How many times more intense is a 60 dB sound than a 30 dB sound?

How many times more intense is a 60 dB sound than a 30 dB sound?
  1. 2
  2. 4
  3. 1000
  4. 10000

Solution

Loudness of two sounds are given as $\mathrm{L}_2=60 \mathrm{~dB}$ and $\mathrm{L}_1=30 \mathrm{~dB}$ Loudness of sound $L=10 \log _{10} \frac{\mathrm{I}}{\mathrm{I}_0}$ $\begin{array}{ll} \therefore \quad & L_2-L_1=10 \log _{10} \frac{I_2}{I_1} \\ & 60-30=10 \log _{10} \frac{I_2}{I_1} \\ \therefore \quad & \log _{10} \frac{I_2}{I_1}=3 \\ & \frac{I_2}{I_1}=10^3 \Rightarrow I_2=1000 I_1 \end{array}$

Asked in: MHT CET 2024 (16 May Shift 1)

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