If intensity is 1×10^-6 W/m^2 and reference intensity is 1×10^-12 W/m^2, what is the sound level β?

If intensity is 1×10^-6 W/m^2 and reference intensity is 1×10^-12 W/m^2, what is the sound level β?

• A. 40 dB
• B. 80 dB
• C. 100 dB
• D. 60 dB

Answer: (D)

Sound level is measured on a logarithmic scale: β = 10 log10(I/I0). Here the intensity is 1×10^-6 W/m^2 and the reference is 1×10^-12 W/m^2, so the ratio I/I0 = 1×10^6. The log base 10 of 1×10^6 is 6, and multiplying by 10 gives β = 60 dB. Since the intensity is a million times the reference, the sound level is 60 dB above the reference. Each factor of 10 in intensity adds 10 dB, so six factors of 10 yield 60 dB.

Sound level is measured on a logarithmic scale: β = 10 log10(I/I0). Here the intensity is 1×10^-6 W/m^2 and the reference is 1×10^-12 W/m^2, so the ratio I/I0 = 1×10^6. The log base 10 of 1×10^6 is 6, and multiplying by 10 gives β = 60 dB. Since the intensity is a million times the reference, the sound level is 60 dB above the reference. Each factor of 10 in intensity adds 10 dB, so six factors of 10 yield 60 dB.