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,

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

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

$d_{2} = 1.53 cm$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Thermodynamics

Radiation

Torque and Rotational Motion

Turning Points in Physics

Measurements

Rotational Dynamics

Study anywhere. Anytime. Across all devices.

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

Thermodynamics

Radiation

Torque and Rotational Motion

Turning Points in Physics

Measurements

Rotational Dynamics

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 $?$