1.4 Doppler effect  (Page 3/3)

The doppler effect with sound

1. Suppose a train is approaching you as you stand on the platform at the station. As the train approaches the station, it slows down. All the while, the engineer is sounding the hooter at a constant frequency of 400 Hz. Describe the pitch and the changes in pitch that you hear.
2. Passengers on a train hear its whistle at a frequency of 740 Hz. Anja is standing next to the train tracks. What frequency does Anja hear as the train moves directly toward her at a speed of 25 m $·$ s ${}^{-1}$ ?
3. A small plane is taxiing directly away from you down a runway. The noise of the engine, as the pilot hears it, has a frequency 1,15 times the frequency that you hear. What is the speed of the plane?

The doppler effect with light

Light is a wave and earlier you learnt how you can study the properties of one wave and apply the same ideas to another wave. The same applies to sound and light. We know the Doppler effect affects sound waves when the source is moving. Therefore, if we apply the Doppler effect to light, the frequency of the emitted light should change when the source of the light is moving relative to the observer.

When the frequency of a sound wave changes, the sound you hear changes. When the frequency of light changes, the colour you would see changes.

This means that the Doppler effect can be observed by a change in sound (for sound waves) and a change in colour (for light waves). Keep in mind that there are sounds that we cannot hear (for example ultrasound) and light that we cannot see (for example ultraviolet light).

We can apply all the ideas that we learnt about the Doppler effect to light. When talking about light we use slightly different names to describe what happens. If you look at the colour spectrum (more details Chapter  [link] ) then you will see that blue light has shorter wavelengths than red light. If you are in the middle of the visible colours then longer wavelengths are more red and shorter wavelengths are more blue. So we call shifts towards longer wavelengths "red-shifts" and shifts towards shorter wavelengths "blue-shifts".

A shift in wavelength is the same as a shift in frequency. Longer wavelengths of light have lower frequencies and shorter wavelengths have higher frequencies. From the Doppler effect we know that when things move towards you any waves they emit that you measure are shifted to shorter wavelengths (blueshifted). If things move away from you, the shift is to longer wavelengths (redshifted).

The expanding universe

Stars emit light, which is why we can see them at night. Galaxies are huge collections of stars. An example is our own Galaxy, the Milky Way, of which our sun is only one of the millions of stars! Using large telescopes like the Southern African Large Telescope (SALT) in the Karoo, astronomers can measure the light from distant galaxies. The spectrum of light can tell us what elements are in the stars in the galaxies because each element emits/absorbs light at particular wavelengths (called spectral lines). If these lines are observed to be shifted from their usual wavelengths to shorter wavelengths, then the light from the galaxy is said to be blueshifted . If the spectral lines are shifted to longer wavelengths, then the light from the galaxy is said to be redshifted . If we think of the blueshift and redshift in Doppler effect terms, then a blueshifted galaxy would appear to be moving towards us (the observers) and a redshifted galaxy would appear to be moving away from us.

Edwin Hubble (20 November 1889 - 28 September 1953) measured the Doppler shift of a large sample of galaxies. He found that the light from distant galaxies is redshifted and he discovered that there is a proportionality relationship between the redshift and the distance to the galaxy. Galaxies that are further away always appear more redshifted than nearby galaxies. Remember that a redshift in Doppler terms means a velocity of the light source away from the observer. So why do all distant galaxies appear to be moving away from our Galaxy?

The reason is that the universe is expanding! The galaxies are not actually moving themselves, rather the space between them is expanding!

Summary

1. The Doppler Effect is the apparent change in frequency and wavelength of a wave when the observer and source of the wave move relative to each other.
2. The following equation can be used to calculate the frequency of the wave according to the observer or listener:
   $$f_L=\frac{v+v_L}{v+v_S}{f}_S$$
3. If the direction of the wave from the listener to the source is chosen as positive, the velocities have the following signs:

   Source moves towards listener	$v_S$ : negative
   Source moves away from listener	$v_S$ : positive
   Listener moves towards source	$v_L$ : positive
   Listener moves away from source	$v_L$ : negative

4. The Doppler Effect can be observed in all types of waves, including ultrasound, light and radiowaves.
5. Sonography makes use of ultrasound and the Doppler Effect to determine the direction of blood flow.
6. Light is emitted by stars. Due to the Doppler Effect, the frequency of this light decreases and the starts appear red. This is called a red shift and means that the stars are moving away from the Earth. This means that the Universe is expanding.

End of chapter exercises

1. Write a definition for each of the following terms.
   1. Doppler Effect
   2. Red-shift
   3. Ultrasound
2. Explain how the Doppler Effect is used to determine the direction of blood flow in veins.
3. The hooter of an appoaching taxi has a frequency of 500 Hz. If the taxi is travelling at 30 m $·$ s ${}^{-1}$ and the speed of sound is 300 m $·$ s ${}^{-1}$ , calculate the frequency of sound that you hear when
   1. the taxi is approaching you.
   2. the taxi passed you and is driving away.
4. A truck approaches you at an unknown speed. The sound of the trucks engine has a frequency of 210 Hz, however you hear a frequency of 220 Hz. The speed of sound is 340 m $·$ s ${}^{-1}$ .
   1. Calculate the speed of the truck.
   2. How will the sound change as the truck passes you? Explain this phenomenon in terms of the wavelength and frequency of the sound.
5. A police car is driving towards a fleeing suspect at $\frac{v}{35}$ m. ${\mathrm{s}}^{-1}$ , where $v$ is the speed of sound. The frequency of the police car's siren is 400 Hz. The suspect is running away at $\frac{v}{68}$ . What frequency does the suspect hear?
6. 1. Why are ultrasound waves used in sonography and not sound waves?
   2. Explain how the Doppler effect is used to determine the direction of flow of blood in veins.