1. Lecture 08 Adding the Physics to the mix

2. Where are we? We have looked at some history of music from the “monkey” to the work of Helmholtz. We have looked at some history of music from the “monkey” to the work of Helmholtz. We found that the Greeks noted that certain fractions of the string lengths led to tones that sounded “well” together. We found that the Greeks noted that certain fractions of the string lengths led to tones that sounded “well” together.

3. What We Found The Original String Length is L 0 LengthNameComment L0L0 Fundemental Tone L 0 /2Octave Men/Women tend to sing one octive apart (2/3)L 0 Fifth Tenors and Bass will sing one fifth apart (4/3)L 0 Fourth Divide by 2 =2/3 = Reduce to same octave

4. We also defined repetitive pulses as having a frequency (f) and a period (T) Frequency, f, is the number of pulses that happen each second. –U–U–U–Unit is Hertz=1 cycle/second The Period (T) is the time BETWEEN pulses of the length of a single pulse. –T–T–T–T=1/f Consequently –f–f–f–fT=1 (IMPORTANT RELATIONSHIP)

5. We introduced the siren (Helmholtz)

6. The siren Sends out a KNOWN number of pulses per second. Sends out a KNOWN number of pulses per second. The pulses sound like tones. The pulses sound like tones. We defined the frequency as the number of puffs produced per second. We defined the frequency as the number of puffs produced per second.

7. Example We turn the belt so that the disk makes 2 rotations per second. We turn the belt so that the disk makes 2 rotations per second. The disk has 50 holes around the circumference. The disk has 50 holes around the circumference. The frequency = (number of rotations per second) x (number of holes in the circumference) = 100 hertz The frequency = (number of rotations per second) x (number of holes in the circumference) = 100 hertz This is a sound that we can hear. This is a sound that we can hear.

8. NOTE The lowest tone the human ear can hear is in the 25-50 hertz region. The lowest tone the human ear can hear is in the 25-50 hertz region. –It varies with the individual. The highest tone the human ear can hear is about 20,000 hertz. The highest tone the human ear can hear is about 20,000 hertz. Dogs hear higher!!! Dogs hear higher!!! But they can’t sing. But they can’t sing.

9. The Helmholtz Resonator

12. For a PARTICULAR sized resonator frequency Sound level F 0 = Resonant Frequency

13. Let’s Look at some Springs Demo-01

14. An Observation from N-1 MM Mg Tension=T M Mg FREE BODY DIAGRAM Because spring is Weightless, T=constant

15. Remember from a few weeks back??? F=-kx

16. We looked at:

17. An Observation from N-1 MM Mg Tension=T M Mg FREE BODY DIAGRAM ½ the length requires twice the force to stretch the same length! k is Bigger

18. The Vertical Spring

19. Un-stretched Hold and Suddenly Release Weight=Mg acceleration

20. Continue On Un-stretched Hold and Suddenly Release Weight=Mg acceleration Spring Force v a

21. Oscillation Repeat

22. Oscillation Position T T

23. Example 0.1 seconds

24. For the SPRING it is found that

25. Conclusions The bigger the mass the lower the frequency. The bigger the spring constant (stiffer) the higher frequency.

26. Let’s Look at a “Springy String” DEMO-02

27. The Tones f0f0

28. The FIFTH (???)

29. Take a look f 0 is the first tone. f 0 is the first tone. The octave is 2f 0. The octave is 2f 0. The NEXT octave is f 0. The NEXT octave is 4 f 0. The NEXT octave is f 0. The NEXT octave is 8 f 0. DOUBLE FOR EACH OCTAVE DOUBLE FOR EACH OCTAVE

30. Another Perspective f 0 2f 0 4f 0 8f 0 octave 3f 0 (3/2)f 0 fifth Next octave

31. Another View (3/4)f 0 =FOURTH Why would a string look like this???