phy C5 doppler effect

doppler effect

• change in measured frequency of a wave due to the motion of a source/observer relative to the medium in which the wave is propagated

moving source stationary observer

• wave speed wrt observer constant

• source moving toward observer → shorter wavelength, higher frequency

• source moving away from observer → longer wavelength, lower frequency

moving observer stationary source

• wavelength constant

• observer moving towards source → higher relative speed wrt observer (more waves received per unit time) → higher frequency wrt observer

• observer moving away from source → lower relative speed wrt observer (fewer waves received per unit time) → lower frequency wrt observer

moving medium (eg wind)

• if wind blowing towards observer,

  • higher speed of wave in medium, v

  • frequency of source constant

  • v = fλ, longer wavelength

  • observed frequency unchanged, since wavelength and speed increase by same factor (based on HL eqns)

doppler effect for EM waves

• if v << c (3×10⁸), then Δf/f = Δ λ/λ = v/c

  • where v is relative speed between source and observer

red shift

• source moving away from observer, light received has longer wavelength

• light shifts towards red end of spectrum

• eg for stars: use hydrogen absorption spectrum to measure shifted position, calculate velocity

radars

1. car approaches beam (moving observer) → constant λ, increased v → increased f

2. car reflects beam (moving source) → assuming the car is still approaching the beam, constant v, decreased λ → increased f

thus, double doppler shift

• calculate frequency of source

• Δf/f = v/c → find Δf

• this value is doubled, so to find actual Δf, need to halve

rate of expansion of the universe

• redshift = Δλ/λ_emitted = v/c

• all galaxies’ spectral lines had red shift → implies all galaxies are moving away from the earth

• v = H₀d

  • v is recessional velocity: rate of expansion of the universe

  • H₀ is the hubble constant: 72 km s^-1 Mpc^-1

  • d is distance to galaxy

  • not a constant rate since gravity might slow down the rate over time