1. April 8 – April 9

2. Can two different objects occupy the exact same location at the exact same time? Of course not … but two waves can! When waves meet, they superimpose (add together), but then continue traveling unaltered, as if they had never had contact. The superimposition of waves can create complex wave patterns.

3. Constructive interference Occurs when both waves oscillate the particles of medium in the same direction at a given point in space. Causes an increase in amplitude (and thus energy) at that point. Causes bright spots / loud sounds / increase in vibration Destructive interference Occurs when the two waves oscillate the particles of the medium in opposite directions at a given point in space. Causes a decrease in amplitude (and thus energy) at that point. Causes a decrease (or absence!) of light, sound, vibration Constructive interference occurs when waves are in phase Completely destructive interference occurs when waves are 180 degrees out of phase Partially destructive interference occurs when waves are out of phase by any value other than 180.

4. When two waves interfere, the resulting displacement of the medium at any location is the sum of the displacements of the individual waves at that same location Example: To find the resulting wave pattern for the two interfering waves shown above, simply add the displacements of each wave at each point. Position Blue Displacement Red Displacement Total A000 B314 C D E F G

5. When two waves interfere, the resulting displacement of the medium at any location is the sum of the displacements of the individual waves at that same location Example: To find the resulting wave pattern for the two interfering waves shown above, simply add the displacements of each wave at each point. Position Blue Displacement Red Displacement Total (green) A000 B314 C426 D314 E000 F-3-4 G -2-6 Is this an example of constructive or destructive interference?constructive

6. Draw the interference pattern for the two waves shown on the graph below. (Do at least to point J) Which points have constructive interference? Which points have destructive interference?

7. Draw the interference pattern for the two waves shown on the graph below. (Do at least to point J) Which points have constructive interference? Which points have destructive interference? G, J H, I

8. Two boys, each 10 m apart, are splashing, creating identical waves of wavelength 2 m that travel towards each other. Their little sister is playing in between them, located 4 m away from one boy, 6 from the other. Will the waves by the sister be big (due to constructive interference) or small (due to destructive interference)? How can we tell? We have to determine whether the waves are in phase at point of the sister, or not. To do this, we can compare the path length of the two waves. If the difference in path length equals a whole wavelength (or a multiple 2λ, 3λ, 4λ, etc.) then the waves will be in phase.

9. Two boys, each 10 m apart, are splashing, creating identical waves of wavelength 2 m that travel towards each other. Their little sister is playing in between them, located 4 m away from one boy, 6 from the other. Will the waves by the sister be big (due to constructive interference) or small (due to destructive interference)? Path for wave from left = 4 m Path for wave from right = 6 m Difference = 6 m – 4 m = 2m 2 m = 1 whole wavelength The two waves will add together constructively, resulting in large waves where the sister is swimming.

10. X and Y are coherent sources of 2cm waves. At each of the following points, determine whether they interfere constructively or destructively. A - B - C - Destructive. Path difference is 1cm which is ½ λ Constructive. Path difference is zero. Constructive. Path difference is two, which is 1λ

11. The wavelength of a transverse wave is 4cm. At some point on the wave the displacement is -4cm. At the same instant, at another point 50cm away in the direction of propagation of the wave, the displacement is A.0cm B.2cm C. 4cm D.-4cm We have to find out what phase of the wave is 50 cm away. 50 cm/ 4cm = 12.5 The other point is half a wavelength off / 180 o out of phase.

13. Homes near cliffs often have interference between direct and reflected signals Momentary interference due to passing airplane! Direct path Reflected path

14. Noise-canceling headphones create sound waves 180 o out of phase with ambient noise to cancel out the sound Instruments are tuned with a tuning fork by listening for beats – fluctuation in the loudness of the sound – when both the instrument and the tuning fork are played together. If the instrument is out of tune, then the wavelengths of the two notes will not match and will fluctuate between constructive and destructive interference, creating the beats. The beats disappear when the instrument is in tune.