Solved Examples of the Doppler Effect: Approaching and Receding Sources

📚 Quick Study Guide

• 🌊 The Doppler Effect is the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source.
• 🚗 For a source approaching an observer, the observed frequency ($f'$) is higher than the source frequency ($f$). The formula is: $f' = f \frac{v + v_o}{v - v_s}$, where $v$ is the speed of the wave, $v_o$ is the observer's speed, and $v_s$ is the source's speed.
• 🚑 For a source receding from an observer, the observed frequency ($f'$) is lower than the source frequency ($f$). The formula is: $f' = f \frac{v - v_o}{v + v_s}$, where $v$ is the speed of the wave, $v_o$ is the observer's speed, and $v_s$ is the source's speed.
• 📢 When the observer is stationary ($v_o = 0$), the formulas simplify to: Approaching: $f' = f \frac{v}{v - v_s}$ and Receding: $f' = f \frac{v}{v + v_s}$.
• 💡 Remember to use consistent units! Speed should typically be in meters per second (m/s).

🧪 Practice Quiz

1. A car is moving towards you at 20 m/s, beeping its horn which has a frequency of 500 Hz. Assuming the speed of sound is 343 m/s, what frequency do you hear?
   1. 472 Hz
   2. 531 Hz
   3. 529 Hz
   4. 469 Hz
2. An ambulance siren emits a frequency of 800 Hz. If the ambulance is moving away from you at 30 m/s, what frequency do you observe? (Assume the speed of sound is 343 m/s).
   1. 732 Hz
   2. 870 Hz
   3. 730 Hz
   4. 868 Hz
3. A train is approaching a station at 25 m/s, blowing its whistle at a frequency of 600 Hz. If the speed of sound is 343 m/s, what frequency is heard by a person standing on the platform?
   1. 646 Hz
   2. 559 Hz
   3. 644 Hz
   4. 557 Hz
4. You are standing still, and a motorcycle is moving away from you at 35 m/s. The motorcycle's engine noise has a frequency of 900 Hz. What frequency do you perceive? (Assume the speed of sound is 343 m/s).
   1. 821 Hz
   2. 982 Hz
   3. 819 Hz
   4. 980 Hz
5. A race car passes by at 50 m/s, its engine producing a sound of 1200 Hz. What is the difference in frequency heard as it approaches and recedes from you? (Assume the speed of sound is 343 m/s).
   1. 350 Hz
   2. 175 Hz
   3. 348 Hz
   4. 173 Hz
6. A police car is chasing a suspect at 40 m/s, with its siren emitting a frequency of 1000 Hz. You are standing still as the police car approaches. What frequency do you hear? (Assume the speed of sound is 343 m/s).
   1. 1134 Hz
   2. 882 Hz
   3. 1132 Hz
   4. 880 Hz
7. A runner sprints away from you at 10 m/s, humming a tune at 440 Hz. What frequency do you hear? (Assume the speed of sound is 343 m/s).
   1. 427 Hz
   2. 453 Hz
   3. 425 Hz
   4. 451 Hz