Answer:
r₂ = 0.2 m
Explanation:
given,
distance = 20 m
sound of average whisper = 30 dB
distance moved closer = ?
new frequency = 80 dB
using formula
[tex]\beta = 10 log(\dfrac{I_1}{I_0})[/tex]
I₀ = 10⁻¹² W/m²
now,
[tex]30 = 10 log(\dfrac{I_1}{10^{-12}})[/tex]
[tex]\dfrac{I_1}{10^{-12}}= 10^3[/tex]
[tex]I_1= 10^{-8}\ W/m^2[/tex]
to hear the whisper sound = 80 dB
[tex]80 = 10 log(\dfrac{I_2}{10^{-12}})[/tex]
[tex]\dfrac{I_2}{10^{-12}}= 10^8[/tex]
[tex]I_2= 10^{-4}\ W/m^2[/tex]
we know intensity of sound is inversely proportional to square of distances
[tex]\dfrac{I_1}{I_2}=\dfrac{r_2^2}{r_1^2}[/tex]
[tex]\dfrac{10^{-8}}{10^{-4}}=\dfrac{r_2^2}{20^2}[/tex]
[tex]10^{-4}=\dfrac{r_2^2}{20^2}[/tex]
r₂ = 0.2 m
