The intensity level of a sound wave is $4\text{ dB}$. If the intensity of the wave is doubled, then the…

The intensity level of a sound wave is $4\text{ dB}$. If the intensity of the wave is doubled, then the intensity level of the sound, as expressed (in dB), would be
  1. 8
  2. 16
  3. 7
  4. 14

Solution

As, $L_2 - L_1 = 10 \log \frac{I_2}{I_0} - 10 \log \frac{I_1}{I_0} = 10 \log \left(\frac{I_2}{I_1}\right)$ $L_2 - 4 = 10 \log (2)$ $\left(\because \frac{I_2}{I_1} = 2\right)$ $\therefore L_2 = 7\text{ dB}$

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