Question

A listener $x$ hears a sound level of $50dB$ when he is at a distance $1km$ from the instrument. Another listener $y$ at a distance $10km$ from the listener $x$ hears a sound level of ____.

Answer 1

Sound intensity $\alpha \frac{1}{{\left(Distance\right)}^2}$

when listener $x$ then $50dB=\frac{k}{{\left(1km\right)}^2}$

for listener $y,$ $I_y=\frac{k}{{\left(11km\right)}^2}$

$\Rightarrow I_y=\frac{50dBk{m}^2}{121k{m}^2}$

$\Rightarrow I_y=0.413dB$

Hence, the answer is $0.413dB.$