AP Physics Questions on Doppler Effect and Radar Guns

📚 Quick Study Guide

• 🚗 Doppler Effect: The change in frequency of a wave in relation to an observer who is moving relative to the wave source.
• 🔊 Formula: $f' = f(\frac{v \pm v_o}{v \mp v_s})$, where $f'$ is the observed frequency, $f$ is the source frequency, $v$ is the speed of sound in the medium, $v_o$ is the speed of the observer, and $v_s$ is the speed of the source. Use the top signs when the observer and source are moving towards each other.
• 📡 Radar Guns: Use the Doppler effect to measure the speed of objects, especially vehicles.
• 💡 Key Concept: The frequency shift is proportional to the relative velocity between the source and the observer.
• ➕ Approaching: When the source and observer are approaching, the observed frequency increases.
• ➖ Receding: When the source and observer are receding, the observed frequency decreases.
• 📐 Angle Matters: If the motion isn't directly towards or away, only the component of velocity along the line of sight contributes to the Doppler shift.

Practice Quiz

1. A police car's radar gun emits a frequency of 10 GHz. A car is moving towards the police car at 30 m/s. What is the approximate change in frequency observed by the radar gun? (Assume the speed of light is $3 \times 10^8$ m/s)

   1. A) 1 kHz
   2. B) 2 kHz
   3. C) 3 kHz
   4. D) 4 kHz

2. A train is moving away from a station at a speed of 20 m/s. The train's whistle emits a sound with a frequency of 500 Hz. What frequency is heard by a stationary observer at the station? (Assume the speed of sound is 343 m/s)

   1. A) 471 Hz
   2. B) 529 Hz
   3. C) 500 Hz
   4. D) 550 Hz

3. A bat emits an ultrasonic wave at 40 kHz to detect insects. If an insect is flying towards the bat at 5 m/s, what is the frequency of the wave reflected back to the bat? (Assume the speed of sound is 340 m/s)

   1. A) 39.4 kHz
   2. B) 40.6 kHz
   3. C) 41.2 kHz
   4. D) 42.4 kHz

4. A radar gun measures the speed of a car to be 25 m/s. If the radar gun emits a frequency of 15 GHz, what is the approximate frequency shift detected by the gun? (Assume the speed of light is $3 \times 10^8$ m/s)

   1. A) 1.25 kHz
   2. B) 2.5 kHz
   3. C) 3.75 kHz
   4. D) 5.0 kHz

5. An ambulance is moving towards you at 35 m/s, and its siren emits a frequency of 800 Hz. What frequency do you hear if the speed of sound is 343 m/s?

   1. A) 718 Hz
   2. B) 882 Hz
   3. C) 898 Hz
   4. D) 920 Hz

6. A race car is moving directly away from you at 50 m/s. The engine noise has a frequency of 1000 Hz. What frequency do you perceive if the speed of sound is 343 m/s?

   1. A) 873 Hz
   2. B) 1146 Hz
   3. C) 1000 Hz
   4. D) 750 Hz

7. A police officer uses a radar gun that emits a frequency of 20 GHz. The car is traveling at an angle of 30 degrees relative to the radar gun's line of sight and the radar gun detects a shift indicating a speed of 20 m/s along its line of sight. What is the car's actual speed?

   1. A) 10 m/s
   2. B) 20 m/s
   3. C) 30 m/s
   4. D) 40 m/s