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Physics 145 Introduction to Experimental Physics I Instructor: Karine Chesnel

Physics 145 Introduction to Experimental Physics I Instructor: Karine Chesnel Office: N319 ESC Tel: 801- 422-5687 kchesnel@byu.edu Office hours: on appointment Class website: http://www.physics.byu.edu/faculty/chesnel/physics145.aspx . Lab 12 Fourier Transform. Tuning fork.

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Physics 145 Introduction to Experimental Physics I Instructor: Karine Chesnel

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  1. Physics 145 Introduction to Experimental Physics I Instructor: KarineChesnel Office: N319 ESC Tel: 801- 422-5687 kchesnel@byu.edu Office hours: on appointment Class website: http://www.physics.byu.edu/faculty/chesnel/physics145.aspx

  2. Lab 12 Fourier Transform

  3. Tuning fork Resonators Spring – mass resonator

  4. Pure sine wave Frequency space Time space Time – frequency

  5. Joseph Fourier 1768 - 1830 french mathematician Decomposition of functions in linear combination of sine waves Discrete Fourier series Example: N = 10 N = 3 Fourier Transform

  6. Using complexe notation Fourier’s trick where Fourier Transform Discrete Fourier series Using sine functions

  7. Integration over time Integration over frequency range Fourier Transform Continuous Fourier transforms

  8. Frequency space Fourier Transform Square wave Time space

  9. Dt= t Dw= 1/t Frequency space Fourier Transform Modulated wave Time space

  10. Power spectrum

  11. Nyquist-Shannon criterion A periodic signal needs to be sampled at least at twice the frequency to be properly measured /reconstructed

  12. Sine wave Square wave Modulated wave Lab 12: Fourier Transform A. Computer generated waveforms • L12.1: open Labview Fourier-waveform.vi • generate different waveform • examine the time functions and the frequency spectra

  13. Lab 12: Fourier Transform C. Fourier spectra of sound-wave • L12.2: open Labview Fourier-sound.vi • plug microphone + headset speakers to computer • sample yourself whistling… sampling at 20kHz for 1s • L12.3: Record notes produced by tuning forks • look at fundamental frequency f0 and harmonics • compare fundamental frequency to nominal value • L12.4: Test the Nyquist criterion • - use sine wave from tuning fork (f0 = 1kHz) • - sample at different frequencies from 1kHz to 10kHz… • - observe what happens to the time and frequency spectra • L12.5: Generate Fourier spectra from different abrupt sounds: • clapping, yelling, popping balloons… • Print spectra

  14. Lab 12: Fourier Transform C. Application: vowel sound recognition • L12.6: generate Fourier spectra from vowels: a, e, o , u • (hold the note steady for entire acquisition) • L12.7: print series of spectra from different persons • play to guess which spectrum correspond to which vowel D. Application: frequency filter to vocal input • L12.8: Record vocal input (sentences, etc…) • - increase the sampling interval to several seconds at 20kHz • - turn the frequency filter ON (band pass) • - compare unfiltered (left) and filtered (right) signals • L12.9: Play with parameters of band-pass filter • ( low band-pass: 100-200Hz…. High band-pass 1kHz and more) • listen to the resulting filtered signal, print spectra

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