IB DP Physics: HL复习笔记9.5.3 The Doppler Equation

Calculating Doppler Shift

• When a source of sound waves moves relative to a stationary observer, the observed frequency can be calculated using the equation below:

Doppler shift equation for a moving source

• The wave velocity for sound waves is 340 ms-1
• The ± depends on whether the source is moving towards or away from the observer
  • If the source is moving towards the observer, the denominator is v - us
  • If the source is moving away from the observer, the denominator is v + us
• When a source of sound waves remains stationary, but the observer is moving relative to the source, the observed frequency can be calculated using the equation below:

Doppler shift equation for a moving observer

• The ± depends on whether the source is moving towards or away from the observer
  • If the observer is moving towards the source, the numerator is v + uo
  • If the observer is moving away from the source, the numerator is v − uo
• These equations can also be written in terms of wavelength
  • For example, the equation for a moving source is shown below:

Doppler shift equation for a moving source in terms of wavelength

Step 1: List the known quantities

Step 5: State final answer

• • The bank robber must be driving away at a constant speed of 17 ms-1 based on the change in frequency heard

Calculating Doppler Shift of Light

• Doppler shift can be calculated with relation to a light emitting source
  • For example, a galaxy moving towards or away from Earth
• Doppler shift for light is complicated, however if the speed of the observer or source is small (non-relativistic) compared to the speed of light, then this equation becomes simpler
• The Doppler shift for a light-emitting non-relativistic source is described using the equation:

Doppler shift equation relating wavelength change for a moving source

• Where:
  • Δf = change in frequency in Hertz (Hz)
  • f0 = reference frequency in Hertz (Hz)
  • λ = observed wavelength of the source in metres (m)
  • λ0 = reference wavelength in metres (m)
  • Δλ = change in wavelength in metres (m)
  • v = velocity of a galaxy in metres per seconds (m/s)
  • c = the speed of light in metres per second (m/s)

• This means that the change in wavelength, Δλ:

Δλ = λ – λ0

• This equation can be used to calculate the velocity of a galaxy if its wavelength can be measured and compared to a reference wavelength
• Since the fractions have the same units on the numerator (top number) and denominator (bottom number), the Doppler shift has no units