y
1
=
y
m
sin(
kx
–
ω
t
),
y
2
=
y
m
sin(
kx
+
t
).
The amplitude
y
m
is half the maximum displacement of the standing wave, or 5.0
×
10
–3
m.
(b) Since the standing wave has three loops, the string is three halfwavelengths long:
L
=
3
λ
/2, or
λ
= 2
L
/3. With
L
= 3.0m,
λ
= 2.0 m. The angular wave number is
k
= 2
π
/
λ
= 2
π
/(2.0 m) = 3.1 m
–1
.
(c) If
v
is the wave speed, then the frequency is
()
()
3 100m s
3
50 Hz.
22
3
.
0
m
vv
f
L
== =
=
λ
The angular frequency is the same as that of the standing wave, or
ω
= 2
π
f
π
(50 Hz) = 314 rad/s.
(d) The two waves are
()
(
)
(
)
31
1
1
5.0 10 m sin
3.14m
314s
y
xt
−−
−
ªº
=×
−
¬¼
and
()
(
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This note was uploaded on 04/16/2011 for the course PHYSICS 191262 taught by Professor Najafzadeh during the Spring '09 term at The Petroleum Institute.
 Spring '09
 NAJAFZADEH
 mechanics

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