Module 8—Mechanical Waves

Lesson 5 Lab: Path Difference and Interference

 

The Interference and Huygens’ Principle applet used for this lab lets you simulate wave motion and interference in a ripple tank. You will explore the concepts of path difference and Huygens' Principle. You can learn more about the simulation and how to use it by reading the Show Me found at the top of the simulation screen.

 
Problem

 

What is the relationship between path difference and interference?

 
Procedure
 

The figure to the right shows two point sources (S1 and S2) producing circular waves that interfere with one another. Set up this situation on the simulator by doing the following:

Observations
 
Self-Check

 

SC 1.

  1. Based on the figure titled “Test Point,” is the length between S1 and the test point identical to the length between S2 and the test point? If so, is there a path difference?

  2. Given the path difference from SC 1.a., predict the type of interference that occurs at the test point.

  3. When the simulation is playing, what do you notice about the waves passing the test point?
Check your work.
Self-Check Answers

 

SC 1.

  1. The lengths are identical, so there is no path difference. (The path difference is given in wavelengths at the top of the screen.)

  2. Since the path length is identical, the waves will arrive in phase; therefore, constructive interference will occur.

  3. The maximum amplitude waves (crests and troughs) pass through this point.

 

Module 8: Lesson 5 Assignment

 

Remember to submit the answers to LAB 1, LAB 2, LAB 3, and LAB 4 to your teacher as part of your Module 8: Lesson 5 Assignment.

 

The following figure shows the interference pattern produced by two wave sources.

 

 

Set up a similar wave pattern on the simulation by setting the resolution at 10.0 and selecting a wavelength of 30.0 m. On the simulation, systematically position the test point at each at each of the first six numbered positions in turn.

 

LAB 1. Complete the following table.

 

Number

Type of Interference

Path Difference
(Number of Wavelengths)

1

destructive

2.5

2

 

 

3

 

 

4

 

 

5

 

 

6

 

 

  1. In the right column, record the path difference that is displayed in the upper left corner of the display. Note that the simulation displays the path difference in terms of the number of wavelengths or waves.

  2. In the left column, list the type of interference at each point and the path difference. The simulation shows destructive interference as grey, while constructive interference alternates between white and black as seen when you press “Play.” The first row is done for you.

LAB 2. Based on your recorded observations on the table, describe the connection between the interference type and path difference.

 

LAB 3. Using the principle of superposition, explain the relationship between constructive interference and path difference. Include a diagram with your answer.

 

LAB 4. Using the principle of superposition, explain the relationship between destructive interference and path difference. Include a diagram with your answer.

 

The figure below shows two sources (S1 and S2) that emit waves. The waves are identical (λ = 1.0 m) and are emitted in phase. A detector (P) is located 6.0 m away from S1. Initially, the sources are separated by 1.0 m; however, S2 is systematically moved closer to the detector in increments of 0.5 m.

 

 

Self-Check 

 

SC 2. Complete the following table. L1 and L2 represent the path length from S1 to P and S2 to P, respectively. For the wave diagram, sketch in the waves emitted by each source—this will help you determine the type of interference. The first row is completed for you. Here is a printable copy of the following table.

 

L1

(m)

L2

(m)

λ

(m)

Wave Diagram

Type of Interference

6.0

5.0

1.0

1

constructive

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SC 3.

  1. What is the relationship between  and constructive interference?
  2. What is the relationship between  and destructive interference?
Check your work.
Self-Check Answers

 

SC 2.

 

L1 (m)

L2 (m)

λ (m)

Wave Diagram

Type of interference

6.0

5.0

1.0

1

constructive

 6.0

 4.5

1.5 

1.5 

destructive 

 6.0

 4.0

 2.0

 2.0

constructive 

6.0 

 3.5

 2.5

 2.5

destructive  

 6.0

3.0

 3.0

 3.0

constructive 

 6.0

 2.5

 3.5

 3.5

destructive  

 6.0

 2.0

 4.0

 4.0

constructive 

6.0 

 1.5

 4.5

 4.5

destructive  

6.0 

 1.0

 5.0

 5.0

constructive 

 

SC 3.

  1. Constructive interference occurs when is a whole number.
  2. Destructive interference occurs when  is a ½ a whole number.

 

Conclusion

 

 Self-Check

 

SC 4.

  1. For constructive interference to occur, the waves must arrive __________. The path difference must be a ________________ of waves.

  2. For destructive interference, the waves must be _______________. The path difference is a _________________ waves.

  3. Express these two conditions mathematically. ΔL is path difference, λ is the wavelength, and n is the number of waves.
Check your work.
Self-Check Answers

 

SC 4.

  1. For constructive interference to occur, the waves must arrive in phase. The path difference must be a whole number of waves.

  2. For destructive interference, the waves must be out of phase. The path difference is a half of a whole number of waves.

  3. Expressed mathematically, constructive interference is as follows:



    Expressed mathematically, destructive interference is as follows:

 

Module 8: Lesson 5 Assignment

 

Remember to submit the answer to TR 2 to your teacher as part of your Module 8: Lesson 5 Assignment.