2. Wave Physics PHYS 2023 Tim Freegarde

3. 2 Spectrum periodic waveform can be expressed as a superposition of harmonics amplitude or intensity commonly represented by spectrum

4. 3 Spectrum periodic waveform can be expressed as a superposition of harmonics commonly represented by spectrum often plotted on log-log or lin-log scales

5. 4 Spectrum periodic waveform can be expressed as a superposition of harmonics commonly represented by spectrum often plotted on log-log or lin-log scales may be plotted with frequency axis upwards...... with marks for integer...... and time on the horizontal axis

6. 5 Boundary conditions for a boundary at : transverse waves on a string: fixed point sound waves in organ pipe:water waves:thermal waves:electromagnetic waves: wall since lagged end conductor open stopped thermal reservoir

7. 6 Open organ pipe first six harmonics lie on major chord J S Bach Toccata & Fugue in D minor BWV565

8. 7 Stopped organ pipe even harmonics are absent register key raises by a twelfth CLARINET:

9. 8 Oboes and saxophones even harmonics are present register key raises by a twelfth CLARINET: register key raises by an octave SAXOPHONE:

10. Wind instruments

11. 10 Spectrum periodic waveform can be expressed as a superposition of harmonics commonly represented by spectrum often plotted on log-log or lin-log scales may be plotted with frequency axis upwards...... with marks for integer...... and time on the horizontal axis

12. 11 Fourier transform Square wave t T/2-T/2 a -a