Question

Given that n="absmiddle" class="latex-formula"> watts/$meters^2$, what is the intensity of a sound for which the decibel level of the sound measures 156? Round off your answer to three decimal places.

Answer 1

The intensity of sound which the decibel level of the sound measures 156 is 3.981 × 10³ W/m²

Decibel level, dB = 10log₁₀(I/I₀) where dB = decibel level = 156, I = intensity at 156 dB and I₀ = 10⁻¹² W/m².

Since we require I, making I subject of the formula, we have

dB/10 = log₁₀(I/I₀)

$\frac{I}{I_{0} } = 10^{\frac{dB}{10} } \\I = I_{0} 10^{\frac{dB}{10} }$

Substituting the values of the variables into the equation, we have

$I = I_{0} 10^{\frac{dB}{10} }\\I = 10^{-12} 10^{\frac{156}{10} }\\I = 10^{-12} 10^{15.6}\\I = 10^{15.6-12} \\I = 10^{3.6} W/m^{2}$

I = 3981.072W/m²

I = 3.981 × 10³ W/m²

So, the intensity of sound which the decibel level of the sound measures 156 is 3.981 × 10³ W/m²

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