If the intensity of a sound doubles, by about how many decibels does it increase?

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Multiple Choice

If the intensity of a sound doubles, by about how many decibels does it increase?

Explanation:
Doubling the intensity changes the sound level on a logarithmic scale. The decibel level is defined as β = 10 log10(I/I0). If I doubles, the increase is Δβ = 10 log10(2) ≈ 3.01 dB, so it is about 3 dB. The log scale means multiplicative changes in intensity translate to fixed additive changes in decibels, which is why a doubling is roughly a 3 dB increase rather than a large or tiny step. That’s why the correct option is the one saying about 3 dB. The other options correspond to smaller or larger intensity ratios (for example, 1 dB ~ 1.26× I0, 2 dB ~ 1.58× I0, and 5 dB ~ 3.16× I0), not a doubling.

Doubling the intensity changes the sound level on a logarithmic scale. The decibel level is defined as β = 10 log10(I/I0). If I doubles, the increase is Δβ = 10 log10(2) ≈ 3.01 dB, so it is about 3 dB. The log scale means multiplicative changes in intensity translate to fixed additive changes in decibels, which is why a doubling is roughly a 3 dB increase rather than a large or tiny step.

That’s why the correct option is the one saying about 3 dB. The other options correspond to smaller or larger intensity ratios (for example, 1 dB ~ 1.26× I0, 2 dB ~ 1.58× I0, and 5 dB ~ 3.16× I0), not a doubling.

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