Wave Equation Parameters

A travelling wave written as E = E_0\sin(kx - \omega t) encodes the angular wave number k as the coefficient of x and the angular frequency \omega as the coefficient of t. Here k = 0.5 \times 10^{3} = 500\ \text{rad/m}. The wavelength follows from \lambda = 2\pi/k = 2\pi/500 = 1.26 \times 10^{-2}\ \text{m}, which equals 1.26 cm. The 2.50 cm option mistakenly uses \lambda = 1/k without the factor 2\pi scaled correctly. The 0.63 cm value halves the true wavelength, perhaps by confusing k with 2k. The 12.6 cm answer misplaces the decimal by a factor of ten. Reading wave parameters directly from the argument of the sine function is a routine JEE skill rooted in the NCERT treatment of progressive waves, where every travelling wave shares the same canonical form regardless of whether it is mechanical or electromagnetic. The positive x and negative t signs together tell us the wave moves in the +x direction, another piece of information hidden in the argument. As a consistency check, the wave speed is \omega/k = (1.5 \times 10^{11})/500 = 3.0 \times 10^{8}\ \text{m/s}, exactly the speed of light, confirming this is a genuine electromagnetic wave in vacuum and that the extracted wave number is correct.