Resonance: More Practice Resonance occurs when the frequency of the forcing vibration is _________...

Resonance: More Resonance: More PracticePractice

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

A. less thanA. less than C. greater thanC. greater than

B. equal toB. equal to D. both B and CD. both B and C

Resonance: More Resonance: More PracticePractice

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

A. less thanA. less than C. greater thanC. greater than

**B. equal toB. equal to D. both B and CD. both B and C

Resonance in Resonance in Open Air Open Air ColumnsColumns

3U Physics3U Physics

Resonance in Open Air Resonance in Open Air Columns:Columns:

Student Success CriteriaStudent Success Criteria I can identify the properties of standing I can identify the properties of standing

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

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

Musical Air ColumnsMusical Air Columns

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


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

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


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

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

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

Resonance in Air Resonance in Air ColumnsColumns

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

Resonance in Air Resonance in Air ColumnsColumns

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

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

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

Resonance in Open-End Air Resonance in Open-End Air ColumnsColumns

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

Resonance in Open-End Air Resonance in Open-End Air ColumnsColumns

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

Note that the wavelength Note that the wavelength is is twice the length twice the length LL of the air of the air column:column:

= 2= 2LL or or LL = ½ = ½

Higher HarmonicsHigher Harmonics

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


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

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


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

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

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

Open-End Air Columns Open-End Air Columns ExampleExample

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


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



?

?

340

480

L

v

Hzf

sm



?

?

340

480

L

v

Hzf

sm

cmor

mmL

mHz

f

vfv

sm

35

35.0708.0

708.0480

340

21

21

More PracticeMore Practice

Your Task: Your Task:

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

Handout: The Physics of MusicHandout: The Physics of Music

More PracticeMore Practice Sound Waves Problem SetSound Waves Problem Set

Resonance: More Practice Resonance occurs when the frequency of the forcing vibration is _________...

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