Modelling the Doppler Effect and Mach Cone Formation

Abstract

The Doppler effect is the apparent change in a wave’s observed frequency caused by relative motion between its source and an observer. This report focuses on sound emitted by a moving source and detected by a stationary observer in a stationary medium, and investigates how the relationship between a supersonic aircraft’s velocity and the local speed of sound dictates the formation of a Mach cone. An interactive digital simulation was created as a learning tool for Year 11 Physics students. Users can vary source speed, wave speed, and emitted frequency continuously and immediately see changes in compression, rarefaction, observed frequency and Mach cone geometry. The model allows experimentation across subsonic, sonic and supersonic conditions, whilst its quantitative readout calculates the source velocity, Mach number and observed frequencies. Although the simulation depicts 2D kinematics effectively, it is restricted to a two-dimensional planar surface and assumes a homogeneous atmosphere. Future versions could add an opacity gradient to approximate intensity attenuation under the Inverse Square Law and a vertical temperature gradient to simulate atmospheric refraction. Nevertheless, the model remains effective because its numerical feedback and interactivity help students connect abstract Doppler-effect equations to observable wavefront behaviour.