Question

# The loudness level at a distance R from a long linear source of sound found to be 40dB. At this point, the amplitude of oscillations of air molecules is 0.01 cm. Then find the loudness level(in dB) at a point located at a distance '10R' from the source.

Solution

## Loudness of the sound        $$L = 10 log_{10} \dfrac{I}{I_o}$$   where  $$I = \dfrac{I_o}{r^2}$$Thus      $$L = 20 log_{10} \dfrac{1}{r}$$ $$\implies$$   $$L_2 - L_1 = 20 log_{10} \dfrac{r_1}{r_2}$$ Given :   $$r_1 = R r_2 = 10 R L_1 = 40 dB$$   $$L_2 - 40 = 20 log_{10} \dfrac{R}{10 R}$$ $$L_2 - 40 = 20 (-1) \implies L_2 = 20 dB$$Physics

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