bowshock · the Doppler effect and the Mach cone

Drag the green ring to move the listener. With "Follow the pointer", drag anywhere else to steer the source. Space pauses, R restarts, M toggles sound.

What the listener hears

higher lower heard backwards

Images: –
Pitch now: –
Delay: –

Microphone

Booms, last 10 s: –
Last boom: –

The pressure the listener's ear would record: one sine per image, each at the phase it left with. A boom, marked in red here and on the pitch chart, is the moment two images are born together at the edge of the cone.

Source

Path Mach number Tone (rings per second)

Speed: –
Ahead: –
Behind: –
Mach angle: –

"Ahead" and "Behind" are the shifts heard at rest along the line of motion: 1/(1 − M) and 1/(1 + M) in still air, (c + w)/(c + w − v) in a wind w. Ahead of a source that outruns its sound nothing arrives at all.

Air and listener

Wind Listener walks at

Mach through the air: –
Listener speed: –

Wind is a fraction of the speed of sound, positive blowing right. It carries the rings along, so sound is slower upwind and faster downwind, and it is the source's speed through the air that decides whether there is a cone. The listener paces its row, turning at the edges.

Scenes

View

Tint rings by pitch shift Mach cone on the straight pass