in this presentation you will: explore the nature of resonance

Resonance

In this presentation you will: explore the nature of resonance explore how musical instruments produce sound

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Resonance

In this presentation, you will look at the way strings and air in pipes vibrate to produce musical sounds.

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You will also explore resonance of solid objects.

Resonance

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Sound and Music

Sound is caused by vibration.

A musical instrument creates sounds that we call music. Each sound is of a different frequency.

For example, the A above middle C has a frequency of 440 Hz.

We call particular frequencies ‘notes’, when the frequencies conform to a pattern on a musical scale.

It can be caused by someone speaking, in which case it is the vocal chords that vibrate, or by something mechanical like a loudspeaker vibrating.

Resonance

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Musical Instruments

Musical instruments have two different methods for making sounds: they use vibrating strings or vibrating columns of air.

Typical stringed instruments include: violin, guitar, double bass and piano.

Typical instruments that use vibrating columns of air include: trumpet, clarinet, bassoon and saxophone.

Resonance

1

What causes a trumpet to emit sound when it is correctly played?

Question

A) The metal of the trumpet vibrates

B) The person playing it vibrates

C) The air inside the trumpet vibrates

D) The strings inside the trumpet vibrate

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Same Note, Different Sounds

If all the instruments played the same note they wouldn’t sound the same!

Even though the note is the same frequency, it sounds different.

In order to answer this question we need to look at how a string or column of air can vibrate.

You would be able to tell which note was played on a piano and which on a trumpet.

We call this the quality or timbre of the note. What is causing this difference?

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Vibrating Strings

Its simplest vibration occurs when the center of the string has the maximum displacement.

A vibrating string must be fixed at both ends.

The wave is effectively reflected back along itself. We call this a standing wave.

The string length is equivalent to half a wavelength and the frequency it emits is called either the fundamental frequency, natural frequency or first harmonic.

Resonance

2

What is a wave that is reflected back on itself called?

Question

A) A walking wave

B) A standing wave

C) A refractive wave

D) A running wave

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3

What fraction of a wavelength is the length of a string vibrating at its first harmonic?

Question

A) One-quarter of a wavelength

B) Half a wavelength

C) Three-quarters of a wavelength

D) One full wavelength

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Vibrating Strings

There are other ways that a string can vibrate.

The next position will occur when the center of the string does not move at all.

In this case, the string length is equivalent to one wavelength, so it will emit a note that is twice the fundamental frequency. We call this note the second harmonic.

The point where a string does not move is called a node. The point where it moves to its maximum is called an antinode.

Nodes

Antinodes

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4

What is the term used to describe the non-moving part of a standing wave?

Question

A) Fundamental frequency

B) Antinode

C) Second harmonic

D) Node

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Vibrating Strings

A range of possible harmonics is shown in the diagram.

Each harmonic has an increase of half a wavelength over the previous harmonic.

When a note is played, it is not just the fundamental frequency that is heard.

λ/2

λ

3λ/2A mix of harmonics will also be present. It is the ratio of this mix that determines the sound.

Resonance

How many antinodes are there in the third harmonic of a vibrating string?

Enter your answer and press Send.

Question 5

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Open and Closed Pipes

There are two different types of vibrating air columns.

These are open columns and closed columns. A closed column occurs in a pipe that is closed at one end.

At the open end of a pipe there is always an antinode. At the closed end of a pipe there is always a node.

The diagrams show the fundamental frequency for both a closed pipe and an open pipe.

Open column

Closed column

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Harmonics of Open Pipes

If we extend the pattern for open pipes we see a similar pattern of harmonics as we did with strings.

Each successive harmonic is one half a wavelength greater.

A standing wave in an open pipe is similar to one in a string.

The only difference is that standing waves in open pipes always have antinodes at the ends of the pipe, rather than nodes.

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Harmonics of Closed Pipes

A closed pipe is slightly different. Because there is a node at one end and an antinode at the other, the pattern is different.

The fundamental frequency is only a quarter of a wavelength.

The next harmonic occurs at three quarters of a wavelength. This is the third harmonic – the even number harmonics do not exist for closed pipes.

1 λ4

3 λ4

5 λ4

Resonance

6

A closed column pipe has an antinode at both ends. Is this true or false?

Answer True or False.

Question

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Resonance in Solid Objects

Just as an air column or a string has a natural frequency of oscillation or vibration, so do solid objects.

If an object is ‘excited’, it will vibrate at its natural frequency. Think of a child’s swing.

If you push the child on the swing (exciting the swing), it always swings at the same frequency.

It is very difficult, if not impossible, to make it swing at the second harmonic frequency.

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Resonance of Solid Objects

During each oscillation, the swing will lose some energy.

When you apply repetitive pushes at the same frequency as the natural frequency, you are compensating for this loss of energy.

If the amount of force (and therefore energy) that you apply is greater than the energy losses, then the swing will oscillate at higher and higher amplitude.

That is resonance.

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Resonance of Solid Objects

The swing we were looking at could go too high, putting the child at risk.

Resonance can be dangerous.

Other structures could vibrate themselves apart.

If you search the internet, you will probably find video footage of the Tacoma Narrows Bridge oscillating at its natural frequency until it disintegrates.

The excitation was caused by a strong wind gusting at the natural frequency of the bridge.

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Resonance of Solid Objects

Bridges are particularly susceptible to forced vibrations.

Consider an army of soldiers marching in step across a wooden bridge.

To avoid the risk of the bridge oscillating and possibly collapsing, soldiers are given the command to “break step”.

If the marching rate is exactly, or nearly, equal to the natural frequency of the bridge, then the whole structure could start vibrating.

The individuals then walk across normally and start marching again on the other side.

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Resonance of Solid Objects

These may include: the mass, the speed of the vibration in the object, and the elasticity of the material from which it is constructed.

The resonance of a solid object depends upon a whole range of factors.

Precise equations are difficult and beyond the scope of this presentation.

Resonance

7

"Solid objects have a natural frequency of vibration." Is this statement true or false?

Answer True or False.

Question

Resonance

Summary

After completing this presentation you should be able to:

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show knowledge and understanding of resonance

show knowledge and understanding of resonance in strings and pipes