An approaching ambulance sounds higher in pitch, and a receding ambulance sounds lower. The spacing between wavefronts and the number arriving in 1 second explain why.
Adjust conditions:
The sliders adjust the values
音源が170 m/sで近づく。止まっている人に聞こえる振動数は？
音源と聞く人が同じ向きに170 m/sで進む。聞こえる振動数は？
The formula follows from the wavefront diagram.
1The spacing between wavefronts from a stationary source is determined.λ=Vf……
2The spacing between wavefronts ahead of a moving source is determined.λ′=V − uf……
3The frequency received by a stationary observer is determined.f′=V fV − u……
4The frequency received by a moving observer is determined.f′=(V + v) fV……
5The 2 cases are compared at the same approach speed.V fV − u＞(V + u) fV……
6The formula for a moving source and a moving observer is derived.f′=f (V − vo)V − vs……
7The ambulance values are substituted for direct approach and recession.1009 Hz→915 Hz……
Extension: a roadside observer and supersonic motion
8The observer is beside the road.f′=f VV − u cosθ……
9The source moves faster than sound.sinθ=Vu……
What this chapter has shown
The wavelength decreases ahead of the ambulance and increases behind it. After the ambulance passes, fewer wavefronts reach a stationary observer in 1 second, so the pitch falls. For a roadside observer, this change occurs smoothly.
1009→915 HzThe source approaches and recedes along a straight line
When the source and observer move in the same direction at 170 m/s, the observed frequency remains 400 Hz.
In everyday lifeBaseball radar guns and weather radar determine the speeds of balls and raindrops from the frequency shift of reflected radio waves.
Detailed summary
The Doppler effect occurs because the spacing between wavefronts and the speed at which the listener encounters them change, even though the pitch emitted by the source remains constant. Motion of the source changes the wavelength in the air, while motion of the listener changes the speed at which the listener encounters the wavefronts. Since the speed of sound is determined relative to the air, these 2 cases produce different results even when the speed of approach is the same. When the motion is not along the line joining the source and the listener, only the component of velocity along that line contributes to the effect, so the perceived pitch changes smoothly.