5.9 Vibrating air column: standing waves in a cylindrical tube closed at one end We'll now turn our attention to the setting up of standing waves in an air column contained within a cylindrical tube that is open at one end but closed at the other. Straight away we can say that the closed end must be a displacement node since the air molecules can't move at this boundary. That means it must be a pressure antinode. The open end, as we saw previously, will be a displacement antinode (that is, a pressure node). Now, you may recall that the distance between a node and a
5.6 Vibrating air column You learned in the previous section that for standing waves to be set up on a string there must be reflection. A travelling wave reaches the end of the string and is reflected. This results in a second travelling wave, which moves back up the string in the opposite direction to the first wave. The two travelling waves interact to produce a standing wave. Standing waves are set up in an air column enclosed within a tube in a very similar way. Again there must be reflection. In this case,
5.4 Vibrating string: normal modes of vibration The frequencies at which standing waves can be set up on a string are the string's natural frequencies. They can be determined quite easily. The first thing to note is that the end of the string being held by the person is tightly gripped so any pulse or wave that returns to the person's hand will be reflected and inverted. Therefore both ends of the string can be considered to be fixed and so must be at nodes of the standing wave. But you learned earlier that the distance between adjacent no
3 Sound production in musical instruments Musical instruments come in all shapes and sizes and produce an enormous variety of different sounds. Yet, with the exception of certain electronic instruments, the basic physical principles by which sound is produced are the same for all instruments – including the human voice. In this section, I shall introduce some of these principles. These will then be expanded upon over the rest of the unit. Remember I told you that when a musician plays an instrument they cause it to vibrate. T
9.1 Frequency range The lowest frequency humans can hear is approximately 20 Hz. The upper limit for humans is nominally 20 000 Hz (20 kHz), but this limit tends to decline with age, and for most of us it is well below this figure. 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 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 2.3 Pressure waves and cycles In this section we shall be looking at the behaviour and properties of pressure waves in the atmosphere. Sound originates from the motion or vibration of an object. Let's look at an example of a sound wave generated by a vibrating tuning fork. The prongs of the tuning fork move backwards and forwards cyclically. A cycle is a complete series of movements up to the point where the movement starts to repeat itself. As the prongs of the fork vibrate back and forth they push on neighbouring 2 Part 1 Starting the unit Welcome to T306_2 Managing complexity: a systems approach – introduction. As I write, I experience a sense of excitement. For me, as for you, this is the beginning of the unit. These are the first few sentences I'm writing and so, although I have a good idea of how the unit is going to turn out, the details are by no means clear. Nevertheless, the excitement and anticipation I, and maybe you, are experiencing now is an important ingredient in what will become our experiences of the u 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 < Acknowledgements The content acknowledged below is Proprietary (see terms and conditions) and is used under licence. Grateful acknowledgement is made to the following sources for permission to reproduce material within this unit: Figures 1 and 64 © DIY Picture Library. Figure 2 Courtesy of Dyson (UK) Ltd. Figures 4 and 70 ©John Frost Historical Newspapers. Figures 4, 5(l), 18, 35, 45, 75 Richard Hearne/ Open University. Part 3: 5 Self-assessment questions A dramatic example of the importance of process innovation for a product's success is mentioned in Author(s): 20 Part 3: 4 Phases and waves of innovation To wrap up this section I'll take a broad look at the innovation process. It's possible to think of innovation at different levels of generalisation. There are individual stages that innovations go through from invention to diffusion – these are sometimes called phases. At a higher level of generalisation each complete set of phases for a group of related technologies can be seen as a wave. Sometimes such waves appear close together and combine to have a revolutionary impact.< 19 Part 3: 3 Sustaining and disruptive innovation Once an innovation starts diffusing into the marketplace it can have differing degrees of impact. As mentioned in Part 1, although innovations generally offer progress, there are some that complement existing ways of doing things and some that are more dramatic in their impact. In his book called The Innovator's Dilemma Clayton M. Christensen (2003) labels these two types of innovation sustaining and disruptive. Sustaining innovations are those that improve the performance of est 18.4 MP3's diffusion depended on innovations in related areas As well as being small and portable, MP3 devices have a number of additional competitive advantages. Digital compression allows the size of recordings to be significantly smaller without noticeable loss of sound quality so the capacity of portable devices can be much greater. Compatibility with computer systems means that music can be acquired from the internet or from a CD and easily manipulated into a sequence desired by the user. Although MP3 players had been around for a number of y 18.3 Characteristics of consumers and the market As well as the characteristics of an innovation affecting the extent of its take-up, the nature of the market and the purchasing behaviour of consumers can influence success. Some people will always try to be among the first to buy a new product – Rogers (2003) calls people in this group innovators (Author(s): 18.2.5 Trialability It helps to be able to try innovations before buying. While this isn't common for most innovations it can reduce any uncertainty the buyer might have about committing to a purchase and can increase the speed of diffusion. Buying a car usually involves a test drive that, although it probably isn't a fair reflection of the range of conditions under which the product will eventually be used, is better than nothing. 18.2.3 Complexity If an innovation is perceived as difficult to use it will diffuse more slowly than one that is easy to understand. For example users of early personal computers needed an understanding of a programming language in order to use their machines. For most potential PC users this made the innovation too complex to consider buying. Then a graphical user interface was developed and incorporated by Apple Computer into the Lisa computer in 1983 (Author(s): 18.2.2 Compatibility An innovation that is compatible with the experiences, values and needs of its potential buyers will be adopted more rapidly than one that isn't compatible. For example mobile phones have spread rapidly because they are compatible with social and cultural trends towards faster communications, increased personal mobility and the desirability of high-tech gadgets. However the car seat belt, patented in 1903, wasn't adopted on any significant scale until the 1970s (Author(s): 17.4 Standards and their role in innovation Standards were originally related to units of measurement. The first ‘standard’ was the Egyptian royal cubit, which was made of black granite and was said to be equivalent to the length of the Pharoah's forearm and hand. This was also subdivided into finger, palm and hand widths – one ‘small cubit’ was equivalent to six palms. But because the human forearm was the master reference this meant that the cubit varied in different parts of the world. Over thousands of years agreement ove
Activity 27 (Self-Assessment)
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SAQ 8
