2. Harmonic Series and Spectrograms

3. 220 Hz (A3) Why do they sound different? Instrument 1 Instrument 2Sine Wave

4. Waveform Piano Guitar Sine Wave

5. Overtones Overtones occur at integer multiples of the fundamental frequency when an object vibrates. The addition of these tones at regular intervals is musical to the human ear. Example: Fundamental (1 st Harmonic): 220Hz 1 st Overtone (2 nd Harmonic): 440Hz 2 nd Overtone (3 rd Harmonic): 660Hz

6. PianoGuitar Spectrogram

7. Modes of Vibration: Standing Waves

8. Harmonic Motion

9. Frequency Decomposition: Pure Sine Wave T = 2ms f = 1/T f = 500Hz

10. Frequency Decomposition: Pure Sine Wave T = 1ms f = 1/T f = 1000Hz

11. Composite Wave

13. Waveform Piano Guitar Sine Wave

14. Spectrogram: Piano

15. Piano: Component Sine Waves

16. Composite Wave (From Previous Slide) Original Piano Wave Look how close with only three sine waves!!!

17. Fourier Series

18. Why you should change strings A quick experiment with a spectrogram Old New