Sound intensity level β in decibels is defined as β = 10 log10(I/I0). What is I0?

Sound intensity level β in decibels is defined as β = 10 log10(I/I0). What is I0?

• A. 1.0 × 10^-6 W/m^2
• B. 1.0 × 10^-12 W/m^2
• C. 1.0 W/m^2
• D. 1.0 × 10^12 W/m^2

Answer: (B)

The main idea here is how the decibel scale for sound uses a fixed reference intensity to compare actual sound levels. The reference intensity I0 is chosen as the faintest sound a healthy human can hear in standard conditions, which is 1.0 × 10^-12 W/m^2. In β = 10 log10(I/I0), the ratio I/I0 is dimensionless, and the logarithm converts the huge range of sound intensities into a more manageable scale. If the actual intensity equals the reference, I/I0 = 1 and β = 0 dB, meaning the sound is right at the threshold of hearing. That’s why I0 is set to 1.0 × 10^-12 W/m^2. The other values would shift the zero point of the scale and don’t represent the standard reference for 0 dB. For example, using 1 W/m^2 would correspond to a much higher decibel level, while 1.0 × 10^-6 W/m^2 would place the reference at a different point on the scale.

The main idea here is how the decibel scale for sound uses a fixed reference intensity to compare actual sound levels. The reference intensity I0 is chosen as the faintest sound a healthy human can hear in standard conditions, which is 1.0 × 10^-12 W/m^2. In β = 10 log10(I/I0), the ratio I/I0 is dimensionless, and the logarithm converts the huge range of sound intensities into a more manageable scale. If the actual intensity equals the reference, I/I0 = 1 and β = 0 dB, meaning the sound is right at the threshold of hearing. That’s why I0 is set to 1.0 × 10^-12 W/m^2. The other values would shift the zero point of the scale and don’t represent the standard reference for 0 dB. For example, using 1 W/m^2 would correspond to a much higher decibel level, while 1.0 × 10^-6 W/m^2 would place the reference at a different point on the scale.