Question

Q2. The intensity of sound from a loud speaker, measured at a distance of 1 meters from the source is 5.0x10--4 W/m2
(a) Calculate the intensity of the sound at a distance 6 m from the source.
(b) Calculate the decibel change between the two positions.

Answer 1

QUESTION

Q2. The intensity of sound from a loud speaker, measured at a distance of $r_1 = 1$ meters from the source is $I_1 = 5.0 \times 10^{-4} \mathrm{~W/m^2}$

(a) Calculate the intensity of the sound at a distance $r_2 = 6$ m from the source.

(b) Calculate the decibel change between the two positions.

SOLUTION

Intensity of sound is

$$I_1 = \frac{P_{acc}}{4\pi r_1^2}$$ $$I_2 = \frac{P_{acc}}{4\pi r_2^2}$$

Hence

$$P_{acc} = I_1 4\pi r_1^2$$ $$I_2 = \frac{I_1 4\pi r_1^2}{4\pi r_2^2} = \frac{r_1^2}{r_2^2} I_1$$ $$I_2 = 0.139 \times 10^{-4} \mathrm{~Wt/m^2}$$

Sound level is

$$L_1 = 10 \lg \frac{I_1}{I_0}$$ $$L_2 = 10 \lg \frac{I_2}{I_0}$$

$I_0 = 10^{-12} \mathrm{~Wt/m^2}$ is the standard reference sound intensity

Hence

$$L_1 = 86.9897 \mathrm{~dB}$$ $$L_2 = 71.4267 \mathrm{~dB}$$

The decibel change between two positions is $L_1 - L_2 = 15,563$ dB