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Resonance: More Practice. Resonance occurs when the frequency of the forcing vibration is _________ the natural frequency of the object. A. less than C. greater than B. equal to D. both B and C. Resonance: More Practice.

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Resonance more practice
Resonance: More Practice

Resonance occurs when the frequency of the forcing vibration is _________ the natural frequency of the object.

A. less than C. greater than

B. equal to D. both B and C


Resonance more practice1
Resonance: More Practice

Resonance occurs when the frequency of the forcing vibration is _________ the natural frequency of the object.

A. less than C. greater than

*B. equal to D. both B and C



Resonance in open air columns student success criteria
Resonance in Open Air Columns:Student Success Criteria

I can identify the properties of standing waves, predict the conditions required to produce resonance in vibrating objects and/or in air columns, and explain how resonance is used in a variety of situations.

I can analyze how properties of mechanical waves and sound influence the design of structures and technological devices.


Musical air columns
Musical Air Columns

Many musical instruments consist of an air column enclosed inside of a hollow tube.


Musical air columns1
Musical Air Columns

Many musical instruments consist of an air column enclosed inside of a hollow tube.

If an end of the tube is uncovered such that the air at the end of the tube can freely vibrate when a sound wave reaches it, then that end is referred to as an open end.


Musical air columns2
Musical Air Columns

Many musical instruments consist of an air column enclosed inside of a hollow tube.

If an end of the tube is uncovered such that the air at the end of the tube can freely vibrate when a sound wave reaches it, then that end is referred to as an open end.

If both ends of the tube are uncovered or open, the instrument is said to contain an open-end air column.


Resonance in air columns
Resonance in Air Columns

The air in an air column can resonate at particular frequencies and a standing wave pattern can be produced.


Resonance in air columns1
Resonance in Air Columns

The air in an air column can resonate at particular frequencies and a standing wave pattern can be produced.

A closed end in a column of air is like the fixed end on a vibrating string because the air is not free to move and the closed end will therefore be a node of the standing wave.

Conversely, the open end of an air column will be an antinode.


Resonance in open end air columns
Resonance in Open-End Air Columns

The first harmonic (also called the fundamental frequency) of an open-end air column would therefore look like:


Resonance in open end air columns1
Resonance in Open-End Air Columns

The first harmonic (also called the fundamental frequency) of an open-end air column would therefore look like:


Resonance in open end air columns2
Resonance in Open-End Air Columns

The first harmonic (also called the fundamental frequency) of an open-end air column would therefore look like:

Note that the wavelength l is twice the length L of the air column:

l = 2L or L = ½l


Higher harmonics
Higher Harmonics

The second and third harmonics (sometimes called the first and second overtones) of an open-end air column would look like:


Higher harmonics1
Higher Harmonics

The second and third harmonics (sometimes called the first and second overtones) of an open-end air column would look like:


Higher harmonics2
Higher Harmonics

The second and third harmonics (sometimes called the first and second overtones) of an open-end air column would look like:


Higher harmonics3
Higher Harmonics

The second and third harmonics (sometimes called the first and second overtones) of an open-end air column would look like:

Question: What is the ratio of the frequency of the second harmonic to the frequency of the first harmonic?


Higher harmonics4
Higher Harmonics

The second and third harmonics (sometimes called the first and second overtones) of an open-end air column would look like:

Question: What is the ratio of the frequency of the second harmonic to the frequency of the first harmonic?

Answer: 2:1 (half the wavelength = twice the frequency)


Open end air columns example
Open-End Air Columns Example

Determine the length of an open-end air column required to produce a fundamental frequency (1st harmonic) of 480 Hz.


Open end air columns example1
Open-End Air Columns Example

Determine the length of an open-end air column required to produce a fundamental frequency (1st harmonic) of 480 Hz. The speed of sound in air is 340 m/s.


Open end air columns example2
Open-End Air Columns Example

Determine the length of an open-end air column required to produce a fundamental frequency (1st harmonic) of 480 Hz. The speed of sound in air is 340 m/s.


Open end air columns example3
Open-End Air Columns Example

Determine the length of an open-end air column required to produce a fundamental frequency (1st harmonic) of 480 Hz. The speed of sound in air is 340 m/s.


Open end air columns example4
Open-End Air Columns Example

Determine the length of an open-end air column required to produce a fundamental frequency (1st harmonic) of 480 Hz. The speed of sound in air is 340 m/s.


Open end air columns example5
Open-End Air Columns Example

Determine the length of an open-end air column required to produce a fundamental frequency (1st harmonic) of 480 Hz. The speed of sound in air is 340 m/s.


More practice
More Practice

Your Task:

To cut open air columns to lengths that will have, as their first harmonic, frequencies that are small, whole-number ratios of a fundamental frequency (and will therefore sound musical when played together).

Handout: The Physics of Music


More practice1
More Practice

Sound Waves Problem Set


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