Assignment_5_09 - Physics 2214 Assignment 5 Concepts:...

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Physics 2214, Spring 2009 1 Cornell University Physics 2214 Assignment 5 Concepts: Fourier Analysis Boundary Conditions Beats Reflection and Transmission of Waves Doppler Effect Reading: AG Notes on Mechanical Waves, Superposition and Standing Waves (from website); Y&F, Vol. 1, Chapter 16; Y&F Vol. 2, Section 37.6 Assignment: Due in lecture on Tuesday, February 24. Please turn in this sheet stapled to the top of your work. Physics Problems: 1. How important is the phase? Let's consider the square wave from problem 7 of Assignment 4, which can be expressed as a Fourier series f(t) = A [sin ( 1 t) + 1/3 sin (3 1 t) + 1/5 sin (5 1 t) +1/7 sin (7 1 t). . .]. (a) Consider a system with a response function i e 0 ( / ) () G . If you drive this system using your square wave, the amplitudes of the Fourier components of the response will be the same as of the drive, but the phases will be different. How does this affect the waveform of the response? Modifying your program from Assignment 4, problem 7, evaluate the output waveform for 10 / 0.1, 0.2, 0.3, 0.5, 1.0 . (If you want to keep things simple, just evaluate the sum of the first three nonzero terms in the Fourier series - don't bother with all the other terms.) Does the phase shift introduced by G - which varies linearly with frequency - affect the shape of the waveform? (b) Repeat (a) with 2 0 ( / ) . Do the phase shifts affect the output waveform in this case? Can you explain why or why not? (c) Some speaker manufacturers brag that their models have a linear phase response as a function of frequency. Why might this be desirable? (In practice, the human auditory system is insensitive to the phase of the Fourier components of a sound, except under special conditions. For a discussion, see http://www.silcom.com/~aludwig/Phase_audibility.htm and http://www.ocf.berkeley.edu/~ashon/audio/phase/phaseaud2.htm 2. Wave interference. Two loudspeakers, A
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Assignment_5_09 - Physics 2214 Assignment 5 Concepts:...

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