Question

A person is standing at a distance $x$ from a jet, its sound level heard by the person is $140\text{dB}.$ If the person moves to a location $10x$ away from the source , then find the loudness intensity of the sound detected by the person at new location (Assume jet as point sized).

• A. $14\text{dB}$
• B. $30\text{dB}$
• C. $90\text{dB}$
• D. $120\text{dB}$

Answer 1

The correct option is D $120\text{dB}$

Sound intensity in decibel is given by , $dB=10\log \frac{I}{I_0}$

$I$ - Intensity of sound wave
$I_0$ - Minimum intensity of hearing.

Also, $I\propto \frac{1}{d^2}$ (For a point source)

Here $\frac{I_1}{I_2}={\left(\frac{d_2}{d_1}\right)}^2={\left(\frac{10x}{x}\right)}^2$

$\Rightarrow I_2=\frac{I_1}{100}$

Given that,
$10\log \frac{I_1}{I_0}=140\text{dB}$

Let, $Z=10\log \frac{I_2}{I_0}=10\log \frac{I_1}{100I_0}=10\log \frac{I_1}{I_0}-10\log 100=140-20$

$\Rightarrow Z=120\text{dB}$

Hence, option $\left(d\right)$ is correct.