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Chapter 9: Problem 301

A signal of \(5 \mathrm{kHz}\) frequency is amplitude modulated on a carrier wave of frequency \(2 \mathrm{MHz}\). The frequencies of the resulting signal is/are (A) \(2005 \mathrm{kHz}\), and \(1995 \mathrm{kHz}\) (B) \(2005 \mathrm{kHz}, 2000 \mathrm{kHz}\) and \(1995 \mathrm{kHz}\) (C) \(2000 \mathrm{kHz}\) and \(1995 \mathrm{kHz}\) (D) \(2 \mathrm{MHz}\) only

Short Answer

Expert verified
The resulting signal frequencies of a 5 kHz signal amplitude modulated on a 2 MHz carrier wave are \(2005 \mathrm{kHz}\) (Upper Sideband) and \(1995 \mathrm{kHz}\) (Lower Sideband). Thus, the correct option is (A).

Step by step solution

01

Understand Amplitude Modulation Frequency Mixing

When a signal is amplitude modulated onto a carrier wave, two sidebands (Upper Sideband - USB, Lower Sideband - LSB) are produced with frequencies that are the sum and difference of the signal and carrier frequencies.
02

Calculate Upper Sideband Frequency

To find the Upper Sideband frequency (USB), we add the signal's frequency (5kHz) to the carrier frequency (2MHz):\[USB = 2000 \mathrm{kHz} + 5 \mathrm{kHz} = 2005 \mathrm{kHz}\]
03

Calculate Lower Sideband Frequency

To find the Lower Sideband frequency (LSB), we subtract the signal's frequency (5kHz) from the carrier frequency (2MHz):\[LSB = 2000 \mathrm{kHz} - 5 \mathrm{kHz} = 1995 \mathrm{kHz}\]
04

Identify the correct answer based on the calculated frequencies

Based on our calculations of the Upper and Lower Sideband frequencies, the resulting signal frequencies are: \(2005 \mathrm{kHz}\) and \(1995 \mathrm{kHz}\). This matches option (A): (A) \(2005 \mathrm{kHz}\), and \(1995 \mathrm{kHz}\)

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