Question

A person standing 1.20 m from a portable speaker hears its sound at an intensity of 5.50 ✕ 10−3 W/m2. HINT (a) Find the corresponding decibel level. dB (b) Find the sound intensity (in W/m2) at a distance of 36.0 m, assuming the sound propagates as a spherical wave. W/m2 (c) Find the decibel level at a distance of 36.0 m. dB

Answer 1

Answer:

PART A)

L = 97.4 dB

PART B)

$I = 6.11 \times 10^{-6} W/m^2$

PART C)

L = 67.9 dB

Explanation:

PART A)

level of sound is given as

$L = 10 Log\frac{I}{I_o}$

now we have

$L = 10 Log\frac{5.50\times 10^{-3}}{10^{-12}}$

$L = 97.4 dB$

PART B)

Since source is a spherical source

so here the intensity of sound is inversely depends on the square of the distance from the source

$\frac{I_2}{I_1} = \frac{r_1^2}{r_2^2}$

$\frac{I_2}{5.50 \times 10^-3} = \frac{1.20^2}{36^2}$

$I_2 = 6.11 \times 10^{-6} W/m^2$

PART C)

level of sound is given as

$L = 10 Log\frac{I}{I_o}$

now we have

$L = 10 Log\frac{6.11\times 10^{-6}}{10^{-12}}$

$L = 67.9 dB$