(a) A wave is described, in SI units, by . Find its wavelength , frequency and phase…

PHYSICS · Subjective · Fermi University Physics · Oscillations, Waves & Acoustics · Optics & Photonics · Wave propagation and light in media

Optics and Photonics, Ch Harmonic waves, phasors and group velocity

Problem

(a) A wave is described, in SI units, by E(x,t)=E0cos⁡(1.05×107 x−3.15×1015 t)E(x,t) = E_0\cos(1.05\times10^{7}\,x - 3.15\times10^{15}\,t). Find its wavelength λ\lambda, frequency ν\nu and phase velocity vv. (b) A different, unrelated wave obeys the dispersion relation ω(k)=8.00×10−3 k2\omega(k) = 8.00\times10^{-3}\,k^{2} (SI units, kk in m−1\mathrm{m^{-1}}, ω\omega in rad s−1\mathrm{rad\,s^{-1}}). Find its group velocity at k=5.00×104 m−1k = 5.00\times10^{4}\ \mathrm{m^{-1}}.

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