The Doppler effect

Analyse qualitatively and quantitatively the relationships of the wave nature of sound to explain:

• beats 𝑓_beat = |𝑓₂ − 𝑓₁ |
• The Doppler effect 𝑓′ = 𝑓 (𝑣_wave+𝑣_observer) / (𝑣_wave−𝑣_source)

Learn.

The doppler effect allowed scientists to determine that the universe is expanding. By looking at the redshift of light which was coming from distant stars which is caused by the universe expanding. When a light source is moving away from you, the light waves will become more stretched increasing the wavelength. Hence the frequency of the wave will increase since the velocity of the speed of light will not change c = λf.

If you listen to an ambulance drive past, you will notice that it goes from high pitched to low pitched, this is due to the Doppler effect. As the waves are being propagated, the ambulance is moving closer and closer to the next wave. This means the frequency of the waves will increase, therefore, they sound higher pitched. When it drives past you, it is moving away from the waves, therefore, the frequency of the waves you hear decreases (becomes lower pitched) since it travels further away each time it propagates the next wave front.

This can be explained by the following formula:

•  𝑓′ = 𝑓 (𝑣_wave+𝑣_observer) / (𝑣_wave− 𝑣_source)
  • 𝑓′ = frequency of sound observed (Hz)
  • 𝑓 = frequency of sound emitted (Hz)
  • 𝑣_wave = velocity of the wave in air (m/s)
  • 𝑣_observer = velocity of the observer (m/s)
  • 𝑣_source = velocity of the source (m/s)

Memorise.

Following formula summarizes doppler effect which can be observed as the change in pitch (frequency) when an ambulance drives past you

• 𝑓′ = 𝑓 (𝑣_wave+𝑣_observer) / (𝑣_wave− 𝑣_source)
  • 𝑓′ = frequency of sound observed (Hz)
  • 𝑓 = frequency of sound emitted (Hz)
  • 𝑣_wave = velocity of the wave in air (m/s)
  • 𝑣_observer = velocity of the observer (m/s)
  • 𝑣_source = velocity of the source (m/s)

Master.

Question 1.

Explain the Doppler effect and what is required for it to occur? [3 marks]

Question 2.

Would the Doppler effect be experienced for the observer if they are travelling towards a stationary sound emitting source at constant velocity? Justify your answer [4 marks]

Question 3.

An ambulance is travelling towards a stationary observer at constant velocity of 40 m/s, the speed of sound in air is 344 m/s and the frequency being emitted by the ambulance is 200 Hz. What is the observed frequency before and after the ambulance passes? [4 marks]