A person speaking normally produces a sound intensity of 40 dB at a distance of 1 m. If the threshold…

A person speaking normally produces a sound intensity of 40 dB at a distance of 1 m. If the threshold intensity for reasonable audibility is 20 dB, the maximum distance at which person can be heard clearly is
  1. (a) 4 m
  2. (b) 5 m
  3. (c) 10 m
  4. (d) 20 m

Solution

Sound level, $L = 10 \log_{10} \left(\frac{I}{I_0}\right)$, where $I_0 = 10^{-12}\text{ Wm}^{-2}$ $\Rightarrow 40 = 10 \log_{10} \left(\frac{I_1}{I_0}\right) \Rightarrow \frac{I_1}{I_0} = 10^4$ ...(i) Also, $20 = 10 \log_{10} \left(\frac{I_2}{I_0}\right) \Rightarrow \frac{I_2}{I_0} = 10^2$ ...(ii) $\Rightarrow \frac{I_2}{I_1} = 10^{-2} = \frac{r_1^2}{r_2^2}$ $\Rightarrow r_2^2 = 100 r_1^2 \Rightarrow r_2 = 10\text{ m} \quad (\cdot\!\cdot\!\cdot\, r_1 = 1\text{ m})$

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