Chapter 31: Q. 52 (page 903)

For radio and microwaves, the depth of penetration into the human body is proportional to $λ^{1 / 2}$ . If $27 MHz$ radio waves penetrate to a depth of $14 cm$ , how far do $2.4 GHz$ microwaves penetrate $?$

Short Answer

Expert verified

Microwaves penetrates at $1.53 cm$ .

Step by step solution

Calculation for wavelength for first frequency

The depth of penetration into the human body for radio and microwaves is provided by $λ^{1 / 2}$ , which is important for our situation.

Formula is,

$c = λ \times f$

For $f = 27 MHz$

$λ_{1} = \frac{c}{f}$

$λ_{1} = \frac{3 \times 10^{8} \frac{m}{s}}{27 \times 10^{6}}$

$λ_{1} = 11 m$

$\sqrt{λ_{1}} = 3.2 m$

Calculation of wavelength for second frequency

For $f = 2.4 GHz$

$λ_{2} = \frac{c}{f}$

$λ_{2} = \frac{3 \times 10^{8} \frac{m}{s}}{2.4 \times 10^{9}}$

$λ_{2} = 0.125 m$

Calculation for distance

The relationship is,

$r = \frac{\sqrt{λ_{1}}}{\sqrt{λ_{2}}}$

$= \frac{3.2 m}{0.35 m}$

$= 9.14$

Depth of penetration is,

$d_{2} = \frac{d_{1}}{r}$

$d_{2} = \frac{14 cm}{9.14}$

$d_{2} = 1.53 cm$

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For radio and microwaves, the depth of penetration into the human body is proportional to $λ^{1 / 2}$ . If $27 MHz$ radio waves penetrate to a depth of $14 cm$ , how far do $2.4 GHz$ microwaves penetrate $?$

Short Answer

Step by step solution

Calculation for wavelength for first frequency

Calculation of wavelength for second frequency

Calculation for distance

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For radio and microwaves, the depth of penetration into the human body is proportional to λ1/2. If27MHzradio waves penetrate to a depth of14cm, how far do2.4GHzmicrowaves penetrate?

Short Answer

Step by step solution

Calculation for wavelength for first frequency

Calculation of wavelength for second frequency

Calculation for distance

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Conservation of Energy and Momentum

Atoms and Radioactivity

Engineering Physics

Rotational Dynamics

Medical Physics

Electrostatics

Study anywhere. Anytime. Across all devices.

For radio and microwaves, the depth of penetration into the human body is proportional to $λ^{1 / 2}$ . If $27 MHz$ radio waves penetrate to a depth of $14 cm$ , how far do $2.4 GHz$ microwaves penetrate $?$