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ClassNotes6 - Physics 434 Module 4 Acoustic excitation of a...

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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
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Physics 434 Module 4 - T. Burnett 2 Frequency domain Last week you measured the frequency domain response to the system where, ϖ =2 π f, and G( ϖ ) is the (complex) response. (Why complex?). H in ( ϖ ) G( ϖ ) H out ( ϖ ) ) ( ) ( ) ( ϖ ϖ ϖ in out H G H =
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Example Physics 434 Module 4 - T. Burnett 3 What is the frequency composition of these signals?
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Today: Frequencies in a pulse Physics 434 Module 4 - T. Burnett 4 ϖ ϖ ϖ ) sin( 2 a dt e a a t i - = Note: exactly the same as a single-slit diffraction pattern
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Physics 434 Module 4 - T. Burnett 5 More generally dt t h e H d H e t h t i t i ) ( ) ( inverse and the ) ( ) ( 2 1 = = - ϖ ϖ π ϖ ϖ ϖ Any time-varying signal is composed of a spectrum of frequencies: Where H( ϖ ) is the Fourier transform, or frequency domain representation of the signal
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Physics 434 Module 4 - T. Burnett 6 The response to a time-varying signal: [ ] dt t h e G d G e t h t t h d t d t h e G e t h dt
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