2 questions, one for each idea where we can. Answer them, then see which ideas to fix.
Question 1 of 2
A fire truck with its siren sounding drives past a pedestrian standing beside a straight road. Which statement describes the Doppler effect that the pedestrian experiences?
Answer and reasoning
AThe siren's sound changes only in loudness, growing louder as the truck nears and quieter as it leaves. A student who thinks the only change is in loudness picks this. The loudness does change with distance, but that is not the Doppler effect: the frequency reaching the pedestrian is also higher than the rest frequency as the truck approaches and lower as it recedes, which is heard as a change of pitch.
BThe frequency reaching the pedestrian differs from the siren's because the two move relative to each other.Correct The Doppler effect is a difference between the frequency an observer measures and the rest frequency of the source, caused by the relative velocity of the source and observer. The siren vibrates at its rest frequency throughout; crests reach the pedestrian more often while the truck approaches and less often while it recedes.
CThe siren vibrates at a different frequency while the truck is moving than while it is parked. A student who thinks a moving source emits a different frequency picks this. The siren vibrates at its rest frequency whatever the truck's motion; a firefighter riding on the truck hears that frequency throughout. The shift is in the frequency that reaches an observer moving relative to the siren.
DThe sound waves travel faster toward the pedestrian because the truck's speed adds to theirs. A student who thinks a moving source adds its velocity to its sound waves picks this. The speed of sound through still air is set by the air, not by the truck; the truck's motion changes the spacing of the crests, not their speed.
An ambulance's siren has rest frequency f₀. The ambulance drives straight toward a listener standing at rest far down the road, once at constant speed v and later at constant speed 2v, both less than the speed of sound. The listener hears frequency f₁ during the first approach and f₂ during the second. Which ranking is correct?
Answer and reasoning
Af₁ = f₂ > f₀ A student who thinks the shift depends only on the direction of motion picks this. Both approaches do give frequencies above f₀, but the size of the shift grows with the relative speed, so the faster approach gives the higher frequency.
Bf₁ = f₂ = f₀ A student who thinks an approaching source only sounds louder picks this. The frequency reaching the listener is greater than f₀ during each approach, which is heard as a higher pitch, and more so at the greater speed.
Cf₂ > f₁ > f₀Correct While a source approaches, the observed frequency is greater than the rest frequency, and a greater relative velocity gives a greater difference between them. The faster approach, at 2v, therefore gives the frequency farthest above f₀.
Df₀ > f₁ > f₂ A student who thinks a shorter wavelength means a lower frequency picks this: the approaching siren crowds its crests together, more so at 2v. Closer crests moving at the speed of sound reach the listener more often, so the frequency is higher, not lower.
Working Qualitative (no equation required). Approaching → observed frequency above f₀; greater relative speed → greater difference from f₀. So f₂ (speed 2v) > f₁ (speed v) > f₀.
In preparation: 0 of 2 sections compiled and reviewed. The rest show key terms and common mistakes from our question bank until they are.
14.5.A.1 Doppler effect Fix
Doppler effect
The difference between the frequency of a wave measured by an observer and the frequency emitted by its source, which occurs when the source and the observer move toward or away from each other. It applies to all waves, including sound and electromagnetic waves; for sound it is heard as a change of pitch.
Rest frequency, f₀
The frequency of the wave emitted by the source: the frequency measured by an observer who has no velocity relative to the source. The source's motion does not change it. SI unit: hertz (Hz).
Observed frequency
The frequency with which wave crests reach a particular observer, which is the frequency that observer measures. It equals the rest frequency when the source and observer have no relative velocity and differs from it when they move toward or away from each other. SI unit: hertz (Hz).
Pitch and loudness
Pitch is how high or low a sound is heard and is set by its frequency; loudness is set by its amplitude, which decreases with distance from the source. The Doppler effect changes the frequency that reaches the listener, so it is heard as a change of pitch, not of loudness.
Wave speed and a moving source
The speed of sound through still air is set by the air, not by the motion of the source. A source moving through the air emits each crest from a new position, so the crests are closer together ahead of it and farther apart behind it; their speed through the air is unchanged.
Students often think The only change heard as a sound source approaches or moves away is a change in loudness; the frequency heard is always the frequency the source emits. In fact No. The siren does sound louder when it is closer, but the frequency that reaches you is also different: higher than the rest frequency while the siren approaches and lower while it moves away. That change of frequency is heard as a change of pitch.
Students often think A moving source itself emits a different frequency: its motion changes the rate at which it vibrates. In fact No. A moving siren vibrates at its rest frequency whatever its motion; a passenger riding with it hears that frequency throughout. What changes is how often the crests reach a listener who is moving relative to the siren.
14.5.A.2 Relative velocity of source and observer Fix
Relative velocity of source and observer
The velocity of the source as measured by the observer. The Doppler effect depends on it: with no relative velocity there is no shift, and the faster the source and observer approach or recede from each other, the greater the difference between the observed and rest frequencies.
No relative velocity
A source and an observer moving with the same velocity (same speed, same direction) keep a constant separation, so crests reach the observer at the rate they are emitted and the observed frequency equals the rest frequency.
Approaching source or observer
When the source and observer move toward each other, crests reach the observer more often than they are emitted, so the observed frequency is greater than the rest frequency. At constant relative velocity along the line joining them, it is a constant value, not a rising one.
Receding source or observer
When the source and observer move away from each other, crests reach the observer less often than they are emitted, so the observed frequency is less than the rest frequency.
Students often think The Doppler shift depends only on whether the source and observer are approaching or receding, not on how fast. In fact It depends on how fast. A greater speed of approach gives an observed frequency farther above the rest frequency, and a greater speed of recession gives one farther below it.
