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
v
f
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
v
s
⋅
.
b)
Solve this equation to find an expression for the wavelength
λ
.
/
v
f
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
.
1
2
T
f
v
π
λ
ω
=
=
=
f)
What is the relationship between
ω
and
f
?
2
f
ω
π
=
⋅
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
π
λ
=
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
λ
=
- the phase velocity remains unchanged (it’s a property of the medium in which the wave
propagates),
λ
also doubles.

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