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Standing Waves Handout
Standing Waves Open Tubes
AP Physics
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Standing Waves
– waves produced when
two waves with the same frequency and wavelength travel in opposite directions in the same medium (Musical
instruments)
I. Standing Waves - Both Ends Closed
A. Nodes and Antinodes, etc
Ex)
a)
Mark the nodes with a dot.
How many are there?
5
b)
Mark the ANTInodes with a large X
How many are there?
4
c)
How many wavelengths do you see above?
2
d)
Maximum CONstructive interference occurs at the
Antinode
e)
Maximum CONstructive interference occurs at the
Nodes
B. 1st
, 2nd , 3rd ….. Harmonic
Closed End Standing
waves always have a node at each end****
1. Fundamental or
First Harmonic (N.A.N.)
Draw the first
harmonic.
How many wavelengths?
Juan Aguirregabiria and lookang
(Standing Wave length) L = 1/2 wavelength
So l = 2L
(Twice the length of the whole standing wave)
2. Second Harmonic
(N. A. N. A. N.)
Draw
the second harmonic.
How many wavelengths?
L = 4/4 or 1 wavelength
3. Third Harmonic
(N. A. N. A. N. A. N.)
Draw
the third harmonic.
How many wavelengths?
L = 6/4 or 3/2 wavelengths
So l = 2/3L (or
2/3 the length of the standing wave)
4. 4th Harmonic
(N. A. N. A. N. A. N. A. N.)
Draw
the fourth harmonic.
How many wavelengths?
L = 8/4 or 2l
so l = L/2 (or
1/2 the length of the standing wave)
5. 5th Harmonic (N.A.N.A.N.A.N.A.N.A.N.)
Draw
the fifth harmonic.
How many wavelengths?
L = 10/4 or 5/2 wavelengths
so l = (2/5)L (or
2/5 the length of the standing wave)
Review - Standing Wave - Both Ends
|
L = 1/2
l
|
Fundamental f |
L = 1
l
|
2x Fundamental |
L = 3/2
l
|
3x Fundamental |
L = 2
l
|
4x Fundamental |
L = 5/2
l
|
5x Fundamental |
L = 3
l
|
6x Fundamental |
L =7/2
l
|
7x Fundamental |
3 antinodes
4
nodes
|
a) Nodes: Max Destructive
Interference
b) Antinodes: Max. Constructive
Interference
|
L = distance between walls
String closed at both ends
or Open Pipe
Both ends
L = (nl/2)
n = 1,2,3 ....
since v = fl
then
fn = n[v/2L]
n = 1,2,3 ....
Each frequency is a multiple of the fundamental frequency
D. Open at Both Ends
1/2, 2/2, 3/2, 4/2
L = n(1/2)λ
showmethphysics.com
showmethphysics.com
Giancoli p. 348) 34, 36
34) Closed
88 Hz is fundamental
36) Open Pipe Fundamental 40 Hz, both are even number multiples of
40 not odd multiple of 20
f = v/2L = 40 Hz = (340 m/s)/2L L = 4.3 m
Review Book p. 302) 10.
Open at one end
n = 1 fundamental
f = v/4L
= 340 m/s/(4 x .17)
= 500 Hz
p. 303) 10
Beats - Rhythmic interference between
two semi identical frequency sources
Beat Frequency = |f1
- f2|
Standing Wave
II
Enrichment
Standing
Waves/Sound/Chladni
Berkeley Univ.
Standing Waves - Wake Forest .U.
(Chladni Disk)
Water Drop in Zero g
School blocks YouTube?
Download the file below.
Large_Free_Sphere_of_Water.mov
Standing Waves
HyperPhysics (offsite)
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