Physics

Physics

Problem

A radio wave has wavelength 300 m300\,\text{m} in free space. Determine its angular frequency. a) 3.0×108 rad s−13.0\times10^{8}\,\text{rad\,s}^{-1} b) 6.3×108 rad s−16.3\times10^{8}\,\text{rad\,s}^{-1} c) 6.3×106 rad s−16.3\times10^{6}\,\text{rad\,s}^{-1} d) 1.0×106 rad s−11.0\times10^{6}\,\text{rad\,s}^{-1}
Intuitive explanation

Radio waves travel at the speed of light, so you can connect wavelength to frequency using the wave equation c=λfc = \lambda f. Once you have the ordinary frequency ff, converting to angular frequency ω\omega is just a proportionality: they're related by a factor of 2π2\pi. The key is remembering that angular frequency counts radians per second rather than cycles per second.

Intuitive explanation

Radio waves travel at the speed of light, so you can connect wavelength to frequency using the wave equation c=λfc = \lambda f. Once you have the ordinary frequency ff, converting to angular frequency ω\omega is just a proportionality: they're related by a factor of 2π2\pi. The key is remembering that angular frequency counts radians per second rather than cycles per second.

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