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 cm2, and concentrates the sound onto two eardrums with a total area of 0.800 cm2 with an efficiency of 38.0%?

Answer 1

Answer: Δβ = 28.5278 dB

Explanation:

from the question we are given that;

the sound gathering area Ga = 15.0 cm²

total area Ae = 0.800 cm²

efficiency ε = 38 %

therefore we have that the effective gathering area of the stethoscope is;

As = ε Ga

As = 38 % × 15 = 5.7 cm²

But I ∝ 1/A

where Ie/Is = As/Ae

Ie/Is = 5.7/0.800 = 7.125

given that we are to assume that  sound is transmitted into a stethoscope 100 times, this gives

I'e/I's = Ie/Is × 100 = 7.125 × 100 = 712.5

Δβ = βe - βs = (10dB) log (I'e/Io) - (10dB) log (I's/Io)

Δβ = (10dB) log (I'e/I's)

Δβ = (10dB) log (712.5) = 28.5278

Δβ = 28.5278 dB

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