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,
Author(s): The Open University

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
Author(s): The Open University

We still haven't answered the question of how standing waves are set up on a string. To do so we need to return to our string, fixed at one end and held in someone's hand at the other end. Imagine now that instead of sending a single pulse along the string, the person flicks their hand up and down periodically and sends a sinusoidal wave along the string. This wave gets reflected and inverted at the fixed end and travels back towards the person holding the string. There are now two waves of t
Author(s): The Open University

If standing waves are set up when two travelling waves moving in opposite directions interact, then how are standing waves set up on a string and why are they set up only at certain frequencies?

To help answer these questions, I want you first to imagine a length of string that is fixed at one end and held in someone's hand at the other. Suppose the person holding the string flicks their end of the string in such a way that an upward pulse is sent along the string.

As the pulse pa
Author(s): The Open University

For a player to be able to sound a musical instrument, there must be a means of inputting energy to set up the vibration. This energy may be introduced in a short, sharp burst or continuously over a period of time.

In the case of brass instruments such as the trumpet and trombone, and woodwind instruments such as the flute and oboe, the player feeds in energy by blowing air into the instrument. The energy can be supplied in a short burst â€“ in which case short-lived â€˜staccatoâ€™ note
Author(s): The Open University

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## Audio Materials

This extract is taken from TA212. Â©
Author(s): The Open University

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
Author(s): The Open University

Two of the properties of sound that we have examined from an objective stance, frequency and amplitude, have a fundamental importance to our appreciation of sound and music. In this section I want to look more closely at the subjective interpretation of these two properties of sound. I should stress that I am talking about sine-wave sounds in this section. The complex, non-sinusoidal sounds encountered in music add extra layers of complexity to the relationships I am discussing here.

Ke
Author(s): The Open University

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
Author(s): The Open University

I think for most people, the CSA case study would be experienced as a complex situation. If so this would be a good example of perceived complexity. Remember though, if you engaged with it as if it were a difficulty, just as the government minister did in Activity 42, you would not d
Author(s): The Open University

It is often claimed that the essence of a systems approach is that of seeing the world in a special way. This immediately prompts the question of what is meant by the phrase â€˜seeing the worldâ€™. Because we live so intimately with the world of objects, categories and people and phenomena, we tend to think our own way of seeing the world is the only way, or even of thinking, â€˜Well that is my view because the world is like thatâ€™. Actually, your view is special in several separate ways.
Author(s): The Open University

Welcome to T306_2 Managing complexity: a systems approach â€“ 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
Author(s): The Open University

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
Author(s): The Open University

There are examples where either technology or the market appears to be more significant in stimulating invention but the majority of innovations involve a creative coupling of technological and market factors. In some respects successful innovation is a case of the survival of the fittest. Failure can come both from not getting the technology right and from misjudging the market. Success is more likely if the focus is not too one-dimensional but rather a balance between technology and market
Author(s): The Open University

Analogy draws on similar situations to provide ideas for invention and design. Alexander Graham Bell used the analogy of the human ear when designing telephone apparatus to receive sound. As mentioned above, his first receivers were much better than his transmitters where the analogy with the ear didn't work as well. When devising their flying machine, the Wright brothers used the analogy of soaring birds twisting their wings to restore balance. They designed the wings of their aircraft to be
Author(s): The Open University

The discovery of new materials, exploration of their properties and the invention of new industrial processes is a huge field of study in its own right. The potential rewards for a company discovering a successful application of a new material are great.

An example of this is shape memory alloys (SMAs). SMAs are mixtures of metals that, after being stress treated, can be deformed significantly but then triggered to return to their original shape. Some display unusual elastic properties
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Even though an invention will have been thoroughly tested before launch it's not possible for a company to test its performance in every situation in which it will be used. Real users are likely to discover how the product might not perform well or how it doesn't meet their needs. Once a company learns about these deficiencies it can address them through redesign. There are a number of incentives to do this: improve the product's performance in order to increase its appeal to larger numbers o
Author(s): The Open University

Some companies have an offensive strategy in which they aim to be first to market with a new product. Such companies can be a major source of new products. This is risky as it requires a large investment in developing the product and cultivating the market before any return can be expected from sales. However it can be the most rewarding strategy, especially if the market can be sustained by continual incremental improvements to the product and the market share defended against competi
Author(s): The Open University

This is a less common motivation but it shows not everyone is driven by money.

In 1991 the inventor Trevor Baylis saw a BBC documentary about the spread of HIV/AIDS in Africa. What was needed was a way of broadcasting the safe-sex message to people in areas without electricity and where batteries for a radio could cost a month's wages. Solar power wouldn't necessarily help as most people who could get to a radio listened in the evening after work. While absorbing this information he ima
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Picture an everyday scene. You're in a high street coffee shop. All around you people are drinking coffee. Some people are chatting with friends, others are using their mobile phone. A few individuals seem to be working â€“ consulting their laptop computers, scribbling notes. In a corner of the coffee shop an internet cafe has been set up. At one table a couple of teenagers are laughing at a message in a chat room, while at another table an old chap searches the Web for something.

Now
Author(s): The Open University