High School

A poor university student is listening to Top 40 music on her FM radio, tuned into a wavelength of 3.23 m. Convert this wavelength into a frequency in MHz. The speed of light is [tex]c = 3.00 \times 10^8 \, \text{m/s}[/tex].

a) 92.9 MHz
b) 97.8 MHz
c) 102.7 MHz
d) 107.5 MHz

Answer :

Final answer:

To convert a wavelength in meters to frequency in MHz, use the formula f = c / λ, where c is the speed of light. In this case, a wavelength of 3.23m corresponds to a frequency of 92.9 MHz. (Option A is the correct answer)

Explanation:

To convert a wavelength in meters to frequency in MHz, employ the formula f = c / λ, where c represents the speed of light. Given a wavelength of 3.23m, its corresponding frequency calculates to 92.9 MHz. This conversion utilizes the fundamental relationship c = fλ, where c denotes the speed of light at 3.00 × 10^8 m/s. Applying the formula λ = c / f, with λ as 3.23m and c as 3.00 × 10^8 m/s, yields the frequency f. Solving for f results in 92.9 MHz, aligning with option A as the correct answer. This process elucidates the wavelength-frequency relationship, crucial in electromagnetic wave analysis.

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