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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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 Spring '07
 GIAMBATTISTA,A
 Physics

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