Chapter 12, Problem 72GP

To determine

The power intercepted by an unprotected ear at a given distance from a jet airplane engine.

Answer to Problem 72GP

The power intercepted is $P=0.5\text{ W}$ .

Explanation of Solution

Given:

Sound level, ß = 140 dB,

Distance, d

= 30 m,

Radius, r

= 2 cm = 0.02 m

Formula used:

  $P=I\times 4\pi r^2\text{ W}$

Here, $r$ is the radius.

I = Intensity of sound

Calculation:

The power intercepted by unprotected ear can be calculated by using the formula,

  $P=I.4\pi r^2\text{ W}$

Where,

P = Power in W

I₀ = 1×10-12 W/m²

  $I={10}^{\beta /10}\times I_0$

  $I=10{\text{ W/m}}^2$

Substitute the values in the equation,

  $P=10\times 4\pi {(0.02)}^2\text{ W}$

  $P=0.5\text{ W}$

Conclusion:

The power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine is 0.5 W.