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1
Waves
1.2
•Transverse waves on a string
– speed
– power
• Intensity
• Wave equation
Speed of the transverse wave on a
string.
F
F
V ->
x
∆
m
∆
m
x
∆
µ=
∆
mass density
F
v
=
µ
speed of transverse wave on a
string depends on the tension on
the string and the mass density
u
Force in the y direction depends on
θ
net force
Derive the wave speed from the mass element at the
peak of the pulse.
b)
In coordinate system
moving with the pulse. The
string is moving.
a) Pulse moving along the string
c) Apply Newton’s law to the
mass at the top of the pulse. For
small angles
θ
net
2
x
F
2F sin
2F
2F
R
v
ma
2
x
R
∆
=θ
≈
θ
=
=µ
∆
x
∆
x
∆
F
v
=
µ
F
F
L
m
=
µ
F
v
=
µ
dimensional check
22
2
Nk
g
m
/
sm
==
kg/m
kg/m
s
⋅
=
m
s
Increasing tension increases speed
Increasing mass/length decreases speed.
A 3.1 kg mass hangs from a 2.7 m long
string whose total mass is 0.62 g. What is
the speed of the transverse wave on the
string?

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