1. Dr. Jie ZouPHY 10711 Chapter 4 (Hall) Sound Propagation (Cont.)

2. Dr. Jie ZouPHY 10712 Outline Interference In phase Out of phase Constructive interference Destructive interference

3. Dr. Jie ZouPHY 10713 Interference What is the combined effect when similar sound waves arrive from several directions at once? They may either cooperate or cancel out. This phenomenon is called interference. Constructive interference Destructive interference

4. Dr. Jie ZouPHY 10714 Interference of two sound waves A pair of speakers (sources) putting out identical sounds. Two sound waves are in phase at A, C, or D: Every time a crest from one speaker reaches A, so does a crest from the other speaker, and the two signals are said to be in phase at A. Two sound waves are out of phase at B or E: Every time a crest from one speaker reaches B, so does a trough from the other speaker. One wave’s compression cancels the other’s rarefaction, and the net result is no disturbance at all, and the two signals are said to be out of phase at B. One would avoid ever driving two speakers in the same room with the same signal.

5. Dr. Jie ZouPHY 10715 Conditions for constructive and destructive interference Constructive interference: The enhance intensity at A (or C or D) is called constructive interference. Condition for constructive interference: When there are one or more full wavelengths difference in distance between the two signals, i.e. L 1 -L 2 = n, n = 0, ±1, ±2…. Destructive interference: The reduced (sometimes zero) intensity at B (or E) is called destructive interference. Condition for destructive interference: When L 1 – L 2 = (n + ½), n = 0, ±1, ±2,...

6. Dr. Jie ZouPHY 10716 Example Sound of frequency f = 688 Hz is sent through two speakers. What are several values for path- length difference L 1 –L 2 that will lead to constructive interference?

7. Dr. Jie ZouPHY 10717 Homework Ch. 4 (Hall), P. 69, Exercises: #7, 8, 9 (#9 is a little more difficult).