The Doppler Effect

中文辅助说明

声源由左向右移动，每个波前都以发出时的位置为圆心向外传播。拖动绿色听者，或使用位置滑杆，比较接近和远离时的音高。可调整声源速率与频率，暂停观察波前，开启声音听实际接收频率；速率为零时波前成为同心圆。动画经过慢放，显示的波前每条代表 20 个周期，数值和音高使用真实频率。

The source moves; the speed of sound stays constant

Sound speed v = 340 m/s

Sound is off by default. Turn it on to hear the received pitch at a low volume.

Compare ahead and behind

Source speed v_s100 m/s · 360 km/h Source frequency f₀440 Hz

Fine-tune the listener position

Horizontal position Distance from the road

Frequency at the listener—

Directly ahead

Directly behind

Wavelength ahead

Wavelength behind

Ahead: compressed wavefronts

f_{\rm front}=f_0\frac{v}{v-v_s}

Behind: spread-out wavefronts

f_{\rm behind}=f_0\frac{v}{v+v_s}

Wavelength ahead

\lambda_{\rm front}=\frac{v-v_s}{f_0}

Wavelength behind

\lambda_{\rm behind}=\frac{v+v_s}{f_0}

Observe and explain

Set the source speed to zero. The wavefronts are concentric and the frequency is f₀ in every direction.
Let the source pass. The wavelength is shorter ahead and longer behind, while the speed of sound stays at 340 m/s.
Move the listener closer to the road and turn on sound. Compare the pitch before and after the pass. The change is quicker closer to the road.

The model uses still air, a stationary listener, and a point source moving at a constant speed below the speed of sound. The animation runs at 7% of real speed and shows one wavefront every 20 cycles. The received frequency accounts for sound travel time. The directly ahead and behind values are ideal comparisons along the line of motion. Changing speed or frequency restarts the pass.