Sample problems in Waves and Optics

Waves and Optics

Propagation of Sound and Light Waves

This page explains concepts at college level in the field of wave propagation. The sound and light waves have been clubbed together to highlight lot of similarity in concepts dealing with wave phenomena such as reflection, transmission, interferences and diffraction.

Analogy and similarity between light and sound waves

Phenomena	Sound Waves	Light Waves
Equation of wave	y = A sinω(t - x/v)	E = E₀ sinω(t - x/v)
Speed of wave	v = [γ*RT]^0.5 in air, v = [B / ρ]^0.5-liquid, v = [Y / ρ]^0.5-solid	v = c / μ
Path difference Multiple of wave-length	Δx Physical distance between sources	μ * Δx_VACUUM
Phase difference Multiple of 2π [ = 1 cycle]	δ = Δx * 2π/λ	δ = Δx * 2π/λ
Constructive Interference	Maxima: Δx = n * λ or δ = 2nπ	Bright fringes: Δx = n * λ or δ = 2nπ
Destructive Interference	Minima: Δx = (2n+1) * λ/2 or δ = (2n + 1)π	Dark fringes: Δx = (2n+1) * λ/2 or δ = (2n + 1)π

Diffraction and Interference

For example, refer to the interference of waves (including diffraction in case of light). The maxima and minima of sound waves are analogous to the bright and dark fringes and their location can be determined in similar ways.
$Diffraction and interference of sound and light waves$
The path difference is given by Δx = d * sinθ ≈ d * tanθ as sinθ ≈ = tanθ for small values of θ.

Note that distance between two consecutive maxima or consecutive minima of sound wave is analogous to the distance between centres of consecutive dark fringes or bright fringes. Note the symmetry of the geometry and wave transmission phenomena. For light wave, the symmetry plane can be also treated as a plane mirror described as follows:

$Symmetry in diffraction of light waves$

Traveling Wave - String in Tension

The equation of traveling wave on a string is given by y = A * sin[ω(t - x/v)] where v is the velocity of the wave moving from left to right. Following animation has been created to describe the wave motion due to transverse [up-down motion] vibration of each particle of the string. The purpose of this animation to improve the understanding of the phenomena described widely in appropriate textbooks on physics.

Standing Wave - String in Tension

The equation of standing wave on a string is given by y = 2A * sin[nπx/L] * cos(ωt). Following animation has been created to describe the location of nodes and antinodes. The purpose of this animation to improve the understanding of the phenomena described widely in appropriate textbooks on physics.

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