Objectives (5 - 10 minutes)

1. Understanding the Doppler Effect: The teacher must ensure that students understand the concept of the Doppler Effect, which is the change in frequency of a wave perceived by an observer in relative motion to the wave source. Students should be able to identify and explain the variables involved in the Doppler Effect.

2. Application of the Doppler Effect: Students should be able to apply the Doppler Effect in real situations, such as the passage of an emergency vehicle with a siren on or the sound of an approaching and receding ambulance. The teacher should encourage students to relate theory to practice so that they can understand how the phenomenon occurs in everyday situations.

3. Problem Solving: The teacher should prepare students to solve problems related to the Doppler Effect. This includes understanding and applying the formulas associated with the phenomenon, such as the formula for apparent frequency and the formula for relative velocity. The teacher should encourage students to work in teams to solve problems, promoting collaboration and discussion.

Secondary objectives:

• Development of Critical Thinking: In addition to understanding the content, the teacher should aim to develop students' critical thinking. This can be done through the discussion of open-ended questions, where students must argue and justify their answers.

• Stimulating Scientific Curiosity: Through the presentation of experiments and practical applications of the Doppler Effect, the teacher should stimulate students' scientific curiosity, encouraging them to explore more about the subject.

• Improving Communication and Presentation Skills: The teacher should provide opportunities for students to share their discoveries and solutions with the class, thus improving their communication and presentation skills. This can be done through oral presentations, group discussions, or research projects.

Introduction (10 - 15 minutes)

1. Review of previous content: The teacher should start the lesson by recalling the basic concepts of waves, such as amplitude, frequency, and velocity. It is important that students have a good foundation of these concepts to understand the Doppler Effect. The teacher can do this through a quick oral review or a multiple-choice quiz.

2. Problem situations: To spark students' interest, the teacher can present two problem situations related to the Doppler Effect. For example, "Why does the sound of an ambulance change when it approaches and moves away?" and "Why does the sound of a motorcycle change when it passes us at high speed?" These questions should serve as a starting point for discussing the Doppler Effect.

3. Contextualization: The teacher should then contextualize the importance of the Doppler Effect, explaining that it is used in various everyday applications and in fields such as astronomy and medicine. For example, the Doppler Effect is used to measure the speed of distant stars and galaxies, and it is also used in ultrasound exams to detect the movement of fluids in the human body.

4. Introduction of the topic: To introduce the topic in an interesting way, the teacher can share some curiosities about the Doppler Effect. For example, the Doppler Effect was discovered by the Austrian physicist Christian Doppler in 1842, and he originally applied the phenomenon to light, not sound. Another curiosity is that the Doppler Effect is the reason why the siren of an emergency vehicle seems to "change pitch" when it passes by us quickly.

5. Gaining students' attention: To gain students' attention, the teacher can show a short video demonstrating the Doppler Effect. For example, a video showing a toy car with a siren passing by quickly, or a video showing a star moving rapidly in the sky and its light spectrum changing due to the Doppler Effect. Additionally, the teacher can share some curiosities about the application of the Doppler Effect in movies and series, such as in car chase scenes.

Development (20 - 25 minutes)

1. Theory of the Doppler Effect (10 - 12 minutes)

   1.1. Definition of the Doppler Effect: The teacher should start by explaining what the Doppler Effect is. They should emphasize that it is a change in the frequency of a wave perceived by an observer in relative motion to the wave source. The example of an emergency vehicle passing by can be used, where the sound of the siren seems to "change pitch" because the vehicle is moving relative to us.

   1.2. Causes of the Doppler Effect: The teacher should explain that the Doppler Effect occurs due to the relative motion between the observer and the wave source. If the wave source moves away from the observer, the perceived frequency decreases (called the receding Doppler effect). If the wave source approaches the observer, the perceived frequency increases (called the approaching Doppler effect).

   1.3. Doppler Effect Formulas: The teacher should present the formulas for the Doppler Effect. The formula for apparent frequency is:

   f' = (v ± vo) / (v ± vs) * f

   Where f' is the apparent frequency, v is the speed of sound, vo is the speed of the observer, vs is the speed of the source, and f is the real frequency. The ± sign should be used to indicate whether the source and observer are approaching or receding.

   The formula for relative velocity is:

   v = (f' * (v ± vs)) / f

   Where v is the speed of sound, f' is the apparent frequency, vs is the speed of the source, and f is the real frequency. The ± sign should be used to indicate whether the source and observer are approaching or receding.

   1.4. Applications of the Doppler Effect: The teacher should conclude the theory explanation by presenting some applications of the Doppler Effect. This can include the detection of exoplanets, measuring the speed of distant stars and galaxies, detecting movement in ultrasound exams, among others.

2. Examples and Demonstration (5 - 7 minutes)

   2.1. Example of an Emergency Vehicle: The teacher should use the example of an emergency vehicle with a siren on to demonstrate the Doppler Effect. They should explain that as the vehicle approaches, the sound frequency seems to increase, and as the vehicle moves away, the sound frequency seems to decrease. The teacher should then use the Doppler Effect formulas to calculate the apparent frequency and relative velocity.

