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physics A-Level Physics
 
Solved problems for the chapter:
 

Amplitude and Frequency Modulations

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https://en.openprof.com/wb/chapter:amplitude_and_frequency_modulations/5148/


Example 1.

  • When audio signals are transmitted over long distances, modulation of radio waves is used. Suggest a reason why modulation is used.


  • State a technical advantage and a technical disadvantage of using frequency modulation rather than amplitude modulation.

    
Example 2.

    • Describe what is meant by frequency modulation.


    • A sinusoidal carrier wave has frequency and amplitude . It is to be frequency modulated by a sinusoidal wave of frequency and amplitude . The frequency deviation of the carrier wave is . Describe, for the carrier wave, the variation (if any) of


      • the amplitude,


      • the frequency.


  • State two reasons why the cost of FM broadcasting to a particular area is greater than that of AM broadcasting.

    
3.

  • An audio signal of amplitude and frequency is to be transmitted using a carrier wave of amplitude and frequency . Either amplitude modulation or frequency modulation may be used. The amplitude modulation is at a rate of . The frequency modulation is at a rate of . Complete the table below to show the maximum and minimum values of the amplitude and of the frequency of the modulated wave for each type of modulation.




  • For the amplitude modulated wave in (a), determine the bandwidth.

    
4.

Many radio stations now broadcast on FM rather than on AM. In general, FM is broadcast at much higher frequencies than AM.


  • Explain what is meant by FM (frequency modulation).


  • State two advantages and two disadvantages of FM transmissions when compared with AM transmissions.

    
5.

  • Describe what is meant by frequency modulation (FM).


  • A sinusoidal carrier wave has a frequency of and an amplitude of . The carrier wave is frequency modulated by a sinusoidal wave of frequency and amplitude . The frequency deviation of the carrier wave is . Determine, for the modulated carrier wave,


    • the amplitude,


    • the maximum frequency,


    • the minimum frequency,


    • the number of times per second that the frequency changes from maximum to minimum and then back to maximum.

    
6.

  • In radio communication, the radio wave is usually modulated. State what is meant by amplitude modulation (AM).


  • A sinusoidal radio carrier wave has a frequency of and an unmodulated amplitude measured to be . The carrier wave is amplitude modulated by a signal of frequency . For the amplitude-modulated wave,


    • determine the wavelength,


    • describe the amplitude variation,


    • state the bandwidth.

    
7.

A radio station emits an amplitude-modulated wave for the transmission of music.


  • State what is meant by an amplitude-modulated (AM) wave.


  • Give two reasons why the transmitted wave is modulated, rather than transmitting the information signal directly as a radio wave.

    
8.

The variation with time of the signal transmitted from an aerial is shown in the figure below.




  • State the name of this type of modulated transmission.


  • Use the figure above to determine the frequency of


    • the carrier wave,


    • the information signal.

    

9.

In commercial radio, transmissions are made by means of carrier waves that are modulated by the audio signals.


  • State what is meant by a modulated carrier wave.


  • State three reasons why modulated carrier waves are used, rather than the direct transmission of electromagnetic waves having audio frequencies.

    
10.

The variation with frequency of the amplitude of the transmitted wave is shown in the figure below.




For this transmission, determine


  • the wavelength of the carrier wave,


  • the bandwidth,


  • the maximum frequency, in , of the transmitted audio signal.

    
11.

The signal from a radio station is amplitude modulated.


  • State what is meant by amplitude modulation (AM).


  • The variation with frequency of the intensity of the signal from the radio station is shown in the figure below.




    State, for this signal,


    • the bandwidth,


    • the maximum audio frequency that is broadcast.

    
12.

In radio communication, the bandwidth of an FM transmission is greater than the bandwidth of an AM transmission. State


  • what is meant by bandwidth,


  • one advantage and one disadvantage of a greater bandwidth.


    
13.

A carrier wave has a frequency of and is measured to have an amplitude of . The carrier wave is frequency modulated by a signal of frequency and amplitude . The frequency deviation of the carrier wave is . Determine, for the frequency modulated carrier wave,


  • the measured amplitude,


  • the maximum and the minimum frequencies,


  • the minimum time between a maximum and a minimum transmitted frequency.

    
14.

  • State what is meant by the amplitude modulation (AM) of a radio wave.


  • A radio wave is modulated by an audio signal. The variation with frequency of the amplitude of the modulated wave is shown in the figure below.




    Determine:


    • the wavelength of the carrier wave


    • the bandwidth of the modulated wave


    • the maximum frequency of the audio signal.

    
15.

A sinusoidal carrier wave has a constant amplitude and a frequency of . The carrier wave is modulated by a signal wave such that a displacement of the signal wave causes a change in frequency of . The signal wave has frequency and amplitude .


  • State the name of this type of modulation of the carrier wave.


  • For this modulated carrier wave, determine the variation, if any, in:


    • its amplitude


    • its frequency.

    
16.

An audio signal is transmitted by means of a modulated radio wave. The variation with frequency of the amplitude of the radio wave is shown in the figure below.




For this transmission, determine:


  • the wavelength, in km, of the carrier wave


  • the bandwidth


  • the frequency of the audio signal.

    
17.

  • State what is meant by the amplitude modulation (AM) of a radio wave.


  • State two advantages of AM transmissions when compared with frequency modulation (FM) transmissions.

    
18.

  • The variation with frequency of the amplitude of a transmitted radio wave after amplitude modulation by an audio signal is shown in the figure below.




    For this transmission, determine:


    • the wavelength of the carrier wave


    • the maximum frequency of the transmitted audio signal.


  • Another audio signal with the same maximum frequency is transmitted using a different carrier wave frequency. The lowest frequency of this modulated wave is equal to the highest frequency of the modulated wave in (a). Determine the frequency of this carrier wave.

    

19.

The variation with time of the displacement of an amplitude-modulated (AM) wave is shown in the figure below.




The sinusoidal information signal has frequency .


  • Determine the frequency of the carrier wave.


  • On the axes of the figure below, sketch the frequency spectrum of the modulated wave.



    
20.

A carrier wave is frequency modulated.


  • Describe what is meant by frequency modulation.


  • The sinusoidal carrier wave has a frequency of and an amplitude of . The carrier wave is frequency modulated by a sinusoidal signal of frequency and amplitude . The frequency deviation of the carrier wave is . Determine, for the frequency-modulated carrier wave,


    • the amplitude,


    • the minimum frequency,


    • the maximum frequency,


    • the number of times per second that the frequency changes from its minimum value to its maximum value and then back to the minimum value