Final answer:
The energy delivered to the eardrum each second when someone whispers at 20 dB can be found by calculating the intensity of the sound from decibels and then multiplying it by the area of the eardrum.
Step-by-step explanation:
To determine how much energy is delivered to the eardrum each second when someone whispers (20.0 dB) a secret in your ear, we need to use the intensity level (in decibels) to find the intensity (in watts per meter squared) and then calculate the energy delivered to the eardrum. The formula to convert from decibels to intensity is I = I0 × 10(dB/10), where I0 is the reference intensity, which is 10−16 watts per meter squared (threshold of hearing). A whisper is 20 dB, or I = 10−16 × 10(20/10) = 10−12 watts per meter squared.
Next, we calculate the area of the eardrum using its diameter, which is 8.40 mm (or 0.0084 m). The area A of a circle is given by A = πr2, where r is the radius of the eardrum. The energy E delivered per second is then E = Intensity × Area, which gives us E = 10−12 × (π × (0.0084 m / 2)2). After calculating, we find the energy delivered to the eardrum each second.