EngineerHub.orgChoose experiment4 connected views
Sound controls
Wavefront geometry
Wavefronts move through the medium at the wave speed while the source and observer may move independently.
fₒ = fₛ(v − vₒ)/(v − vₛ)
What the picture is showing
A moving source changes the spacing of successive wavefronts in the medium. A moving observer does not change that spacing; instead, it changes how rapidly the observer encounters the wavefronts.
Source approachesFront wavelength becomes shorter, so the received frequency rises.
Source recedesRear wavelength becomes longer, so the received frequency falls.
Observer movesWave spacing in the medium stays the same; encounter rate changes.
At Mach 1The source catches its own disturbances; above Mach 1 they form a shock cone.
Core relationships
fₒ = fₛ (v − vₒ)/(v − vₛ)
λ₀ = v/fₛ
λfront = (v − vₛ)/fₛ
λrear = (v + vₛ)/fₛ
Velocity signs in the main sound experiment use the diagram axis: positive is to the right. Because the source starts left of the observer, positive source velocity is approaching while positive observer velocity is moving away.
- The classical sound formula is for waves propagating through a medium. Source and observer velocities are measured relative to that medium.
- The standard one-dimensional moving-source expression is used only while the source is subsonic. At and above Mach 1, the simulator switches to shock-cone geometry rather than displaying the denominator singularity as a physical infinite pitch.
- The air sound speed is calculated from a = √(γRT) with γ = 1.4 and R = 287.05 J/(kg·K), an ideal-gas educational approximation.
- Water and steel speeds are representative constants for comparison; real values vary with temperature, composition and wave mode.
- The fly-by model uses the instantaneous line-of-sight component of source velocity and ignores acoustic propagation delay in the plotted and audible frequency. This keeps source position and pitch synchronized for teaching; it is an explicitly stated approximation for an off-axis pass.
- The light tab uses the special-relativistic longitudinal Doppler formula. Unlike sound, light does not require a material medium.
- OpenStax, University Physics Volume 1, §17.7 — classical moving-source and moving-observer Doppler equations.
- OpenStax, Physics, §14.3 — train-horn worked example and sonic-boom discussion.
- NASA Glenn Research Center — Speed of Sound — ideal-gas speed-of-sound relation.
- NASA Science — Doppler effect / redshift — approaching light is blueshifted and receding light is redshifted; relativistic redshift relation.