# IB DP Physics: HL复习笔记9.5.1 The Doppler Effect

### The Doppler Effect

• When a source of sound, such as the whistle of a train or the siren of an ambulance, moves away from an observer:
• It appears to decrease in frequency, i.e. it sounds lower in pitch
• Although, the source of the sound remains at a constant frequency
• This frequency change due to the relative motion between a source of sound or light and an observer is known as the Doppler effect (or Doppler shift)
• When the observer and the source of sound (e.g. ambulance siren) are both stationary:
• The waves appear to remain at the same frequency for both the observer and the source

Stationary source and observer

• When the source starts to move towards the observer, the wavelength of the waves is shortened
• The sound, therefore, appears at a higher frequency to the observer

Moving source and stationary observer

• Notice how the waves are closer together between the source and the observer compared to point P and the source
• This also works if the source is moving away from the observer
• If the observer was at point P instead, they would hear the sound at a lower frequency due to the wavelength of the waves broadening
• The frequency is increased when the source is moving towards the observer
• The frequency is decreased when the source is moving away from the observer

#### Worked Example

A cyclist rides a bike ringing their bell past a stationary observer. Which of the following accurately describes the doppler shift caused by the sound of the bell?

• If the cyclist is riding past the observer, the wavelength of sound waves are going to become longer
• This rules out options A and C
• A longer wavelength means a lower frequency (from the wave equation)
• Lower frequency creates a lower sound pitch
• Therefore, the answer is row D

### Representing The Doppler Effect

• Wavefront diagrams help visualize the Doppler effect for moving wave sources and stationary observers

Wavefronts are even in a stationary object but are squashed in the direction of the moving wave source

• A moving object will cause the wavelength, λ, (and frequency) of the waves to change:
• The wavelength of the waves in front of the source decreases (λ – Δλ) and the frequency increases
• The wavelength behind the source increases (λ + Δλ) and the frequency decreases
• This effect is known as the Doppler effect or Doppler shift
• Note: Δλ means 'change in wavelength'
• The Doppler shift is observed by all waves including sound and light
• When the source starts to move towards the observer, the wavelength of the waves is shortened
• For sound waves, sound, therefore, appears at a higher frequency to the observer
• For light waves, the light shifts towards blue due to its higher frequency

Representing red-shifted and blue-shifted light

• When the source starts to move away from the observer, the wavelength of the wave broadens
• For sound waves, sound therefore appears at a lower frequency to the observer
• For light waves, the light shifts towards red due to its lower frequency
• When the source starts to move towards the observer, the wavelength of the wave shortens
• For sound waves, sound therefore appears at a higher frequency to the observer
• For light waves, the light shifts towards blue due to its higher frequency
• This is because red light has a longer wavelength than blue light