Calculate the range of wavelengths for the frequencies found on the FM band. Take a look at the “whip” radio antennas on cars, comment on th

Question

Calculate the range of wavelengths for the frequencies found on the FM band. Take a look at the “whip” radio antennas on cars, comment on the size of the wavelength and the antenna. {2.8 – 3.4 m}

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Thành Công 1 year 2021-09-02T07:18:42+00:00 1 Answers 14 views 0

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    2021-09-02T07:20:04+00:00

    Answer:

    2.8m-3.4m

    Explanation:

    Radio waves are electromagnetic waves and they all travel with a speed of

    [tex]3*10^8m/s[/tex] in air.

    The range of frequencies in the FM band is from 88MHz to 108MHz.

    Generally, the relationship between velocity, frequency and wavelength for electromagnetic waves is given by equation (1);

    [tex]v=\lambda f…………..(1)[/tex]

    From equation (1), we can write,

    [tex]\lambda=\frac{v}{f}……………(2)[/tex]

    For the upper frequency of 108MHz, the wavelength is given by;

    [tex]\lambda_1=\frac{3*10^8}{108*10^6}\\\lambda_1=0.02778*10^2\\\lambda_1=2.78m[/tex]

    Similarly, for the lower frequency of 88MHz, the wavelength is given by;

    [tex]\lambda_2=\frac{3*10^8}{88*10^6}\\\lambda_2=0.0341*10^2\\\lambda_2=3.41m[/tex]

    The range of wavelength therefore  is [tex]\lambda_1-\lambda_2=2.8m-3.4m[/tex] approximately.

    Please note the following:

    [tex]108MHz=108*10^6Hz\\88MHz=88*10^6Hz[/tex]

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