Question

Suppose a popular FM radio station broadcasts radio waves with a frequency of 108. MHz. Calculate the wavelength of these radio waves. Round your answer to 3 significant digits.

Answers

  1. Answer:

    The wavelength is 1.87m

    Explanation:

    Radio waves are part of the electromagnetic spectrum, any radiation of that electromagnetic spectrum has a speed of 3.00×10^{8}m/s in vacuum.

    Therefore, the wavelength can be determined by the following equation:

    c = \lambda \cdot \nu  (1)

    Where c is the speed of light, \lambda is the wavelength and \nu is the frequency.  

    Then, \lambda can be isolated from equation 1

    \lambda = \frac{c}{\nu}   (2)

    Notice that it is necessary to express the frequency in units of Hz.  

    \nu = 160MHz . \frac{1000000Hz}{1MHz} ⇒ 160000000Hz

    \lambda = \frac{3x10^{8}m/s}{160000000Hz}  

    But 1Hz = s^{-1}

    \lambda = \frac{3x10^{8}m/s}{160000000s^{-1}}  

    \lambda = 1.87m

    Hence, the wavelength is 1.87m

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