Lesson Plan | Traditional Methodology | Waves: Doppler Effect

Objectives

Duration: 10 to 15 minutes

This stage of the lesson plan aims to present the main learning objectives related to the Doppler Effect, ensuring that students understand the importance of the topic and know what to expect throughout the lesson. The focus is to provide a solid foundation that enables the practical application of concepts in real-life situations.

Main Objectives

1. Explain the concept of the Doppler Effect and its application in different contexts.

2. Teach students to identify and calculate the apparent frequency perceived by an observer in motion relative to a sound source.

3. Provide practical examples and problems to illustrate the application of the Doppler Effect.

Introduction

Duration: 10 to 15 minutes

The purpose of this stage is to capture the students' attention and contextualize the relevance of the Doppler Effect in everyday situations and different fields of knowledge. By connecting the topic with practical and interesting examples, the introduction aims to spark students' curiosity and prepare them for the theoretical concepts that will be addressed next.

Context

To start the lesson on the Doppler Effect, begin by presenting a scenario that is familiar and intriguing for the students. Ask them if they have ever noticed how the sound of an ambulance changes as it approaches and then moves away. Explain that this occurs due to the Doppler Effect, a phenomenon that describes the change in frequency of a wave in relation to an observer who is moving relative to the wave source. Use a short video or an animated graphic that shows the sound of a racing car as it approaches and moves away from an observer to illustrate this change in frequency visually and auditorily.

Curiosities

Did you know that the Doppler Effect does not only apply to sound? It is also used in astronomy to measure the speed and direction of stars and galaxies. Additionally, speed radars used by the police to catch speeding cars also utilize the Doppler Effect!

Development

Covered Topics

1. Concept of the Doppler Effect: Explain that the Doppler Effect is the change in frequency or wavelength perceived by an observer in motion relative to the wave source. Emphasize that this phenomenon occurs for both sound waves and electromagnetic waves. 2. Doppler Effect Formula for Sound: Present the formula for the Doppler Effect for sound waves, which is f' = f (v + vo) / (v - vs). Where f' is the apparent frequency, f is the frequency of the source, v is the speed of sound in the medium, vo is the speed of the observer, and vs is the speed of the source. Explain each term in detail and how it impacts the final result.

Questions Discussion

Duration: 20 - 25 minutes

The purpose of this stage is to ensure that students consolidate the knowledge acquired throughout the lesson by discussing the answers to the presented questions and reflecting on the application of the Doppler Effect in different contexts. This discussion allows for identifying possible doubts and reinforcing understanding of the content, as well as promoting student engagement through reflective questions.

Discussion

•  Discussion of the Resolved Questions:

• 1. Question 1: A police car with a siren emitting a sound at 700 Hz is approaching an observer at a speed of 30 m/s. What is the apparent frequency perceived by the observer? (Assume the speed of sound in air is 343 m/s)
• • Explanation: Here, the source (police car) is moving towards the observer. Applying the Doppler Effect formula, f' = f (v + vo) / (v - vs), where:

•  - f = 700 Hz (frequency of the source)
  

•  - v = 343 m/s (speed of sound in air)
  

•  - vo = 0 m/s (observer at rest)
  

•  - vs = 30 m/s (speed of the source towards the observer)
  

• • Substituting the values: f' = 700 (343 + 0) / (343 - 30) = 700 * 343 / 313 ≈ 767 Hz
• 2. Question 2: An observer is moving away from a sound source that emits a frequency of 500 Hz at a speed of 20 m/s. What is the apparent frequency perceived by the observer? (Assume the speed of sound in air is 343 m/s)
• • Explanation: In this case, the observer is moving away from the source. Applying the Doppler Effect formula, f' = f (v - vo) / (v), where:

•  - f = 500 Hz (frequency of the source)
  

•  - v = 343 m/s (speed of sound in air)
  

•  - vo = 20 m/s (speed of the observer moving away)
  

•  - vs = 0 m/s (source at rest)
  

• • Substituting the values: f' = 500 (343 - 20) / 343 = 500 * 323 / 343 ≈ 471 Hz
• 3. Question 3: An ambulance is moving away from a stationary observer at a speed of 25 m/s and emits a sound at 800 Hz. What is the apparent frequency perceived by the observer? (Assume the speed of sound in air is 343 m/s)
• • Explanation: Here, the source (ambulance) is moving away from the observer. Applying the Doppler Effect formula, f' = f (v) / (v + vs), where:

•  - f = 800 Hz (frequency of the source)
  

•  - v = 343 m/s (speed of sound in air)
  

•  - vo = 0 m/s (observer at rest)
  

•  - vs = 25 m/s (speed of the source moving away)
  

• • Substituting the values: f' = 800 * 343 / (343 + 25) = 800 * 343 / 368 ≈ 746 Hz

Student Engagement

1. 1. How does the relative motion between the observer and the source affect the perceived frequency? 2. 2. In what other everyday situations do you notice the Doppler Effect? 3. 3. What is the importance of the Doppler Effect in medicine and astronomy? 4. 4. How does the Doppler Effect formula change if both the source and the observer are in motion? 5. 5. Discuss how the Doppler Effect can be applied to measure the speed of a car using a speed radar. 6. 6. If the speed of sound in the medium were different, how would this affect the calculations of apparent frequencies?

Conclusion

Duration: 10 - 15 minutes

The purpose of this stage is to summarize and consolidate the knowledge acquired throughout the lesson, reinforcing key points and highlighting the practical importance of the Doppler Effect. This final review helps ensure that students leave the lesson with a clear and solid understanding of the content covered.

Summary

• The Doppler Effect is the change in frequency or wavelength perceived by an observer in motion relative to the wave source.
• The formula for the Doppler Effect for sound waves is f' = f (v + vo) / (v + vs), where f' is the apparent frequency, f is the frequency of the source, v is the speed of sound in the medium, vo is the speed of the observer, and vs is the speed of the source.
• Practical applications of the Doppler Effect include speed radars, Doppler ultrasound, and astronomy.
• Calculating the apparent frequency in different scenarios, such as when the source is in motion, the observer is in motion, or both are in motion.

The lesson connected theory with practice by presenting real examples and solving practical problems. By demonstrating how to calculate the apparent frequency in different scenarios and discussing applications of the Doppler Effect, students could see how the theoretical concept is used in everyday and professional situations, such as in speed radars and medicine.

The Doppler Effect is a phenomenon that has a great impact on our daily lives. From the way we perceive the sound of moving vehicles to its application in medical diagnostic technologies and astronomical measurements, understanding this concept allows us to appreciate the interconnections between physics and the world around us. Furthermore, it is fundamental for the development of safety technologies like speed radars.