Question

Find the intensity of a 55 dB sound given lo-10-12 wm2

Answer 1

Answer:

Intensity=$I=3.16\times 10^{-7}\ W\ m^{-2}$

Explanation:

Given:

$\beta=55\ dB\\I_o=10^{-12}\ W\ m^{-2}$

The sound level $\beta$ in dB with intensity $I$

and reference intensity $I_0$ is given by:

$\beta(dB)=10 \log_{10}(\frac{I}{I_0})$

Plugging in values.

$55=10 \log_{10}(\frac{I}{10^{-12}})$

Dividing both sides by 10.

$\frac{55}{10}=\frac{10 \log_{10}(\frac{I}{10^{-12}})}{10}$

$5.5=\log_{10}\frac{I}{10^{-12}}$

The above can be written as

$10^{5.5}=\frac{I}{10^{-12}}$

Multiplying both sides by $10^{-12}$

$10^{5.5}\times 10^{-12}=10^{-12}\times \frac{I}{10^{-12}}$

$10^{(5.5-12)}=I$

$10^{(-7.5)}=I$

∴ $I=3.16\times 10^{-7}\ W\ m^{-2}$

Intensity =$I=3.16\times 10^{-7}\ W\ m^{-2}$