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Question

(D) The sound level $\beta$ in decibels $(dB)$ is defined as $\beta = 10 \log_{10} \left( \frac{I}{I_0} \right)$,where $I$ is the intensity and $I_0$

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$80 \, dB$ to $100 \, dB$

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(D) The sound level $\beta$ in decibels $(dB)$ is defined as $\beta = 10 \log_{10} \left( \frac{I}{I_0} \right)$,where $I$ is the intensity and $I_0$ is the reference intensity.Let the initial intensity be $I_1 = I$ and the final intensity be $I_2 = 100I$.The initial sound level is $\beta_1 = 10 \log_{10} \left( \frac{I}{I_0} \right)$.The final sound level is $\beta_2 = 10 \log_{10} \left( \frac{100I}{I_0} \right)$.Using the property of logarithms,$\beta_2 = 10 \left( \log_{10} 100 + \log_{10} \left( \frac{I}{I_0} \right) \right)$.Since $\log_{10} 100 = 2$,we have $\beta_2 = 10(2) + 10 \log_{10} \left( \frac{I}{I_0} \right) = 20 + \beta_1$.Thus,the sound level increases by $20 \, dB$. Among the given options,an increase from $80 \, dB$ to $100 \, dB$ represents a rise of $20 \, dB$.

The intensity of sound during the festival season increased by $100$ times. This could imply a decibel $(dB)$ level rise from

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