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5.1 Standing waves

You learned earlier that when a musician plays a note on an instrument, they supply it with energy that causes the primary vibrator to oscillate at certain specific frequencies. In Section 5 we are going to look at what determines these specific frequencies for some of the primary vibrators found in different instruments.

In Unit TA212_1 Sound for music technology: an introduction, we talk about travelling waves: that is, waves that propagate outwards away from their sourc
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8.3 Summary

A fundamental musical and acoustical relationship is the octave. Pitches that are one or more octaves apart are heard musically as different instances of the same sound. A one-octave increase in pitch corresponds to a doubling of frequency.

For musical purposes, a pitch range of one octave is divided into discrete steps, known as scales, the individual pitches of which are given letter names (A, A

8.2 Octave pitch and frequency increments

Because a doubling of frequency corresponds to an octave increase of pitch, it follows that there is no constant increment of frequency that always corresponds to a one-octave increment of pitch. That is to say, there is no fixed amount by which a frequency can be augmented that will always produce a one-octave pitch rise.

For instance, starting at the pitch A4 with a frequency of 440 Hz, we need to augment the frequency by 440 Hz to get the pitch one octave above (880 Hz). B
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8.1 The octave sound

One feature of pitch that seems to be universal to all cultures is that for musical purposes the pitch range is divided into discrete steps: for instance, the notes of a scale. This is not to say that musicians rigidly adhere to those steps when they play, but the existence of such steps is fundamental to the way music is conceived and organised. Different cultures have different ways of defining the steps in their scale of pitches, but nearly all cultures take the octave as their starting po
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6.3 Root-mean-square amplitude

One drawback of the amplitude as I have defined it is that although it allows the relative sizes of sine waves to be compared, it does not give a good idea of what a sine wave can deliver in absolute terms. For instance, a sine wave with an amplitude of 10 volts has twice the amplitude of one with an amplitude of 5 volts. But is a power source that delivers a sine wave with an amplitude of 10 volts as powerful as, say, a 10 volt battery? Could you use it to drive a bulb and get the same illum
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6.1 Defining amplitude

Another important property of a sine wave we need to be able to specify is its amplitude. In essence, the amplitude of a sine wave is its size. Unfortunately there are various ways of defining what is meant by the size of a sine wave, and you are likely to come across many of them in material you look at outside this unit. Before I explain what our definition is, it will help matters if we look at what is meant by the average value of a sine wave.

Figure 16 shows a sinusoidally a
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16.5 Where does the systems practitioner stand in relation to a system of interest?

Systems practice may be carried out individually or as part of a team. In doing action research – which is a form of managing – an important question is: On us or with us? (Figure 47). This question seems pertinent to the process that led to the establishment of the Child Support
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10 Part 2: 6 Review

In Part 2 of this unit, you have undertaken a major piece of work. In encountering the case study you were engaging with a set of events, issues, actors, stakeholders and intentions that was, by any standards, complex. In addition, you brought your own complexity to it, your own stakeholdings and understandings, your own reactions and feelings.

You used systems diagrams to structure the complexity you encountered in the case study. That then structured and clarified the situation in way
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Introduction

This course aims to develop skills of thinking systematically and creatively about issues of complexity. It enables you to appreciate and manage these issues in ways that can lead to improvement. It adopts the most recent and innovative advances in systems thinking and applies them to topical areas of concern. It is designed to help build your capacity to manage complexity and to develop a deep understanding of contemporary systems thinking. It may be helpful to study OpenLearn units T551_1 <
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18.5 Government regulations and legislation

You saw earlier in Part 2 how governments can stimulate invention by providing incentives for manufacturers to develop new products. The example given was in the field of alternative fuel vehicles in the USA and Europe. As well as influencing the development of innovations, government legislation and regulations can also affect diffusion by creating conditions that encourage consumers to buy and use particular innovations.

In the UK the government has introduced a mixture of incentives
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17.1 Getting the technology to work

A fundamental requirement for successful innovation is that the invention must work. It mustn't violate any scientific laws and it must be capable of being transformed into a working prototype. In addition to getting the technology to work it must be designed to be easy to use and reliable, attractive, safe and environmentally friendly. It must also be designed so it's capable of being manufactured on a scale that makes it economic to produce and to buy.

Sometimes an idea for an inventi
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15 Part 2: 6 Key points of Part 2

  • Individuals are motivated to invent by one or more factors: curiosity; constructive discontent about a product; a desire to help others; a desire to make money.

  • Organisations invent for a number of reasons: business strategy; the need to improve existing products and processes; new materials become available, as do technologies and manufacturing processes; government policy, legislation and regulations.

  • The process of invention
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13 Part 2: 4 Preparing for innovation

Many inventors have said that having the idea for an invention is the easy part. This is often demonstrated by the frequency of examples of simultaneous invention. At one exhibition of inventions I attended there were three separate portable ladders to escape from fires, two systems for using rainwater to flush toilets, two types of portable vehicle wheel clamp, and two methods of reducing red-eye in flash photography. In most cases of technological innovation only one of the competing techno
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4.7 Has telephone design changed over time?

As you can see from Figure 5 the design of the telephone has changed considerably over its lifetime, reflecting the improvements in technology, materials, components and manufacturing processes. Figures 1(a) to (f) show some of the early progress. Author(s): The Open University

1.3.2 Systems diagrams and diagrams helpful for systems work

Diagrams are used extensively in systems thinking and practice. All of those types included in the animated tutorial, as well as other types not covered there, can or have been used in systems studies. As mentioned at the beginning of the unit the use of diagrams is very personal. For instance I find it helpful to group diagrams into three sorts depending on when they are to be used:

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1.2.5 Thinking through diagrams

One of the features that characterises complex situations is the interconnectedness of the components within them. Understanding such situations can defeat our descriptive abilities. Words alone either confuse still further or misrepresent the situation altogether. For this reason, diagrams are a characteristic feature of systems approaches to understanding complex situations. Diagrams allow the relationships between parts of the situation to be seen at the same time as the parts themselves.
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1.1.2 Diagrams as models

Diagrams come in many forms and uses, but for systems thinking and practice it is useful to think of them as models (meaning ‘representations of reality’ in everyday usage). The term ‘model’ is used in a variety of contexts, even when there is a more commonly used term especially appropriate to its own context: models of terrain are usually called ‘maps’; models of electrical components wired together are usually called ‘circuit diagrams’; and models of the configuratio
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Learning outcomes

After reading this unit you should be able to:

  • appreciate diagrams as a powerful aid to thinking and acting;

  • distinguish between systems diagrams and diagrams helpful in systems work;

  • demonstrate sufficient skills to ‘read’ and ‘draw’ a wide range of diagrams, following given conventions, that help improve your understanding of a situation;

  • select diagrams suited to the needs of the situation you are investigating and the purp
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Introduction

Pictures speak louder than words. But how can you use diagrams to help you? This unit looks at how diagrams can be used to represent information and ideas about complex situations. You will learn how to read, draw and present diagrams to help illustrate how ideas or processes are connected.

This unit is from our archive and is an adapted extract from Systems thinking and practice: diagramming (T552) which is no longer taught by The Open University. If you want to study formally with us
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