Doppler Effect
Moving Source Sound moves equally in all directions from a source. Circular (or spherical) pattern If the source is moving the origin of successive circles moves.
Wavelength Shift The normal period is T and the observer moves at speed u. The wavelength ahead of the source is shorter. l’ = l - uT The wavelength behind the source is longer. l’ = l + uT
Frequency Shift The period is related to the wavelength. This can be converted into a frequency shift. Insert + for – to get the shift behind the source.
Ambulance An ambulance is approaching at 130 km/h with a siren at 1.2 kHz. What pitch do you hear? Change speed to m/s (130 km/h)/3.6 = 36 m/s Find the Doppler shift. u/v = (36 m/s)/(343 m/s) u/v = 0.105 f’ = f/(1-1.05) = 1340 Hz
Moving Observer If the observer is moving toward the sound the effect is similar, but the wave crests have a different relative spacing. A speed gun uses a double Doppler shift. There is a shift for both the pulse out and reflected signal.
Shock Wave A moving source can exceed the speed of sound. The sound waves constructively interfere on a front at an angle to the motion. This is called a shock wave.
Sonic Boom The speed of sound is called Mach 1. Faster than that speed causes a shock wave – a sonic boom.