Question

The intensity level at $10m$ away is 40 dB. What will be the intensity level $100m$ away? Assume isotropic source.

• A. 4 dB
• B. 0.4 dB
• C. 30 dB
• D. 20 dB
• E. none of these

Answer 1

The correct option is D 20 dB

Intesity $I=\frac{p}{A}$ where p is power and A is area

$I=\frac{p}{4\pi d^2}$ $d$ is distance
Case (i) Intensity level at 10 m=$10log$ $\frac{\frac{p}{4\pi {10}^2}}{I_0}$
$40=10log$ $\frac{\frac{p}{4\pi {10}^2}}{I_0}$
Case (ii) Intensity level at 100m =$10log$ $\frac{\frac{p}{4\pi {100}^2}}{I_0}$
$x=10log$ $\frac{\frac{p}{4\pi {100}^2}}{I_0}$
or $40-x=10log$ $\frac{{100}^2}{{10}^2}$
or $40-x=10log$ ${10}^2$
or $x=40-20=20dB.$