Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 20: Problem 2716

The relation between the maximum electron density \(\mathrm{N}\) max and the critical frequency \(\mathrm{f}\) for the ionosphere can be given as (A) \(\left.f_{c}=\sqrt{(9 N}_{\max }\right)\) (B) \(\mathrm{f}_{\mathrm{c}}=\sqrt{9}\left(\mathrm{~N}_{\max }\right)\) (C) \(\left.f_{c}=9 \sqrt{(N}_{\max }\right)\) (D) None of these

Short Answer

Expert verified
Based on the examination of options A, B, and C, all of them lead to a mismatch of units and don't provide a meaningful relationship between the maximum electron density (N_max) and the critical frequency (f_c) for the ionosphere. Hence, the correct answer is (D) None of these.

Step by step solution

01

Understanding the variables and their physical units

Before we examine each option, let's make sure we understand the physical meaning of the variables involved and their corresponding units. The maximum electron density, denoted by N_max, is a measure of the number of free electrons in a given volume of the ionosphere. It is expressed in SI units as m^(-3), or electrons per cubic meter. The critical frequency, denoted by f_c, represents the highest frequency of an electromagnetic wave that can be reflected by the ionosphere. It is expressed in SI units as Hz (Hertz), or cycles per second.
02

Examining Option A

First, let's consider option A: \(f_{c} = \sqrt{(9 N}_{\max})\). To check whether this equation makes physical sense, we must determine whether the square root of electron density yields a frequency. Taking the square root of N_max would result in units of m^(-3/2). Based on the units alone, this equation is not correct because a square root of electron density doesn't yield a frequency. Therefore, we can eliminate option A.
03

Examining Option B

Next, let's consider option B: \(f_{c} = \sqrt{9}(\mathrm{~N}_{\max})\). In this equation, we have N_max multiplied by a dimensionless constant, \(\sqrt{9}\), which won't result in a proper frequency dimension. Like in step 2, this equation leads to a mismatch of units and doesn't make physical sense. So, we can eliminate option B.
04

Examining Option C

Now, let's consider option C: \(f_{c} = 9 \sqrt{(N}_{\max})\). In this equation, we are multiplying the square root of N_max by a dimensionless constant, 9. As in steps 2 and 3, this equation also results in mismatched units and doesn't make physical sense. So, we can eliminate option C.
05

Conclusion

Based on our examination of options A, B, and C, all of them lead to a mismatch of units and don't provide a meaningful relationship between the maximum electron density (N_max) and the critical frequency (f_c) for the ionosphere. Hence, the correct answer is (D) None of these.

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!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In modulation process radio signal is called (A) modulating wave (B) Carrier wave (C) modulated wave (D) transmitting wave

Tank Circuit Contains 1 nf capacitor and 10 microhenry inductor What is the carrier frequency generated by it? (A) \(1629 \mathrm{KHz}\) (B) \(1592 \mathrm{KHz}\) (C) \(1582 \mathrm{MHz}\) (D) \(156.2 \mathrm{KHz}\)

The band width of Audio signal is (A) \(20 \mathrm{HZ}\) (B) \(20 \mathrm{KHZ}\) (C) \(20 \mathrm{MHZ}\) (D) \(20 \mathrm{GHZ}\)

For an amplitude modulated wave, the maximum amplitude is found to be $9 \mathrm{~V}\( while the minimum amplitude is found to be \)3 \mathrm{~V}$. The modulation index is (A) \(100 \%\) (B) \(75 \%\) (C) \(50 \%\) (D) \(25 \%\)

A transmitting antenna at the top of a tower has a height of \(50 \mathrm{~m}\) and the height of the receiving antenna is \(32 \mathrm{~m}\). The maximum distance between them for satisfactory communication in line of sight mode is Given radius of earth \(\mathrm{R}=6400 \mathrm{~km}\) (A) \(25.29 \times 10^{3} \mathrm{~km}\) (B) \(20.23 \times 10^{3} \mathrm{~km}\) (C) \(45.5 \mathrm{~km}\) (D) None of these.
See all solutions

Recommended explanations on English Textbooks

Listening and Speaking

Read Explanation

Cues and Conventions

Read Explanation

Semiotics

Read Explanation

English Language Study

Read Explanation

Synthesis Essay

Read Explanation

Research and Composition

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free