If sound A has an intensity 10 times that of sound B, by how many decibels is A louder?

If sound A has an intensity 10 times that of sound B, by how many decibels is A louder?

• A. 1 dB
• B. 10 dB
• C. 20 dB
• D. 0 dB

Answer: (B)

Loudness differences on the decibel scale come from a logarithm of the intensity ratio. The change in level from one sound to another is ΔL = 10 log10(I1/I2). If sound A has ten times the intensity of sound B, then ΔL = 10 log10(10) = 10 × 1 = 10 dB. So A is louder by 10 dB. For context, a 10 dB increase is a noticeable boost (often described roughly as about twice as loud to the listener). The other options don’t fit because 1 dB would require about a 1.26× increase, 0 dB would mean equal intensities, and 20 dB would require a 100× increase.

Loudness differences on the decibel scale come from a logarithm of the intensity ratio. The change in level from one sound to another is ΔL = 10 log10(I1/I2). If sound A has ten times the intensity of sound B, then ΔL = 10 log10(10) = 10 × 1 = 10 dB. So A is louder by 10 dB.

For context, a 10 dB increase is a noticeable boost (often described roughly as about twice as loud to the listener). The other options don’t fit because 1 dB would require about a 1.26× increase, 0 dB would mean equal intensities, and 20 dB would require a 100× increase.