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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