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A radio can tune into any station in the 6 MHz to 12 MHz band. What is the corresponding wavelength band? (c=3×10⁸ m s⁻¹)

Asked in GUJCET 2022 · Wavelength, frequency and photon energy

• (1) 40 m to 60 m
• (2) 25 m to 50 m
• (3) 20 m to 30 m
• (4) 10 m to 20 m

Step-by-step solution

Why the other options are wrong

• (1) comes from no single slip produces 40 m to 60 m. Sanity check: λ=c/u gives (3×10⁸)/(6×10⁶)=50 m and (3×10⁸)/(12×10⁶)=25 m.
• (3) comes from fails the ratio test: the two frequencies differ by a factor 2, so the two wavelengths must differ by 2 as well, and (30)/(20) is only 1.5.
• (4) comes from has the right 2:1 ratio but the wrong scale. 10 m to 20 m is the band a set tuned from 15 MHz to 30 MHz would cover.

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