PHY138 – Waves, Lecture 5
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Today’s overview
Standing Waves
Harmonics
Beats
Reading Assignment
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Please read the following from Serway
and Jewett before class on Wednesday:
Chapter 24, Sections 24.3, 24.7 and 24.9,
and Context 7, pg. 896-897. Only the
concepts of 24.3 are important, not the
equations.
A Web-CT quiz is due Wednesday
morning, which tests your basic familiarity
with Chapter 24 and 25 assigned reading.
Written Homework
The assignment due on Monday,
November 29 at 5:00 PM is now
available online. It includes problems
from Chapter 14 and one from
Chapter 24.
Some Announcements:
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Calculator hint: “Exp” key stands for “times
10 to the power”. ie, to type 10-3, type 1
Exp (-) 3, not 10 Exp (-) 3. (the latter will be
interpreted as 10×10-3=10-2 !)
Friday Tutorials Representative Assembly:
this Friday, noon-1:00PM, MP713.
New medical technique to help stroke
victims: ultrasound. Sound waves can
dissolve brain blockages. (J.P. Polak, New
England Journal of Medicine v.351 n.21,
pg. 2154, Nov. 18 2004)
Doppler Effect sign conventions
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Serway and Jewett say “A
positive value is used for
 v  vO
motion of the observer or f   f 
 v  vS
the source toward the
other.”
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Other texts say: “A positive
value is used for motion to
 v  vO
the right, where the source f   f 
v

v
S

is located to the right of the
observer.”
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Some results of superposition
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14.2: Two waves, same frequency, same
direction, diffferent phase:
Interference
14.3-5: Two waves, same frequency,
opposite direction:
Standing Wave
14.6 Two waves, same direction, slightly
different frequency:
Beats
Harmonic frequencies
Transverse standing wave on a string
clamped at both ends: there are nodes in
displacement at both ends.
v
fn  n
2L
(n  1,2,3,...)
Standing sound wave in a tube open at both
ends: there are nodes in pressure both ends.
v
fn  n
2L
(n  1,2,3,...)
Quiz 1
a
b
c
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A string is clamped at both ends and plucked so
creates a standing wave. Define upward motion to
be positive velocities. When the string is in position
b, the instantaneous velocity of points along the
string
1. is zero everywhere
2. is positive everywhere
3. is negative everywhere
4. depends on location
Quiz 2
a
b
c
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A string is clamped at both ends and plucked so
creates a standing wave. Define upward motion to
be positive velocities. When the string is in position
c, the instantaneous velocity of points along the
string
1. is zero everywhere
2. is positive everywhere
3. is negative everywhere
4. depends on location
Harmonic frequencies
Standing sound wave in a tube closed at one
end: there is a node in pressure at the open
end, and an anti-node at the closed end.
v
fn  n
4L
(n  1,3,5,...)
Beat frequency
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The beat frequency is the difference of
the frequencies of the two waves that are
being added:
f b  f1  f 2