Doppler Effect

• When the observer and the source of sound are moving relative to each other

  The waves appear to have a different frequency for both the observer and the source
• Effect of source moving away from the observer

  The wavelength of the waves is lengthened, making the sound appear at a lower frequency to the observer
• Red light has a longer wavelength than blue light, causing red shift and blue shift for electromagnetic waves
• Doppler effect


  The frequency change due to the relative motion between a source of sound or light and an observer
• When the observer and the source of sound are both stationary


  The waves appear to remain at the same frequency for both the observer and the source
• When a source of sound moves away from an observer, it appears to decrease in frequency, i.e. it sounds lower in pitch
• For electromagnetic waves

  • Waves moving away from the observer are red-shifted, shifting to the red end of the electromagnetic spectrum
  • Waves moving towards the observer are blue-shifted, shifting to the blue end of the electromagnetic spectrum
• Effect of source moving towards the observer

  The wavelength of the waves is shortened, making the sound appear at a higher frequency to the observer
• Frequency and wavelength are related by the wave equation, where the speed of the wave remains constant
• This equation only works if v << c
• The bigger the change, the bigger the Doppler shift
• The speed v of the wave does not change
• A stationary source of light is found to have a spectral line of wavelength 438 nm. The same line from a distant star that is moving away from us has a wavelength of 608 nm. Calculate the speed at which the star is traveling away from Earth
• The Doppler shift is observed by all waves including sound and light
• The relative speed between the source and observer along the line joining them is given by: ∆v = vs - vo
• Δλ

  Change in wavelength
• A moving object will cause the wavelength, λ, (and frequency) of the waves to change

  • The wavelength of the waves in front of the source decreases (λ – Δλ) and the frequency increases
  • The wavelength behind the source increases (λ + Δλ) and the frequency decreases
• The relationship between frequency and wavelength is determined by the wave equation
• Wavefront diagrams help visualise the Doppler effect for moving wave sources and stationary observers
• The Doppler shift for a light-emitting non-relativistic source can be described using the equation: ∆f/f = ∆λ/λ ≈ ∆v/c
• The Doppler shift has no units
• Usually, we are calculating the speed of the source of electromagnetic waves relative to an observer which we assume to be stationary
• Spectral lines showing red shift indicate that the galaxy is traveling away from Earth
• Stars and galaxies can be red or blueshifted to an observer on Earth
• Doppler equation

  ∆λ/λ = v/c
• Blueshift


  Object is moving towards Earth, wavelength is decreasing, frequency is increasing
• Light from a distant galaxy is shifted towards the red end of the spectrum compared to the Sun's spectra, providing evidence that the universe is expanding
• Redshift is the fractional increase in wavelength (or decrease in frequency) due to the source and observer receding from each other
• Calculate velocity v


  v = c∆λ/λ
• Positive and Negative Velocities


  If speed of the galaxy relative to Earth is positive, the galaxy is moving towards Earth. If negative, the galaxy is moving away from Earth
• Redshift

  Object is moving away from Earth, wavelength is increasing, frequency is decreasing
• An expanding universe was discovered after the Doppler redshift
• Redshift can be observed by comparing the light spectrum produced from a close object, such as our Sun, with that of a distant galaxy
• If the speed of the galaxy relative to Earth is negative then the galaxy is moving away from the Earth
• The space between the Earth and the galaxies must be expanding due to the receding galaxies
• Expansion of the universe

  • The expansion can be compared to dots on an inflating balloon
  • As the balloon is inflated, the dots all move away from each other
  • In the same way, as the rubber stretches when the balloon is inflated, space itself is stretching out between galaxies
  • Galaxies move away from each other due to the stretching of space
• The speed of light is 3.0 × 10^8 m/s
• When a source of sound waves moves relative to a stationary observer, the observed frequency can be calculated using the Doppler shift equation for a moving source
• Observation from looking at light spectra produced by distant galaxies

  • The greater the distance to the galaxy, the greater the redshift
  • The greater the degree of redshift, the faster the galaxy is moving away from Earth
  • The further a galaxy is from Earth, the greater its redshift tends to be
  • The furthest galaxies appear to be redshifted the most and are receding the fastest
• After the discovery of Doppler redshift, astronomers began to realize that almost all the galaxies in the universe are receding