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Exploring Drum Resonance & Energy Transmission in Acoustics

Dive deep into the world of drum modes, energy transfer, and sound resonance, covering topics like sonograms, tuning forks, sphere energy spread, and decibel measurement. Understand the complex relationship between vibrating objects and resonant frequencies.

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Exploring Drum Resonance & Energy Transmission in Acoustics

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  1. Lecture 17 October 29, 2004

  2. On Wednesday - Thumping

  3. The Drum • Each of these modes are usually excited. • The tension of the drum determines the frequency of each mode. • The modes may NOT be harmonic • Each mode dies out at a different rate. • The player can change the basic “tone” of the drum by changing the tension of the drum head.

  4. Kettle Drum INITIAL Spectrum

  5. Drum Frequencies

  6. The Sonogram

  7. Modes • All modes are excited at first strike. • These vibrations may excite others … resonance. • Each mode decays in a different time. Amplitude time

  8. So … back to the tuning forks RESONANCE !

  9. Objects will resonate when • They are in contact with something that vibrates at its resonant frequency. • Buzz in cars is a good example • Sound can cause resonance if it is at a frequency that is the resonant frequency of another object nearby. • It must have enough energy.

  10. Back to the trip from the instrument into our heads

  11. The Trip TRAVEL AND ROOM ACOUSTICS CREATION Of Sound

  12. Sound Travels ENERGY

  13. Something is Missing • As time progresses, the amount of energy received by the ear increases. • We need a measure of energy per unit time. ENERGY

  14. ENERGY PER UNIT TIME

  15. Example = The Light Bulb • Consider a 60 Watt light bulb. • It requires 60 Joules of energy each second. • One Joule = 1 Newton Meter • Joule=1( N-m)x (1 lb/4.45N) x (3.28ft/m) • Joule=0.738 ft-lbs

  16. Thinking about light bulbs • 60 Joules = 44.2 ft-lbs • Lift a ~4 pound weight 10 ft. or about one story of a building. • Do this every second for 60 watts. Joule=0.738 ft-lbs A 100 lb woman would have to run up about 2 floors of a building per second to generate this much power!

  17. About Spheres …. r

  18. Energy Spreads Out These AREAS increase with r2. Power per unit area therefore DECREASES with r2.

  19. Let’s go to a concert. 50 Meters 30 watts Ear Canal ~ 0.5 cm = 0.005 m Area = (0.005)2=0.000025 m2

  20. Houston we have another problem 30 watts, 50 meters Ear Area = (0.005)2=0.000025 m2 How much energy gets to the ear?

  21. To the ear …. Area of Sphere =pr2 =3.14 x 50 x 50 = 7850 m2 50m Ear Area = 0.000025 m2 30 watt

  22. In the ear… How do we deal with all of these zeros???

  23. Answer: Scientific NotationChapter 1 in Bolemon, Appendix 2 in Johnston 0.000000095 watts = 9.5 x 10-8 watts

  24. NOTE • 10a/10b=10a-b • Example • 1000/10=103/101=10(3-1)=102=100 • 10000/0.005=104/5 x 10-3=(1/5)x10(4-(-3)) =(1/5)x 107 =(10/5) x 106 = 2,000,000 • You can actually get used to doing it this way! But you probably won’t!

  25. Q:Can we hear 9.5 x 10-8 watts? ?

  26. Acoustic Power (Watts)

  27. Decibels - dB • The decibel (dB) is used to measure sound level, but it is also widely used in electronics, signals and communication.

  28. Suppose we have two loudspeakers, the first playing a sound with power P1, and another playing a louder version of the same sound with power P2, but everything else (how far away, frequency) kept the same. The difference in decibels between the two is defined to be 10 log (P2/P1) dB        where the log is to base 10. Decibel continued (dB) ?

  29. What the **#& is a logarithm? • Bindell’s definition: • Take a big number … like 23094800394 • Round it to one digit: 20000000000 • Count the number of zeros … 10 • The log of this number is about equal to the number of zeros … 10. • Actual answer is 10.3 • Good enough for us!

  30. Back to the definition of dB: 10 log (P2/P1) • The dB is proportional to the LOG10 of a ratio of intensities. • Let’s take P1=Threshold Level of Hearing which is 10-12 watts/m2 • Take P2=P=The power level we are interested in.

  31. An example: • The threshold of pain is 1 w/m2

  32. Take another look.

  33. The sensitivity range for human hearing depends on the loudness and pitch. Noises along each black line would be heard with the same volume.

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