1. Constructive Interference – Result is a larger amplitude When Two Waves Meet…  Destructive Interference – Result is a smaller amplitude  Waves pass through each other afterwards.  If two waves combine...

2. Constructive Interference– Waves must be a whole-number wavelength apart Interference by Position  Destructive Interference– Waves must be a half wavelength apart  If you have the same sound but from two different speakers…

3. Path difference of ½ λ leads to destructive interference Interference by Position  Destructive  Constructive

4. A real problem for acoustical engineers Dead Zones in Concert Halls Ex. Avery Fisher Concert Hall – Lincoln Center Newly designed concert hall, Minneapolis, MN

5. Two speakers are 1.00 m apart. A person stands 4.00 m away from one of the speakers. How far must this person be from the second speaker in order to detect destructive interference when the speakers emit a 1150 Hz sound in room temperature air. Example 7

6. If two sounds are only slightly off in terms of frequency The ‘Beats’  Produce a periodic rise and fall of amplitude (volume)  Throbbing Sound = Beats

7. #‘beats’ = how far apart the two frequencies are The ‘Beats’  Ex. Tuning Fork 1: f = 440 Hz Tuning Fork 2: f = *Beat Frequency of 2 Hz?

8. A guitar string produces 4 beats per second when tuned with a 350 Hz tuning fork and 9 beats per second when tuned with a 355 Hz tuning fork. What is the actual frequency of the guitar? Example 8

9. What about the rubber bands determines pitch? Musical Instruments - Strings  The pitch or frequency of a string is determined by the string’s velocity (how fast it can move back and forth) F T = Force of Tension m/L = (mass)/(Length) = Linear Density  Tension  Thickness