1. Moving Source Going Faster Moving at the Speed of Sound Moving Faster than Sound Supersonic Mach I Pressure wave, piled up at nose Shock wave of constructive interference

2. When the wave of sound passes you – Sonic Boom! Sonic Boom  Do you see the plane or hear it first?

3. Sonic Boom High pressure Low pressure Moisture condenses in low pressure region

4. Wave Interference  Wave interaction, described by SUPERPOSITION !  Superposition –constructive or destructive combination of waves if present at the same place, same time

5. 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...

6. 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…

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

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

9. You are setting up a surround-sound system at your home. You have two speakers, each with an output of 214 Hz initially. You would like to place your favorite chair in a place where it can receive the loudest sound from these two speakers. You set up the speakers and chair in the configuration shown below. Is this a good place for the chair? Example 6 3.20 m 2.40 m

10. 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

11. #‘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?

12. 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 7

13. 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