A graph shows the sum of two sine waves of equal amplitude and nearly equal wavelength
PHYSICS · Multi-part · Fermi University Physics · Oscillations, Waves & Acoustics · Quantum Mechanics · Origins of quantum theory
Quantum Mechanics: From the Photon to the Hydrogen Atom, Ch Matter waves and wave-particle duality
Problem
A graph shows the sum of two sine waves of equal amplitude and nearly equal wavelength, plotted against position x. Two features can be read off the picture: inside each swell the crests are 480 nm apart, and the places where the sum fades to zero are 24μm apart.
((a)) Find the difference between the two wavelengths, in nm. (For two nearby wavelengths the fades repeat every λ1λ2/(λ2−λ1), which for nearby wavelengths is λˉ2/Δλ with λˉ the mean.)
((b)) State the two wavelengths, in nm.
((c)) Find the spread of wavenumber Δk=k1−k2 present in the sum, in nm−1, using k=2π/λ.
((d)) Take the length of the central lump to be half the distance between fades, Δx=12μm, and evaluate the product ΔxΔk. Comment on its size.