Doppler Effect (SL IB Physics)

Every year, an alien species holds a race between two teams. One of the teams has green lights on its spaceships and the other has purple light. During the race the two ships approach a space station.

From the point of view of the space station commander on the space station, the two colours appear to be identical as the ships approach the station.

Explain how the commander knows which spaceship is travelling faster.

The wavelength of light from the purple ship is 420 nm but is observed to be 405 nm at the space station.

Determine the speed of the purple ship. 

The purple ship accelerates to four times its speed in (b) and then remains at this speed as it approaches the space station.  

Determine the new wavelength of observed visible light coming from this spaceship as it approaches the space station. 

The space station also can detect light from other galaxies. In a laboratory, the frequency of electromagnetic radiation from a distant galaxy has been redshifted by 5.108 × 10⁹ Hz. In the laboratory, the same light has a frequency of 5.103 × 10⁹ Hz.

Calculate the speed of recession of the galaxy.

An emission spectrum of light was obtained from a light source in a laboratory. 

The same wavelengths of light were observed on an emission spectrum from a distant galaxy but were found to be redshifted.

An astronomer observes that light from a galaxy has been shifted towards the blue end of an emission spectrum.

Hydrogen is an element of particular interest to cosmologists, as it can emit visible light waves.

A lot of useful information can be obtained by measuring the wavelength of the emitted light from the hydrogen in distant galaxies and comparing them to a laboratory sample.

Galaxies 1 and 2 are both moving relative to Earth.

Compare the motions of galaxies 1 and 2 relative to Earth.

Calculate the speed of galaxy 1 relative to Earth.

Astronomers can determine whether a star is moving away from or towards the Earth. 

State and explain what is meant by 'Doppler effect' in this context.

In a laboratory, hydrogen is found to emit light of wavelength 621.89 nm. The spectrum of a star observed on Earth is found to have the same line in the spectrum shifted to 623.22 nm.

Show that the star is moving away from the Earth at a speed of 6.42 × 10⁵ m s⁻¹. 

A second spectral line from the same star is observed at 621.49 nm in the laboratory.

Determine the frequency of the spectral line from the star as observed on Earth.

Explain the effect on the colour of light from the star if it were travelling towards the Earth.

The Doppler effect can be used to determine whether a star is moving away from or towards the Earth. 

Outline what is meant by 'Doppler effect' in this context.

In a laboratory, the spectrum of atomic hydrogen has a wavelength of 656.61 nm. The spectrum of a star observed on Earth is found to have the same line in the spectrum shifted to 656.54 nm.

A second spectral line is observed at 567.34 nm in the laboratory. 

Determine the frequency of the spectral line from the star, as observed on Earth.

Explain the effect on the colour of light from the star if it were travelling towards the Earth.

A police officer is standing on the side of the road pointing a radar gun at an approaching car. The gun emits microwaves which are reflected off the car and then received again by a detector on the gun. The gun measures the change in frequency between the emitted and received microwaves. This is calculated by the equation:

Where:

• f is the frequency of the emitted microwaves
• v is the speed of the approaching car
• c is the speed of the microwaves through the air

The following data are available:

• Frequency of emitted microwaves = 50 GHz
• Frequency of detected microwaves = 50.0000056 GHz
• Speed limit on the road = 30 mph

Explain why the frequency of the microwaves emitted and detected by the gun are different. 

Explain why there is a factor of two in the equation. 

Determine whether the car is breaking the speed limit.

1 mile = 1.6 km

An astronomer analyses the light from a distant galaxy.

One of the observed spectral lines of hydrogen has a wavelength of 849 nm. The same spectral line has a wavelength of 767 nm when measured in the laboratory.

Cosmologists commonly quote the recessional velocity v of astronomical objects in relation to the speed of light c. This ratio is known as redshift z:

The Andromeda galaxy is the closest galaxy to our own Milky Way. Andromeda has a redshift value of z = −0.001.

The table shows some information about two galaxies. 

Hubbles Law is

Where:

• v is the recessional velocity of the galaxy
• H₀ is the Hubble constant
• d is the distance between the galaxy and the Earth

Two stars, A and B, in a binary system, move in a clockwise direction around a common centre of mass.

Mark the positions of stars A and B corresponding to their spectra as observed on Earth.

When measured in the laboratory, one of the spectral lines of hydrogen has a wavelength of 4.942 × 10⁻⁷ m. The same hydrogen line in the spectrum of one of the stars fluctuates from its laboratory wavelength by ± 0.310 × 10⁻⁷ m and the line in the spectrum of the other star fluctuates by ± 0.994 × 10⁻⁷ m. Both stars have the same time period.

Calculate the orbital velocity of each star in the binary system and determine which of the stars, A or B, is faster.

In a different binary star system, also rotating clockwise, star C has an orbital velocity of 8.92 × 10⁷ m s⁻¹ and star D an orbital velocity of 1.2 × 10⁷ m s⁻¹. Both stars have the same time period.

Identify the possible positions of stars C and D and an absorption spectrum as star C moves towards Earth and star D away from Earth. 

Two stars, A and B, in a binary system move in an anti-clockwise direction. Both stars emit light with wavelength, λ = 5.89 × 10⁻⁷ m, which reaches an observer on Earth. In the laboratory, the light is shown to fluctuate between wavelengths of 5.86 × 10⁻⁷ m and 6.02 × 10⁻⁷ m.

Assume they orbit in a circle around their common centre of mass.

Draw a diagram which indicates the position of the stars relative to the Earth when:

The radius of orbit of star B is 4.98 × 10¹¹ m. 

Calculate the time taken for one orbit of star A about the common centre of mass.