Using an intensity of 1 1012 Wm2 as a reference the thresho

Using an intensity of 1 × 10-12 W/m2 as a reference, the threshold of hearing for an average young person is 0 dB. Person 1 and person 2, who are not average, have thresholds of hearing that are 1 = -14.0 dB and 2 = +23.0 dB. What is the ratio I1/I2 of the sound intensity I1 when person 1 hears the sound at his own threshold of hearing compared to the sound intensity I2 when person 2 hears the sound at his own threshold of hearing?

Solution

I = 1 * 10^-12 * 10^[dB/10]

I₁ = 1 * 10^-12 * 10^{[-14 / 10 ]}

= 3.98 * 10^-14 w/m²

I₂ = 1 * 10^-12 * 10^{[23 / 10 ]}

= 1.99 * 10^-10 w/m²

ratio = (3.98 * 10^-14) / (1.99 * 10^-10)

= 2.00 * 10^-4