Superposition of Waves: Free Body Diagram Example

📚 Quick Study Guide

• 🌊 Superposition Principle: When two or more waves overlap in a medium, the resultant displacement at any point is the vector sum of the displacements due to each individual wave.
• 📏 Free Body Diagram (FBD): A diagram representing all the forces acting on an object. It's essential for visualizing and analyzing forces in equilibrium or non-equilibrium conditions.
• ➕ Constructive Interference: Occurs when waves are in phase, resulting in a larger amplitude. The amplitude of the resulting wave is the sum of the amplitudes of the individual waves.
• ➖ Destructive Interference: Occurs when waves are out of phase, resulting in a smaller amplitude or cancellation. If the waves have the same amplitude, complete destructive interference occurs.
• 📐 Phase Difference: The difference in phase between two waves, usually measured in degrees or radians. A phase difference of $0$ or $2\pi$ radians indicates constructive interference, while a phase difference of $\pi$ radians indicates destructive interference.
• ✏️ Steps to Solve:
  1. Draw the Free Body Diagram showing forces/waves.
  2. Resolve forces/waves into components.
  3. Apply the Superposition Principle to find the resultant wave.

🧪 Practice Quiz

1. Two waves with amplitudes of 3 cm and 4 cm, respectively, interfere constructively. What is the amplitude of the resulting wave?

   1. 5 cm
   2. 1 cm
   3. 7 cm
   4. 12 cm

2. Two waves with the same amplitude interfere destructively. What is the amplitude of the resulting wave?

   1. Twice the original amplitude
   2. The same as the original amplitude
   3. Zero
   4. Half the original amplitude

3. What is a Free Body Diagram used for in the context of wave superposition?

   1. To calculate the speed of the waves
   2. To visualize the forces or waves acting at a point
   3. To measure the wavelength of the waves
   4. To determine the frequency of the waves

4. Two waves are said to be in phase when their phase difference is:

   1. $\pi$ radians
   2. $\pi/2$ radians
   3. $2\pi$ radians
   4. $3\pi/2$ radians

5. What type of interference occurs when two waves are $180$ degrees out of phase?

   1. Constructive Interference
   2. Destructive Interference
   3. Refraction
   4. Diffraction

6. If two waves with amplitudes $A_1$ and $A_2$ interfere constructively, what is the amplitude of the resultant wave?

   1. $|A_1 - A_2|$
   2. $\sqrt{A_1^2 + A_2^2}$
   3. $A_1 + A_2$
   4. $\frac{A_1 + A_2}{2}$

7. Which of the following is NOT a necessary step in solving wave superposition problems using Free Body Diagrams?

   1. Drawing the Free Body Diagram
   2. Resolving forces into components
   3. Applying the Superposition Principle
   4. Calculating the average speed of the waves