𝜆
=
𝑐
𝜈

𝜈
=
𝑐
𝜆

WUKF FM transmits at a frequency of 93.5 MHz. What is the wavelength (
𝜆
) of the electromagnetic radiation that carries the station's signal?

Question

𝜆
=
𝑐
𝜈
                                      
𝜈
=
𝑐
𝜆

WUKF FM transmits at a frequency of 93.5 MHz. What is the wavelength (
𝜆
) of the electromagnetic radiation that carries the station's signal?

BlackTom AI · Accepted Answer

To determine the wavelength, we start from the basic relationship for electromagnetic waves: lambda = c / f, where c is the speed of light and f is the frequency.
Option-by-option analysis helps verify the correct choice:
- Option A: 6.42 × 10^-9 m. This is far too small for a radio frequency of tens of MHz. Such a wavelength would correspond to extremely high frequencies in the GHz to THz range, not to 93.5 MHz. Thus this is incorrect.
- Option B: 3.21 m. This value results from substituting f = 93.5 MHz into lambda = c / f: lambda ≈ (3.0 × 10^8 m/s) / (93.5 × 10^6 Hz) ≈ 3.21 m. This is a reasonable radio-wavelength for a station in the FM band, so this appears correct.
- Option C: 3.21 × 10^6 m. This would be an enormous wavelength, corresponding to a frequency about 100 times lower than 1 MHz. It does not match the given frequency of 93.5 MHz, so this is incorrect.
- Option D: 3.12 × 10^15 m. This wavelength is astronomical in scale, equivalent to roughly 10^6 times the distance to the Sun, and utterly incompatible with a terrestrial FM transmission. Therefore this is incorrect.
In summary, evaluating lambda = c / f with c ≈ 3.0 × 10^8 m/s and f = 93.5 × 10^6 Hz yields about 3.21 meters, confirming that Option B is the correct wavelength for this station.

𝜆 = 𝑐 𝜈 𝜈 = 𝑐 𝜆 WUKF FM transmits at a frequency of 93.5 MHz. What is the wavelength ( 𝜆 ) of the electromagnetic radiation that carries the station's signal?

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