๐งฒap physics 2 (2025) review
14.5 The Doppler Effect
Verified for the 2025 AP Physics 2 (2025) examโขCitation:
Wave Properties from Relative Motion
Doppler Effect
The Doppler effect is a phenomenon where the frequency of a wave appears to change when there is relative motion between the wave source and an observer. This effect occurs with all types of waves, including sound waves, light waves, and water waves.
- Rest frequency is what the source emits when there is no relative motion between source and observer
- Observed frequency is what the observer actually detects, which can be different from the rest frequency
- The difference between these frequencies is called the Doppler shift
When a source and observer move relative to each other, wave crests either bunch together or spread apart. This causes the observer to experience more or fewer wave crests per second than if there was no relative motion.
"The Doppler effect explains why an ambulance siren sounds higher pitched as it approaches you and lower pitched as it drives away."
Frequency vs Velocity
The relationship between velocity and frequency change follows clear patterns:
- Source approaching observer: Wave crests bunch together, causing the observer to detect more waves per second
- Results in higher observed frequency (positive Doppler shift)
- The faster the approach, the greater the frequency increase
- Source moving away from observer: Wave crests spread out, causing the observer to detect fewer waves per second
- Results in lower observed frequency (negative Doppler shift)
- The faster the recession, the greater the frequency decrease
- No relative motion: Observed frequency equals rest frequency (no Doppler shift)
The magnitude of the Doppler shift depends directly on the relative velocity between source and observer. Higher relative speeds produce more dramatic frequency shifts, while slower speeds result in smaller shifts.
Real-world applications of the Doppler effect include:
- Radar systems for measuring vehicle speeds
- Astronomical measurements of stellar and galactic motion (redshift/blueshift)
- Medical ultrasound to measure blood flow direction and velocity
- Weather radar to track precipitation and storm movement
๐ซ Boundary Statement
AP Physics 2 only requires a qualitative understanding of the Doppler effect, without the need for quantitative calculations.
Practice Problem 1: Ambulance Siren
An ambulance with its siren blaring at a constant frequency drives past you as you stand on a sidewalk. Describe what happens to the pitch (frequency) of the siren that you hear as the ambulance approaches, passes by, and then moves away from you. Explain why this happens in terms of the Doppler effect.
Solution
As the ambulance approaches you, the pitch (frequency) of the siren will sound higher than the actual siren frequency. This happens because the ambulance is moving toward you, causing the sound waves to be compressed. The wave crests arrive at your ears more frequently than they would if the ambulance were stationary.
At the exact moment when the ambulance passes you, the pitch will suddenly drop. This is the transition point where the ambulance changes from moving toward you to moving away from you.
After the ambulance passes and moves away, the pitch will sound lower than the actual siren frequency. This occurs because the ambulance is now moving away from you, causing the sound waves to be stretched out. The wave crests arrive at your ears less frequently than they would if the ambulance were stationary.
This entire phenomenon is explained by the Doppler effect, which describes how wave frequencies change based on relative motion between the source and observer.
Practice Problem 2: Astronomical Applications
Astronomers observe that the spectral lines from a distant galaxy appear shifted toward the red end of the spectrum compared to the same spectral lines measured in a laboratory on Earth. What can astronomers conclude about this galaxy's motion relative to Earth, and what principle explains this observation?
Solution
When astronomers observe spectral lines from a distant galaxy shifted toward the red end of the spectrum (longer wavelengths, lower frequencies), they can conclude that the galaxy is moving away from Earth. This phenomenon is known as "redshift."
The principle that explains this observation is the Doppler effect. As the galaxy moves away from Earth, the light waves it emits are stretched out from our perspective. This stretching causes the wavelength to increase (and frequency to decrease), shifting spectral lines toward the red end of the spectrum.
The greater the redshift, the faster the galaxy is receding from Earth. This application of the Doppler effect was crucial in the discovery of the expanding universe and forms the basis for the Big Bang theory in cosmology.