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The FM radio station WHMS is broadcast using a carrier frequency f = 97.5 MHz. What is the wavelength in air of the radio wave for this station? Checkbox options (a) λ= 0.33 m (b) λ= 3.08 m (c) λ= 612.61 m

Answer :

To find the wavelength [tex]\lambda[/tex] of a radio wave, you can use the equation that relates the speed of light [tex]c[/tex], frequency [tex]f[/tex], and wavelength [tex]\lambda[/tex]:

[tex]c = f \times \lambda[/tex]

Where:

  • [tex]c[/tex] is the speed of light in a vacuum, approximately [tex]3 \times 10^8[/tex] meters per second (m/s).
  • [tex]f[/tex] is the frequency of the radio waves.
  • [tex]\lambda[/tex] is the wavelength, which is what we want to find.

Given that the frequency [tex]f[/tex] of the radio station WHMS is [tex]97.5[/tex] MHz, we first convert this frequency into hertz (Hz), as [tex]1[/tex] MHz = [tex]10^6[/tex] Hz:

[tex]f = 97.5 \times 10^6 \text{ Hz}[/tex]

Now, we rearrange the formula to solve for wavelength [tex]\lambda[/tex]:

[tex]\lambda = \frac{c}{f}[/tex]

Substitute the values for [tex]c[/tex] and [tex]f[/tex] into the equation:

[tex]\lambda = \frac{3 \times 10^8 \text{ m/s}}{97.5 \times 10^6 \text{ Hz}}[/tex]

Calculate [tex]\lambda[/tex]:

[tex]\lambda \approx 3.08 \text{ m}[/tex]

Therefore, the wavelength of the radio wave for radio station WHMS is approximately [tex]3.08[/tex] meters. Thus, the correct answer is option (b) [tex]\lambda = 3.08 \text{ m}[/tex].

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