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Resonance: More Practice

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

A. less thanC. greater than

B. equal toD. both B and C

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

A. less thanC. greater than

*B. equal toD. both B and C

Resonance in Open Air Columns

3U Physics

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.

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

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.

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.

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

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.

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

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

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

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

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

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?

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)

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

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.

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.

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.

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

Sound Waves Problem Set