Discussion
An electromagnetic wave travelling in vacuum has its electric field component, E = 15 sin \([1.57y + 5.4t]\hat{j}\) The wavelength of the wave is
Answer: A
The wavelength is 4.0 m.
Compare the phase \(1.57y + 5.4t\) with \(ky + \omega t\). The coefficient of y is the wave number, k = 1.57 m\(^{-1}\), which is \(\frac{\pi}{2}\).
\[ \lambda = \frac{2\pi}{k} = \frac{2\pi}{\pi/2} = 4\ \text{m} \]
Taking \(\lambda = \frac{1}{k}\) or \(\frac{\pi}{k}\) gives about 0.64 m or 2.0 m. The coefficient of t gives the angular frequency, not the wavelength.
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