summary sinusoidal wave on a string wavefunction
TRANSCRIPT
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Summary
Sinusoidal wave on a string
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Wavefunction
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Superposition of Waves
For more than one wave on a string, add the wavefunctions together. This is called the superposition, which means to add.
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Reflection at a boundary
When a wave reflects from a fixed boundary, the reflected wave is inverted (i.e. upside down or the negative of the wavefunction).
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Standing Wave
A standing wave is produced by two waves of the same amplitude, frequency, and phase traveling in opposite directions.
A node is a point on the string that oscillates with zero amplitude.
An antinode is a point on the string that oscillates with maximum amplitude.
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Standing waves with nodes at both ends
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Harmonics
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Speed of a wave on a string
For a standing wave on a string, the speed has to be just right.
The speed of any wave is
The speed of a wave on a string depends on the tension and the linear density of the string
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Guitar String
A guitar string mostly vibrates with the fundamental standing wave (and a few harmonics added in with it; this is called superposition). The frequency of the fundamental depends on L, T, and the linear density of the string.
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Poll
How many nodes and antinodes does this standing wave have?
1. 5 nodes, 4 antinodes
2. 4 nodes, 4 antinodes
3. 5 nodes, 5 antinodes
4. 3 nodes, 2 antinodes
5. 6 nodes, 5 antinodes
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Poll
If the length of the string is 2 m, what is the wavelength of the wave?
1. 0.5 m
2. 1.0 m
3. 1.5 m
4. 2.0 m
5. 4.0 m
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Poll
What harmonic (N) is a standing wave with this shape?
1. 2
2. 3
3. 4
4. 5
5. 6
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Poll
If you decrease the length of a guitar string by pressing on one of the frets with your finger, the frequency will
1. Increase
2. Decrease
3. Remain constant
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Poll
If you decrease the tension in the string by turning the key on the neck of the guitar, then the frequency will
1. Increase
2. Decrease
3. Remain constant
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Poll
The B string has a lower linear density than the A string on a six-string guitar. For which string, does the fundamental standing wave have the lowest frequency?
1. B string
2. A string
3. Neither, they vibrate with the same frequency.
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Longitudinal Standing Wave
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Displacement node is a pressure antinode
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Boundary conditions: closed pipe
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Boundary conditions: open pipe
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Pipe closed at one end and open at the other end
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Pipe open at both ends
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Poll
At the open end of a pipe, the is a node and the is an antinode.
1. pressure, displacement
2. displacement, pressure
3. None of the above; both displacement and pressure are nodes
4. None of the above; both displacement and pressure are antinodes.
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Poll
At the closed end of a pipe, the is a node and the is an antinode.
1. pressure, displacement
2. displacement, pressure
3. None of the above; both displacement and pressure are nodes
4. None of the above; both displacement and pressure are antinodes.
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Poll
What is the harmonic (N) for the standing wave shown below.
1. 3
2. 4
3. 5
4. 6
5. 7
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Poll
What is the harmonic (N) for the standing wave shown below.
1. 1
2. 3
3. 5
4. 7
5. 9