Doppler Effect for Sound Waves (CIE AS Physics)

• The whistle of a train or the siren of an ambulance appears to decrease in frequency (sounds lower in pitch) as it moves further 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

Waves Emitted from a Stationary Source

According to the observer stationary relative to the source, the frequency is equal to that measured by the source

• 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

Waves Emitted by a Moving Source

The source and observer disagree on their measurements of the frequency of the wave

• 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

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

$f_o = f_s\left(\frac{v}{v \pm v_s}\right)$

where f_o is the observed frequency in Hz, f_s is the source frequency in Hz, v is wave velocity in m s⁻¹ and v_s is the velocity of the source relative to the observer, again in m s⁻¹

• 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 - v_s
  • If the source is moving away, the denominator is v + v_s