Students often think Only the motion of the source produces a Doppler shift: a moving source is heard shifted by every observer, and a source at rest is heard at its rest frequency, whatever the observers are doing. In fact No. The shift depends on the relative velocity of the source and observer. An observer moving with the same velocity as the source hears the rest frequency even though the source is moving, and an observer moving toward a source at rest hears a higher frequency even though the source is not moving.
4 more questions. Every wrong answer here is a real mistake students make, and you see why it is wrong as soon as you answer.
Question 1 of 4
The diagram shows the crests of the sound waves from a source S that moves to the right at constant speed through still air. Listeners A and B are at rest. Listener A hears a higher frequency than listener B does. Which explanation, based on the diagram, is correct?
Answer and reasoning
ACrests are closer together on A's side of S, so they reach A more often.Correct Each crest spreads out at the speed of sound from the point where S was when it emitted that crest. Because S moves toward A, the crests on A's side are closer together; moving at the same speed, they pass A more often than they pass B, so A measures the higher frequency.
BThe crests travel faster toward A, as the motion of S adds to their speed. A student who thinks a moving source adds its velocity to its waves picks this. Every crest in the diagram is a circle, which shows that it spreads at the same speed in all directions through the air; what differs on the two sides is the spacing of the crests.
CS emits a higher frequency toward A than toward B, since it moves toward A. A student who thinks the source's motion changes the frequency it emits picks this. S emits one frequency, its rest frequency, in every direction; the circles are emitted at equal time intervals. The difference comes from where each crest starts, which changes how often crests reach each listener.
DThe sound reaching A is louder than at B, and a louder sound has a higher pitch. A student who thinks a louder sound has a higher pitch picks this. Loudness depends on amplitude and pitch on frequency; a louder sound is not a higher one. The diagram shows the reason A hears a higher frequency: the crests are more closely spaced on A's side.
The diagram shows a fire truck T sounding its siren, whose rest frequency is f₀, a car 1 and a person 2 beside a straight road; the velocity arrows are drawn to the same scale. The driver of car 1 hears frequency f₁ and person 2 hears frequency f₂. Which relationship is correct?
Answer and reasoning
Af₁ = f₂ < f₀ A student who thinks only the source's motion matters picks this: the truck is moving away from both, so both seem to hear a lower frequency. The driver of car 1 moves with the same velocity as the truck, so there is no relative velocity and no shift for that driver.
Bf₁ = f₂ = f₀ A student who thinks a moving siren changes only in loudness picks this. Person 2 is at rest while the siren moves away, so the crests reach person 2 less often than they are emitted and f₂ is less than f₀.
Cf₁ = f₀ < f₂ A student who thinks a longer wavelength means a higher frequency picks this: behind the receding truck the crests are spread out. Spread-out crests moving at the speed of sound reach person 2 less often, so f₂ is lower than f₀.
Df₁ = f₀ > f₂Correct Car 1 moves with the same velocity as the truck, so it has no velocity relative to the siren and its driver hears the rest frequency. The truck is moving away from person 2, who is at rest, so person 2 hears a frequency lower than f₀.
Working Car 1 and T: same velocity → no relative velocity → f₁ = f₀. Person 2 at rest, T receding → f₂ < f₀.
A student stands at the end of a long, straight track. A cart carrying a buzzer with rest frequency f₀ rolls directly toward the student at constant speed. Which describes the sound the student hears while the cart approaches?
Answer and reasoning
AA frequency that keeps rising as the cart nears A student who thinks the pitch rises steadily during an approach picks this. The sound does grow louder as the cart comes closer, but at a constant speed of approach the frequency stays at one value above f₀.
BThe frequency f₀, louder as the cart nears A student who thinks an approaching source only sounds louder picks this. The sound does grow louder, but the frequency reaching the student is also greater than f₀ because the cart is moving toward the student.
CA constant frequency that is less than f₀ A student who thinks crowded crests (a shorter wavelength) mean a lower frequency picks this. The crests ahead of the moving cart are closer together, so they reach the student more often, which is a higher frequency.
DA constant frequency that is greater than f₀Correct The cart approaches with a constant velocity along the line toward the student, so crests arrive at a steady rate that is greater than the rate at which they are emitted. The frequency is constant and higher than f₀; only the loudness grows as the cart comes closer.
A car sounding its horn, whose rest frequency is f₀, moves along a straight road near a microphone that is at rest. The graph shows the frequency f measured by the microphone as a function of time t. Which claim is supported by the graph?
Answer and reasoning
AThe car moved toward the microphone before t₁ and away from it after t₁.Correct Before t₁ the measured frequency is above f₀, so the car and microphone were approaching each other; after t₁ it is below f₀, so they were moving apart. The frequency is steady on each side of t₁, consistent with a constant speed.
BThe car moved away from the microphone before t₁ and toward it afterward. A student who links a higher frequency with a longer wavelength, and so with the stretched crests behind a receding source, picks this. A receding source gives a frequency below f₀; the graph is above f₀ before t₁, so the car was approaching then.
CThe car kept approaching the microphone after t₁, but at a lower speed. A student who thinks a drop in the observed frequency means the source slowed down picks this. A source that is still approaching, however slowly, gives a frequency above f₀; after t₁ the graph is below f₀, so the car was moving away.
DThe car's horn itself was emitting a higher frequency before t₁ than after. A student who thinks a moving source changes the frequency it emits picks this. The horn emits f₀ throughout; the measured frequency changes because the car's velocity relative to the microphone changes from approaching to receding.
Compiled from the AP Physics 2 Course and Exam Description (effective Fall 2024, 2026 reissue) and our question bank · Specialist review in progress. How these pages are made · Free, no account
