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1
HW 6 Solutions
Wave Notation
a)
Traveling waves propagate with a fixed speed usually denoted as
v
(but sometimes
c
). The
velocity
v
is the
phase
velocity.
The waves are called
periodic
if their waveform repeats every
time interval
T
.
The fundamental relationship among frequency, wavelength, and velocity is
vf
λ
=
⋅
.
This relationship may be visualized as follows: In 1 s,
( )
1
f
s
⋅
cycles of the wave move past an
observer. In this same second the wavetrain moves a distance
( )
1
vs
⋅
.
b)
Solve this equation to find an expression for the wavelength
λ
.
/
=
c)
If the velocity of the wave remains constant, then as the frequency of the wave is increased,
the wavelength
decreases
.
d)
The difference between the frequency
f
and the frequency
ω
is that
f
is measured in cycles per
second or hertz (abbreviated Hz) whereas the units for
ω
are radians per second.
e)
Find an expression for the period of a wave
T
in terms of other kinematic variables.
Express
your answer in terms of any of
f
,
v
,
ω
, and simple constants such as
π
.
12
T
f
v
π
ω
=
==
f)
What is the relationship between
ω
and
f
?
2
f
=
⋅
g)
What is the simplest relationship between the angular wavenumber
k
and just one of the other
kinematic variables?
Express your answer using only one of the other kinematic variables plus
constants like
π
.
2
k
=
Vibrating String
An oscillator creates periodic waves on a stretched string.
a)
If the period of the oscillator doubles, what happens to the wavelength and wave speed?
T
v
=
 the phase velocity remains unchanged (it’s a property of the medium in which the wave
propagates),
λ
also doubles.
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View Full Document b)
If the
Both wav
speed rem
varied on
the wave
Test You
the w
point
the w
point
the w
the w
point
the w
point
none
not e
A onedi
determin
that are
waveleng
apart osc
The poin
Q are ½ c
e amplitude
velength and
mains uncha
nly by chang
es.
ur Understa
wave has the
ts are 1/4 cy
wave has the
ts are in pha
wave has a d
wave has the
ts are 1/2 cy
wave has the
ts are 1/8 cy
e of the abov
enough infor
imensional s
ne the phase
1, 2, 3, .
..
gths apart os
cillate ¼ cycl
nts P and Q a
cycle out of
of the oscill
d wave spee
anged, unless
ging the freq
anding 15.2:
same ampli
ycle out of ph
same ampli
ase
ifferent amp
same ampli
ycle out of ph
same ampli
ycle out of ph
ve
rmation is gi
sinusoidal w
relationship
. wavelengt
scillate ½ cy
le out of pha
are 0.375 m a
phase.
lator doubles
ed are uncha
s the propert
quency, or a
: Periodic W
itude at poin
hase
itude at poin
plitude at poi
itude at poin
hase
itude at poin
hase
ven to decid
wave has the
between th
hs apart os
cle out of ph
ase. In this si
apart, which
2
s, what happ
anged.
Whe
ties of the str
alternatively
Waves
Cons
tube
sinus
8
×
10
wave
statem
nt P as at poin
nt P as at poin
int P than at
nt P as at poin
nt P as at poin
de
e same amp
e oscillation
scillate in p
hase; and po
ituation the w
h is 1.50 wav
pens to the w
en waves tra
ring are chan
the period,
sider two po
as shown. T
soidal longi
0
2
Hz is pro
e speed in th
ment is corre
nt Q, but the
nt Q, and the
point Q
nt Q, but the
nt Q, but the
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This note was uploaded on 09/15/2011 for the course APHY 124 taught by Professor Eins during the Spring '11 term at SUNY Albany.
 Spring '11
 EIns

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