to a factor of 100, and -10 dB would be a tenfold decrease.

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