1. Physics 434 Module 4 – Thanks to Prof. Toby Burnett for writeups & labs 1 Physics 434 Module 4 Acoustic excitation of a physical system: time domain

2. Physics 434 Module 4 - T. Burnett 2 Frequency domain Last week you measured the frequency domain response to the system where,  =2  f, and G(  ) is the (complex) response. (Why complex?). H in (  ) G(  ) H out (  )

3. Example Physics 434 Module 4 - T. Burnett 3 What is the frequency composition of these signals?

4. Today: Frequencies in a pulse Physics 434 Module 4 - T. Burnett 4 Note: exactly the same as a single-slit diffraction pattern

5. Physics 434 Module 4 - T. Burnett 5 More generally Any time-varying signal is composed of a spectrum of frequencies: Where H(  ) is the Fourier transform, or frequency domain representation of the signal

6. Physics 434 Module 4 - T. Burnett 6 The response to a time-varying signal:

7. Physics 434 Module 4 - T. Burnett 7 Time domain system response: Goals of this section of the Module Apply a pulse to the system, measure the system response Adapt the test VI to accumulate and average multiple “shots” Understand the signal processing requirements, and capabilities of the AT-E data acquisition board Use a Fast Fourier Transform (FFT) VI to obtain the frequency spectrum from the time series Understand how a FFT works

8. Physics 434 Module 4 - T. Burnett 8 Setup: almost same as Module 3…

9. Physics 434 Module 4 - T. Burnett 9 New elements: triggering & counter TRIG1 GPCTR0_OUT digital ground To scope and speaker in To scope and microphone in

10. Physics 434 Module 4 - T. Burnett 10 Run the demo VI Response of an ideal tube!

11. Physics 434 Module 4 - T. Burnett 11 A second advantage: signal averaging