Question

You are trying to hear your friend give directions to new store in town. But from your distance (1 point) of 15 m you only hear a whisper of about 20 dB intensity. You move closer to bring the conversation up to a sound level of about 50 dB. How close do you need to be?
A. 100 cm
B. 333 cm
C. 90 cm
D. 47 cm

Answer 1

Answer:

option D

Explanation:

given,

Intensity of sound = 20 dB

distance = 15 m

intensity of sound is increased to = 50 dB

distance between the sound level = ?

Using relation

$L_2 = L_1 - |20(log \dfrac{r_2}{r_1})|$

L₁ = 20 dB        L₂ = 50 dB         r₁ = 15 m      r₂ = ?

$log (\dfrac{r_2}{r_1}) = \dfrac{L_1 -L_2}{20}$

$\dfrac{r_2}{r_1}= 10^{\dfrac{|L_1 -L_2|}{20}}$

$r_2 =r_1 10^{\dfrac{|L_1 -L_2|}{20}}$

$r_2 =15 \times 10^{\dfrac{|20-50|}{20}}$

$r_2 =15 \times 10^{-1.5}$

r₂ = 0.47 m

r₂ = 47 cm

hence, the correct answer is option D