# Calculate the level in decibels for a sound having an intensity of 5.00x10^-4Wm^-2?

$76.99 \setminus \mathrm{db}$

#### Explanation:

Intensity level of sound of power $I$ in $\mathrm{db}$ as follows

$| \textrm{\int e n s i t y \le v e l o f s o u n d} = 10 \setminus {\log}_{10} \left(\setminus \frac{I}{{I}_{o}}\right) \setminus \mathrm{db}$

Hence, intensity level of sound of power $I = 5 \setminus \times {10}^{- 5} \setminus \frac{W}{m} ^ 2$ in $\mathrm{db}$ as follows

$| \textrm{\int e n s i t y \le v e l o f s o u n d} = 10 \setminus {\log}_{10} \left(\setminus \frac{5 \setminus \times {10}^{- 5}}{{10}^{- 12}}\right) \setminus \mathrm{db}$

$= 10 \setminus {\log}_{10} \left(5 \setminus \times {10}^{7}\right) \setminus \mathrm{db}$

$= 10 \left(\setminus {\log}_{10} \left(5\right) + 7\right) \setminus \mathrm{db}$

$= 10 \left(0.699 + 7\right) \setminus \mathrm{db}$

$= 76.99 \setminus \mathrm{db}$