Waves
Thursday, November 14, 13
Instantaneous Velocity
Aside from the velocity of the wave, we can also ask what is the
velocity of the individual components that make up the medium. In
the case of transverse waves, they just move up and down. But, at
any given moment each of them have some velocity.
Thursday, November 14, 13
Instantaneous Velocity
Aside from the velocity of the wave, we can also ask what is the
velocity of the individual components that make up the medium. In
the case of transverse waves, they just move up and down. But, at
any given moment each of them have some velocity.
If the position function is
What is the velocity function?
Thursday, November 14, 13
Instantaneous Velocity
Aside from the velocity of the wave, we can also ask what is the
velocity of the individual components that make up the medium. In
the case of transverse waves, they just move up and down. But, at
any given moment each of them have some velocity.
If the position function is
What is the velocity function?
dy(x, t)
v(x, t) =
=
dt
Thursday, November 14, 13
A! cos (kx
!t + )
Thursday, November 14, 13
Thursday, November 14, 13
Speed of Waves
What controls the speed of a wave?
Thursday, November 14, 13
Speed of Waves
What controls the speed of a wave?
The properties of the medium control the speed of the wave.
One very important example is that of strings, the speed is
Thursday, November 14, 13
Speed of Waves
What controls the speed of a wave?
The properties of the medium control the speed of the wave.
One very important example is that of strings, the speed is
Thursday, November 14, 13
Speed of Waves
What controls the speed of a wave?
The properties of the medium control the speed of the wave.
One very important example is that of strings, the speed is
string tension
Thursday, November 14, 13
Speed of Waves
What controls the speed of a wave?
The properties of the medium control the speed of the wave.
One very important example is that of strings, the speed is
string tension
linear mass density
Thursday, November 14, 13
Speed of Waves
What controls the speed of a wave?
The properties of the medium control the speed of the wave.
One very important example is that of strings, the speed is
string tension
linear mass density
The linear mass density of a string is the amount of mass per unit
length.
Thursday, November 14, 13
Thursday, November 14, 13
Thursday, November 14, 13
If the mass density is 2700kg/m^3, then the linear mass density is
2
2
µ = (⇡r )⇢ = (⇡0.0025 ) ⇥ 2700 = 0.0449 kg/m
Thursday, November 14, 13
If the mass density is 2700kg/m^3, then the linear mass density is
2
2
µ = (⇡r )⇢ = (⇡0.0025 ) ⇥ 2700 = 0.0449 kg/m
Thursday, November 14, 13
If the mass density is 2700kg/m^3, then the linear mass density is
2
2
µ = (⇡r )⇢ = (⇡0.0025 ) ⇥ 2700 = 0.0449 kg/m
Thursday, November 14, 13
If the mass density is 2700kg/m^3, then the linear mass density is
2
2
µ = (⇡r )⇢ = (⇡0.0025 ) ⇥ 2700 = 0.0449 kg/m
Then the speed of the wave in the string is simply
s
r
T
58.0
vw =
=
= 36.0 m/s
µ
0.0449
Thursday, November 14, 13
Strength of a Piano
Approximately, what is the force exerted on the body of a piano by
the strings?
A piano has about 100 strings (88 to be precise, but that doesn’t matter) each weighs about 5 g.
The waves on the string move at about 300 m/s.
a)
b)
c)
d)
e)
150 N
1,500 N
45,000 N
500,000 N
3,000,000 N
Thursday, November 14, 13
Strength of a Piano
Approximately, what is the force exerted on the body of a piano by
the strings?
A piano has about 100 strings (88 to be precise, but that doesn’t matter) each weighs about 5 g.
The waves on the string move at about 300 m/s.
a)
b)
c)
d)
e)
150 N
1,500 N
45,000 N
500,000 N
3,000,000 N
Thursday, November 14, 13