Physic Labs

Oscillations and waves

Interference of mechanical waves

Map the constructive and destructive regions produced by two in-phase circular sources; check the path-difference conditions Δr=kλ\Delta r = k\lambda and Δr=(k+12)λ\Delta r = (k+\tfrac{1}{2})\lambda across the fringe system.

High school

Equipment

  • Two in-phase point sources on a virtual water surface, rotatable in 3D
  • “Amplitude of each source” slider
  • “Wavelength λ” and “Source separation d” sliders
  • “Pause” button to freeze the wave pattern

Procedure

  1. Freeze the pattern and find the nodal lines

    Press “Pause” for a static view: between the strongly oscillating regions lie nearly still hyperbolic bands — the nodal lines where the two waves always cancel. Drag the canvas to rotate and view the surface from above.

  2. Change λ and check the path-difference conditions

    Sweep “Wavelength λ”: larger λ spreads the maxima and minima further apart. From the position of a nodal line, argue that minima satisfy Δr=(k+12)λ\Delta r = (k+\tfrac{1}{2})\lambda while maxima satisfy Δr=kλ\Delta r = k\lambda.

  3. Change the source separation and amplitude

    Increase “Source separation d” and count the hyperbolic maxima appearing between the sources: more fringes fit because the maximum path difference Δrmax⁡=d\Delta r_{\max} = d contains more wavelengths. Change “Amplitude” to see contrast change while fringe positions stay fixed.

Simulation

Experiment history

The superposition principle was stated clearly by Thomas Young in 1801–1802 from observations of water waves and sound, even before his double-slit work: when two waves meet, the total displacement is the sum of the individual ones — which immediately explains zones of cancellation. He wrote in his lectures that two wave trains “may either augment or destroy one another”. For mechanical waves the idea was verified by many nineteenth-century devices: Georg Quincke's interference tube (1866) split sound into two branches and recombined it into audible minima; the ripple tank became the standard laboratory and classroom tool to visualize the same hyperbolic fringe system shown in this simulation.

Related physicists

Galileo GalileiIsaac NewtonThomas YoungAugustin-Jean Fresnel

Related library topics

Interference of mechanical waves