1. Predict what will happen in the following situation. Sketch below your prediction of the interference pattern when the waves overlap:

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Conrad Spencer
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1 Name P Physics1 Waves Unit WVE EHVIOR Date INTRODUCTION y the end of these activities you should have: an understanding of interference as a behavior which occurs as two waves interfere while moving through the same medium; an ability to distinguish between constructive and destructive interference; an ability to use the principle of superposition in order to determine the resultant shape and size of a wave pattern produced by two interfering waves; an ability to predict the behavior of a wave pulse after reflecting from a boundary between 2 different media and the pulse that gets transmitted into the new medium. WVE INTERFERENCE What happens when two waves meet while they travel through the same medium? What effect will the meeting of the waves have upon the appearance of the medium? Will the two waves bounce off each other upon meeting or will the two waves pass through each other? Wave Interference occurs when two waves meet while traveling along the same medium. To begin our exploration of wave interference, consider two pulses of the same amplitude traveling in different directions along the same medium. 1. Predict what will happen in the following situation. Sketch below your prediction of the interference pattern when the waves overlap: efore Interference During Interference 2. Open the simulation found at Make the heights and widths of Pulse 1 and 2 the same. Observe what happens when the waves pass through each other. Pause/slow down the simulation at various places. Describe what you observe before, during and after the pulses meet (in clear full sentences): Does the behavior shown in the simulation agree with your prediction? This type of interference is called CONSTRUCTIVE INTERFERENCE. Constructive Interference occurs when the wave amplitudes reinforce each other, building a wave of even greater amplitude. 3. What would happen if the pulses are inverted, i.e. a trough meets a trough? Sketch below your prediction of the interference pattern when the waves overlap:

2 efore Interference During Interference 4. nother type of interference occurs when the waves are out of phase i.e. a crest meets a trough. Sketch below your prediction of the interference pattern when the waves overlap: efore Interference During Interference 5. Click Pause on the simulation and set pulse1 height to -3 and pulse2 height to 3. Describe what you observe before, during and after the pulses meet: Does the behavior shown in the simulation agree with your prediction? This type of interference is called DESTRUCTIVE INTERFERENCE. Destructive Interference occurs when the wave amplitudes oppose each other, resulting in waves of reduced amplitude. 6. Now suppose that the pulses have different amplitudes. Predict what would happen by drawing a sketch of the interference pattern when the waves overlap: efore Interference During Interference

3 7. Click Pause on the simulation and set pulse1 height to 1 and pulse2 height to -3. Describe what you observe before, during and after the pulses meet: PRINCIPLE OF SUPERPOSITION To determine the resultant wave we can use the Principle of Superposition: When two waves interfere, the resulting displacement of the medium at any location is the algebraic sum of the displacements of the individual waves at that same location. 1. To determine the precise shape of the medium at a given instant in time, the principle of superposition must be applied to several locations along the medium. In this example several locations have been labeled. a) Use the principle of superposition for each location and mark the resultant amplitude with a dot. Neatly connect the dots to find the resultant waveform. b) Several positions along the medium are labeled with a letter. Categorize each labeled position along the medium as being a position where either constructive or destructive interference occurs. ll positions except for, E, I, M, Q, and U involve constructive interference.

4 2. pply the principle of superposition of waves to find the interference pattern of the 2 waves shown below. Mark the resultant amplitude with a dot at several key locations (every grid) and neatly connect the dots to find the resultant waveform Constructive Interference: G, J, M, N Destructive Interference: H, I, K, L QUESTIONS 1. Sound is a pressure wave that consists of compressions and rarefactions. Explain constructive interference of two sound waves in terms of pressure variations. 2. friend tells you that the word destructive tends to imply that the energy as well as the form of the waves is destroyed. Do you agree with your friend? Explain your answer.

5 t=0s t=2s t=4s 3. Each column below shows two pulses and, traveling on a string as they head toward each other (t =0,) when they are superimposed (at t =2 s) and a blank grid for t = 4s. Using the principal of superposition, show the resultant displacement of the string at 2 sec and at 4 s (use a solid line in a different color).

6 WVE REFLECTION ND TRNSMISSION For each of the problems, indicate direction of travel, speed of wave relative to the incident wave (same, faster, slower) and draw the amplitudes and wavelengths of each wave qualitatively accurately. 1. a) In the box below, draw the pulse as it b) Draw the pulse as it returns returns after reflecting from a fixed end. after reflecting from a free end. 2. Reflected Wave (circle correct answer) Reflected Wave (circle correct answer) Speed of wave faster, slower, same Speed of wave faster, slower, same Wavelength - longer, shorter, same Wavelength - longer, shorter, same mplitude - larger, smaller, same mplitude - larger, smaller, same a) Draw the pulse as it returns after b) Draw the pulse as it returns reflecting from a fixed end. after reflecting from a free end. 3. Reflected Wave (circle correct answer) Reflected Wave (circle correct answer) Speed of wave faster, slower, same Speed of wave faster, slower, same Wavelength - longer, shorter, same Wavelength - longer, shorter, same mplitude - larger, smaller, same mplitude - larger, smaller, same The sketch above shows a pulse traveling from a light string to a heavy string. In the box below, draw the reflected and transmitted pulses after the original pulse has reached the boundary.

7 Reflected Pulse Transmitted Pulse Speed of wave : faster, slower, same faster, slower, same Wavelength: longer, shorter, same longer, shorter, same mplitude : larger, smaller, same larger, smaller, same 4. The sketch above shows a pulse traveling from a heavy string to a light string. Draw the reflected and transmitted pulses after the original pulse has reached point P. Reflected Pulse Transmitted Pulse Speed of wave : faster, slower, same faster, slower, same Wavelength: longer, shorter, same longer, shorter, same mplitude : larger, smaller, same larger, smaller, same 5. elow is a pulse in a light rope approaching a heavy rope. Sketch the two rope system just after the pulse hits the wall.

8 6. To the right is a two-rope system soon after a pulse arrived at the center. a) If the right rope is the heavy rope, what did the system look like just after the system was shaken? In other words, show with a sketch which end was shaken and if the shake was up or down. b) If the left rope is the heavy rope, what did the system look like just after the system was shaken? 7. On the lines below draw the pulses as they would appear after they have completed their reflection from the free end or fixed end. Use the grid below to show the reflected pulse, using the right edge as the boundary. Make your drawing at the time the leading point of the pulse reflects to the 7 th box from the left. (Where the * is on the grid.) * Free end Free end * Fixed end Fixed end

1. Predict what will happen in the following situation. Sketch below your prediction of the interference pattern when the waves overlap:

1. Predict what will happen in the following situation. Sketch below your prediction of the interference pattern when the waves overlap: Name P Physics1 Waves Unit WVE EHVIOR Date INTRODUCTION y the end of these activities you should have: n understanding of interference as a behavior which occurs as two waves interfere while moving through