When the intensity increases 10-fold the relative change is _____.

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Multiple Choice

When the intensity increases 10-fold the relative change is _____.

Explanation:
Decibels represent ratios on a logarithmic scale. The formula is 10 log10(I2/I1). If the intensity increases by a factor of ten, I2/I1 = 10, so 10 log10(10) = 10 dB. Hence the relative change is +10 dB. The other options don’t fit because a hundredfold increase would be +20 dB, a tenfold decrease would be -10 dB, and +1 dB corresponds to only about a 26% increase, not tenfold.

Decibels represent ratios on a logarithmic scale. The formula is 10 log10(I2/I1). If the intensity increases by a factor of ten, I2/I1 = 10, so 10 log10(10) = 10 dB. Hence the relative change is +10 dB. The other options don’t fit because a hundredfold increase would be +20 dB, a tenfold decrease would be -10 dB, and +1 dB corresponds to only about a 26% increase, not tenfold.

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