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Wave Physics PHYS 2023 Tim Freegarde

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

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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

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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

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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

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

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

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

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Wind instruments

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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

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