   2.2. Example of a Moving Star: The teacher should use the example of a star moving rapidly in the sky to demonstrate the Doppler Effect. They should explain that as the star moves away, the light frequency seems to decrease, and as the star approaches, the light frequency seems to increase. The teacher should then use the Doppler Effect formulas to calculate the apparent frequency and relative velocity.

3. Practical Activity (5 - 6 minutes)

   3.1. Problem Solving: The teacher should propose some problems for students to solve in groups. The problems should involve applying the Doppler Effect formulas to calculate the apparent frequency and relative velocity. The teacher should circulate around the room, assisting groups that are having difficulties and checking if the calculations are being done correctly.

   3.2. Discussion of Results: After the groups finish solving the problems, the teacher should promote a class discussion about the results. The teacher should ask each group how they solved the problem and if they arrived at the same answer. The teacher should correct any misunderstandings and clarify any doubts the students may have.

   3.3. Reflection on the Activity: To conclude the activity, the teacher should ask students to reflect on what they learned. The teacher should ask: "What did you find most difficult about solving these problems?" and "What do you think you could do to improve next time?" The teacher should encourage students to honestly reflect on their skills and identify areas that need improvement.

Return (10 - 15 minutes)

1. Group Discussion (5 - 7 minutes)

   1.1. Sharing Solutions: The teacher should ask each group to share their solutions to the proposed problems. A representative from each group should present the solution the group found, explaining the reasoning used and how the Doppler Effect formulas were applied.

   1.2. Teacher Feedback: After each presentation, the teacher should provide constructive feedback, highlighting the strengths of the group's work and suggesting improvements. The teacher should also correct any conceptual errors that may have occurred during the presentations.

   1.3. Class Discussion: After all presentations, the teacher should promote a class discussion, relating the presented solutions to the theory discussed in the lesson. The teacher should encourage students to ask questions and express their opinions, thus promoting everyone's participation.

2. Connection with Theory (3 - 5 minutes)

   2.1. Identification of Key Concepts: The teacher should guide students in identifying the key concepts discussed during the lesson. Students should be able to relate these concepts to the solutions they found for the proposed problems.

   2.2. Reflection on Learning: The teacher should then ask students to reflect on what they learned. The teacher can ask questions like: "What was the most important concept you learned today?" and "What questions remain unanswered?" The teacher should encourage students to think critically and express their opinions.

3. Student Feedback (2 - 3 minutes)

   3.1. Learning Verification: The teacher should check if the learning objectives were achieved by asking students to answer questions like: "Do you feel confident in applying the Doppler Effect in real situations?" and "Do you think you could solve other problems involving the Doppler Effect?" The teacher should record the students' answers and use them to plan future lessons and activities.

   3.2. Suggestions for Improvements: The teacher should also ask students to provide suggestions for improvements. This can include suggestions for topics they would like to learn more about, suggestions for future practical activities, or feedback on the lesson dynamics. The teacher should record these suggestions and use them to improve their future lessons.

4. Closure (1 - 2 minutes)

   4.1. Content Recap: The teacher should conclude the lesson by briefly recapping the main points discussed. They should reiterate the definition of the Doppler Effect, the associated formulas, and the main applications of the phenomenon.

   4.2. Preparation for the Next Lesson: The teacher should then prepare students for the next lesson, informing them about the next topic to be covered and any necessary materials or preparations. For example, if the next lesson is about sound waves, the teacher can ask students to research the topic and bring examples of everyday sound waves.

   4.3. Farewell: Finally, the teacher should thank the students for their participation and effort, and wish everyone a good day. The teacher should be available to answer any additional questions from students and provide extra support if needed.

Conclusion (5 - 7 minutes)

1. Lesson Summary (1 - 2 minutes): The teacher should start the Conclusion by summarizing the main points covered during the lesson. This includes the definition of the Doppler Effect, the associated formulas, the situations in which the phenomenon occurs, and its practical applications. The teacher should reiterate the importance of understanding the Doppler Effect to comprehend how sound waves behave in relation to a moving observer.

2. Theory-Practice Connection (1 - 2 minutes): The teacher should then explain how the lesson connected theory with practice. They should highlight how the initial discussion, problem situations, and practical examples helped illustrate and apply the theories of the Doppler Effect. The teacher should emphasize that the ability to apply theory in practice is essential for effective learning in Physics.

3. Supplementary Materials (1 - 2 minutes): The teacher should suggest additional study materials for students. This can include supplementary readings, explanatory videos, interactive simulations, and practice exercises. The teacher can recommend reliable physics websites, such as Khan Academy, Physics Classroom, and HyperPhysics, which offer a variety of educational resources on the Doppler Effect.

4. Real-World Applications (1 - 2 minutes): Finally, the teacher should emphasize the importance of the Doppler Effect in the real world. They should explain that although the Doppler Effect is a complex concept, it has significant practical applications, such as in astronomy, medicine, and even in our daily lives. The teacher can cite examples of how the Doppler Effect is used to detect exoplanets, measure the speed of distant stars, monitor blood flow in ultrasound exams, and alert us to the approach of emergency vehicles.

5. Closure (1 minute): To conclude, the teacher should thank the students for their participation and effort, and remind them of the importance of studying and preparing for future lessons. The teacher should encourage students to explore the Doppler Effect further at home and to bring any questions they may have to the next lesson.