MCAT Physics Question — Sound Level

This question requires the examinee to understand the logarithmic relationship between the sound level and intensity. As a general rule, an increase in 10 dB corresponds to an increase in intensity by a factor of 10. Therefore, the 80-decibel difference in sound levels in this problem corresponds to a difference in intensity by a factor of 10⁸.

dB = 10log₁₀(I/I_o)

120 = 10log₁₀(I₁₂₀/I_o)

12 = log₁₀(I₁₂₀/I_o)

I₁₂₀ = I_o10¹²

dB = 10log₁₀(I₄₀/I_o)

40 = 10log₁₀(I₄₀/I_o)

4 = log₁₀(I₄₀/I_o)

I₄₀ = I_o10⁴

I₁₂₀/I₄₀ = I_o10¹²/I_o10⁴

I₁₂₀/I₄₀ = 10⁸

Thus, the intensity of the sound at 120 decibels is eight orders of magnitude greater than sound at 40 decibels making B the correct answer.