Question

this is one question with 3 parts

D. From a location 4.0 m away, you listen to a jackhammer breaking concrete. 1. How far away would you have to stand in order to reduce the sound intensity by a factor of 8 (12 = 11/8)? Show your calculation. 2. If the intensity of the sound has decreased by a factor of 8, by what factor has the amplitude of the sound wave decreases? Explain your answer. 3. If the intensity of the sound wave has decreases by a factor of 8, by how many decibels has the decibel level decreased? Show your calculation.

Answer 1

$intensity=\frac{energy}{time \times area}$

$intensity\propto \frac{1}{r^2}$

11 12 NA 5

$\frac{I_1}{\frac{I_1}{8}}=\frac{r_2^2}{(4)^2}$

r2 8 X 11 11 2

${r_2^2}=8\times (4)^2$

(2) $I\propto A^2$

$\frac{I_1}{I_2}=\frac{A_1^2}{A_2^2}$

$8=\frac{A_1^2}{A_2^2}$

$A_2=\frac{A_1}{\sqrt{8}}$

(3)$\beta(dB)=10log(\frac{I_2}{I_1})$

$\beta(dB)=10 log(\frac{1}{8})$

$\beta(dB)=-9.03$