A radio can tune in to any station in the 7.5 MHz to 12 MHz band. What is the corresponding wavelength band?
A radio can tune in to any station in the 7.5 MHz to 12 MHz band. What is the corresponding wavelength band?
Solution and Explanation
A radio can tune to minimum frequency, \(ν_1 = 7.5 \ MHz= 7.5 × 10^6 Hz \)
Maximum frequency, \(ν_2 = 12\ MHz = 12 × 10^6 Hz \)
Speed of light, \(c = 3 × 10^8 \ m/s \)
Corresponding wavelength for \(ν_1\) can be calculated as:
\(λ_1 = \frac {c}{v_1}\)
\(λ_1 = \frac {3\times 10^8}{7.5\times 10^6 }= 40 \ m\)
Corresponding wavelength for \(ν_2\) can be calculated as:
\(λ_2 = \frac {c}{v_2}\)
\(λ_2 = \frac {3\times 10^8}{12\times 10^6 }= 25 \ m\)
Thus, the wavelength band of the radio is \(40 \ m\) to \(25 \ m\).
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Concepts Used:
Electromagnetic Spectrum
The term used by scientists to describe the entire range of light that exists is the electrostatic spectrum. Light is a wave of alternating electric and magnetic fields. The propagation of light doesn't vary from waves crossing an ocean. Like any other wave, light also has a few fundamental properties that describe it. One is its frequency. The frequency is measured in Hz, which counts the number of waves that pass by a point in one second.
The electromagnetic waves that your eyes detect are visible light and oscillate between 400 and 790 terahertz (THz). That’s several hundred trillion times a second.