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Chapter 20: Problem 2719

If the band width is \(1.6 \times 10^{12} \mathrm{~Hz}\), how many communication channels can be obtained with \(16 \mathrm{KHz}\) band width radio signal ? (A) \(10^{15}\) (B) \(10^{11}\) (C) \(10^{10}\) (D) \(10^{8}\)

Short Answer

Expert verified
The number of communication channels that can be obtained with the given bandwidth is \(10^8\). Hence, the correct answer is option (D).

Step by step solution

01

Convert Bandwidth per Channel to Hz

First, we will convert the \(16 \mathrm{kHz}\) bandwidth per communication channel into Hz (Hertz) units: \(16 \mathrm{kHz} = 16 \times 10^3 \mathrm{Hz}\)
02

Calculate Number of Communication Channels

Now we will divide the total bandwidth by the bandwidth per communication channel to find the number of communication channels: Number of channels = Total bandwidth / Bandwidth per channel Number of channels = \( (1.6 \times 10^{12} \mathrm{Hz}) / (16 \times 10^3 \mathrm{Hz})\)
03

Simplify the Expression

Simplify the division by dividing the coefficients and subtracting the exponents of 10: Number of channels = \( (1.6 / 16) \times 10^{(12-3)}\) Number of channels = \( 0.1 \times 10^9\)
04

Convert the Number to Standard Form

Now, we will convert the coefficient 0.1 into standard form by moving the decimal over one place and increasing the exponent by 1: Number of channels = \( 1 \times 10^8\) Thus, the number of communication channels that can be obtained is \(10^8\), which is option (D).

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