1. Sound and adding waves Interference

2. Types of Waves Longitudinal –Sound waves –Motion of the medium is parallel to the wave Transverse –Motion of the medium is perpendicular to the wave –Waves in a string Remember, for waves, there is no net displacement of the medium

3. Two waves at the same place When multiple waves meet at the same spot in the same medium, they interact. This is called wave interference. At the moment they overlap, their amplitudes add, so we get a bigger wave for a moment This only lasts until they pass by each other.

4. Positive (red) combines with positive (blue) and add to result in a bigger amplitude (green) Negative(red) combines with negative (blue) and add to result in a bigger amplitude (green) Constructive Interference

5. Destructive Interference Negative (blue) meets positive (red), so a portion or all of the wave is canceled, resulting in a smaller amplitude (green)

6. Beats Beats are alternations in loudness, due to interference Waves have slightly different frequencies and the time between constructive and destructive interference alternates The beat frequency equals the difference in frequency between the two sources: Beats make a “wah, wah” sound Happens only when the two frequencies are close Instruments or voices close, but out of tune Different from really bad musicians

7. The two small graphs below are sine plots of two different but similar frequencies. Notice that the wave crests are closer together on the first graph. Y = 3sin(5x)Y = 3sin(4x)

8. Note the difference Notice that at times the waves are perfectly matching and at others they are exactly opposite. When they interfere When the waves match perfectly they will add and when they are opposite the cancel each other out. The result is the pattern below and is termed beats.

9. In a series of waves, all the waves interfere making huge wave patterns Think of “donuts” while tubing at the lake