Yareli Bowman

2022-08-20

What are the sound intensity levels for sound waves of intensity (a) $3.0×{10}^{-6}W/{m}^{2}$ and (b) $3.0×{10}^{-2}W/{m}^{2}$?

Paityn Arroyo

Expert

The decibel scale:
$\beta =\left(10dB\right)\mathrm{log}\frac{I}{{I}_{0}}$
$\beta ⇒$ sound intensity level, $I⇒$ intensity of sound wave,
${I}_{0}={10}^{-12}W/{m}^{2}⇒$ the reference intensity.
a) $\beta =\left(10db\right)\mathrm{log}\frac{I}{{I}_{0}}=\left(10dB\right)\mathrm{log}\frac{3×{10}^{-6}W/{m}^{2}}{{10}^{-12}W/{m}^{2}}=65dB$
b) $\beta =\left(10dB\right)\mathrm{log}\frac{I}{{I}_{0}}=\left(10dB\right)\mathrm{log}\frac{3×{10}^{-2}W/{m}^{2}}{{10}^{-12W/{m}^{2}}}=105dB$
Result:
a) 65dB
b) 105dB

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