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24 May, 10:47

A radio station's channel, such as 100.7 FM or 92.3 FM, is actually its frequency in megahertz (MHz), where 1MHz=106Hz and 1Hz=1s-1. Calculate the broadcast wavelength of the radio station 91.10 FM. Express your answer to four significant figures and include the appropriate units.

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  1. 24 May, 14:43
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    3.293 m

    Explanation:

    Data Given:

    Frequency of radio wave = 91.10 FM or 91.10 MHz

    1 MHz = 10⁶ Hz

    1 Hz = 1 s⁻¹

    wavelength = ?

    Solution:

    As Frequency of radio wave is 91.10 FM or 91.10 MHz

    if we look for conversion of MHz to Hz

    So,

    1 MHz = 10⁶ Hz

    91.10 MHz = (91.10) (10⁶) = 91.1 x 10⁶ Hz

    So

    91.10 MHz = 91.1 x 10⁶ Hz

    Now we look for conversion of Hz to s⁻¹

    1 Hz = 1 s⁻¹

    91.1 x 10⁶ Hz = 91.1 x 10⁶ s⁻¹

    So

    91.1 x 10⁶ Hz = 91.1 x 10⁶ s⁻¹

    Now equation used to calculate wavelength

    f = c/λ

    rearrange the above equation

    λ = c/f ... (1)

    Where:

    c = speed of light = 3 x 10⁸ ms⁻¹

    λ = wavelength

    put the values in above equation 1

    λ = 3 x 10⁸ ms⁻¹ / 91.1 x 10⁶ s⁻¹

    λ = 3.293 m

    So the wavelength of radio station wave = 3.293 m
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