# 8.4.1 Doppler Effect

### Doppler Shift of Sound

• The whistle of a train or the siren of an ambulance appears to increase in frequency (sounds higher in pitch) as it moves away from you
• 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 (e.g. yourself) and the source of sound (e.g. ambulance siren) are both stationary, the waves are 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

### Calculating Doppler Shift

• When a source of sound waves moves relative to a stationary observer, the observed frequency can be calculated using the equation below:

Doppler shift equation

• The wave velocity for sound waves is 340 ms-1
• The ± depends on whether the source is moving towards or away from the observer
• If the source is moving towards, the denominator is v – vs
• If the source is moving away, the denominator is v + vs

#### Worked Example

A police car siren emits a sound wave with a frequency of 450 Hz. The car is travelling away from an observer at speed of 45 m s-1. The speed of sound is 340 m s-1.

Which of the following is the frequency the observer hears?

A. 519 Hz               B. 483 Hz               C. 397 Hz               D. 358 Hz

#### Exam Tip

Be careful as to which frequency and velocity you use in the equation. The ‘source’ is always the object is moving and the ‘observer’ is always stationary.

### The Doppler Effect

• The doppler shift is observed by all waves including sound and light
• A 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 (e.g. yourself) and the source of sound (e.g. ambulance siren) are both stationary, the waves are at the same frequency for both the observer and the source
• 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

The observer in front observes a blue shift, the observer behind observes a red shift

• When the source starts to move away the observer, the wavelength of the waves is 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
• For light waves, remember that red light has a longer wavelength than blue light
• Red and blue shift is observed in spectral lines of planets and is used to find the radius of the planets orbit around distant stars

### Author: Ashika

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.
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