The intensity level of a sound wave is 4 dB. If the intensity of the wave is doubled, then the intensity level of the sound wave would be [Given $\log_{10} 2 = 0.301$ ]

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14 dB

8 dB

7 dB

16 dB

answer is C.

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Detailed Solution

$\begin{array}{l} L = 10 \log_{10} (\frac{I}{I_{0}}) \\ ∴ L_{2} - L_{1} = 10 l o g_{10} \frac{2 I}{I_{0}} - 10 l o g_{10} \frac{I}{I_{0}} \\ ∴ L_{2} = L_{1} + 10 l o g_{10} 2 = (4 + 3) d B = 7 d B . \end{array}$

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