Question

Sound is more effectively transmitted into a stethoscope by direct contact than through the air, and it is further intensified by being concentrated on the smaller area of the eardrum. It is reasonable to assume that sound is transmitted into a stethoscope 100 times as effectively compared with transmission though the air. What, then, is the gain in decibels produced by a stethoscope that has a sound gathering area of 15.0 cm_2 , and concentrates the sound onto two eardrums with a total area of 0.900 cm_2 with an efficiency of 40.0%?

a) 48.0 dB
b) 50.5 dB
c) 53.2 dB
d) 55.8 dB

Answer 1

The gain in decibels produced by the stethoscope is approximately 40.12 dB.

Step-by-step explanation:

The gain in decibels produced by a stethoscope can be calculated using the formula:

Gain (dB) = 10 * log10(Efficiency * Gathering Area / Eardrum Area)

Given that the sound gathering area of the stethoscope is 15.0 cm², the eardrum area is 0.900 cm², and the efficiency is 40.0%, we can substitute these values into the formula:

Gain (dB) = 10 * log10(0.40 * 15.0 cm² / 0.900 cm²)

Simplifying the expression gives:

Gain (dB) = 10 * log10(26.67)

Using a calculator, this evaluates to approximately 40.12 dB. Therefore, the gain in decibels produced by the stethoscope is approximately 40.12 dB.