What frequency produces a 1-wavelength length of 10 ft?

What frequency produces a 1-wavelength length of 10 ft?

• A. 93.6 MHz
• B. 94.0 MHz
• C. 9.36 MHz
• D. 23.4 MHz

Answer: (A)

The main idea is that wavelength and frequency are inversely related in free space: λ = c / f. A wavelength of 10 ft is about 3.048 meters. Using c ≈ 3.00 × 10^8 m/s, the frequency comes out to f ≈ 3.00 × 10^8 / 3.048 ≈ 9.8 × 10^7 Hz, or about 98.4 MHz. Among the given options, 93.6 MHz is the closest match to that computed value, while the other two lower frequencies correspond to much longer wavelengths (9.36 MHz gives ~32 m, and 23.4 MHz gives ~12.8 m). Small differences due to rounding or air vs vacuum speed show up here, so 93.6 MHz is the best fit for producing a 1-wavelength length near 10 ft.

The main idea is that wavelength and frequency are inversely related in free space: λ = c / f. A wavelength of 10 ft is about 3.048 meters. Using c ≈ 3.00 × 10^8 m/s, the frequency comes out to f ≈ 3.00 × 10^8 / 3.048 ≈ 9.8 × 10^7 Hz, or about 98.4 MHz.

Among the given options, 93.6 MHz is the closest match to that computed value, while the other two lower frequencies correspond to much longer wavelengths (9.36 MHz gives ~32 m, and 23.4 MHz gives ~12.8 m). Small differences due to rounding or air vs vacuum speed show up here, so 93.6 MHz is the best fit for producing a 1-wavelength length near 10 ft.