Intensity level of a sound of intensity $I$ is $30\text{ dB}$. The ratio $I/I_0$ is (where, $I_0$ is the…

Intensity level of a sound of intensity $I$ is $30\text{ dB}$. The ratio $I/I_0$ is (where, $I_0$ is the threshold of hearing)
  1. 30
  2. 300
  3. 1000
  4. 3000

Solution

Intensity level $= 10 \log \left(\frac{I}{I_0}\right)$ $30 = 10 \log \left(\frac{I}{I_0}\right)$ or $3 = \log \left(\frac{I}{I_0}\right)$ $\therefore \frac{I}{I_0} = 10^3 = 1000$

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