2 Construction with lipids The cell membrane is constructed from lipids. Chemically, lipids are a rather varied group of compounds that include all the substances you might already think of as fats or oils. What they have in common is that they are all insoluble in polar liquids like water, but soluble in organic (carbon-based) solvents: by this I mean the sort of smelly solvents you tend to find in paints, glues and degreasing agents; chloroform is one example. Lipids make up the fatty components of living organisms a
5.13.4 Pitches of notes produced by percussion instruments We have seen that none of the rectangular bar, the circular membrane and the circular plate have harmonically related natural frequencies. It may not surprise you to learn, therefore, that instruments containing these primary vibrators tend to produce notes that don't have a very well-defined sense of pitch. This is certainly true in the case of the cymbal, which has a circular plate as its primary vibrator. Whether a single cymbal is struck with a drumstick or two cymbals are crashed t
5.13.1 Rectangular bar If a solid rectangular bar is excited by striking it, energy is supplied that starts the bar vibrating transversely. The bar will vibrate in a number of modes simultaneously since the striking action supplies energy over a range of frequencies. The motion of the bar will be the superposition of the standing-wave patterns of the excited modes. Assume for the moment that the rectangular bar is supported in such a way that both ends are free to vibrate and the effects of the supports can b
5.13 Other primary vibrators You saw in the previous two sections that stringed instruments and wind instruments possess primary vibrators that have harmonically related natural frequencies. As a result, these two classes of instruments produce notes that have a well-defined sense of pitch. In this section, I want to briefly introduce you to some primary vibrators that don't have harmonically related natural frequencies. Specifically we shall take a look at a rectangular bar, a circular membrane and a circular plat
5.10 Vibrating air column: end effects In the previous two sections on standing waves in cylindrical tubes, we assumed that at an open end there must be a pressure node. In fact, the pressure node (and the corresponding displacement antinode) actually lies a small distance outside the tube. The effect is that the air column behaves as though it were a little longer than it really is by an amount called the end correction. Because of this end correction, the resonance frequencies will be a little lower than originally expect
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
5.7 Vibrating air column: reflection at the end of an air column When a sound wave reaches the end of an air column, it is clear that it will be reflected if the tube end is closed. You only have to imagine yourself standing some distance, let's say 50 metres, away from a flat wall. If you shout, you will hear an echo – the reflection of the sound wave you projected. There is one difference, though, between the reflection of a sound wave and the reflection of the wave on a string that you met previously. When a sound wave is reflected from a closed
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,
5.5 Vibrating string: pitches of notes produced by stringed instruments When a string is bowed, plucked or struck, energy is supplied that starts the string vibrating. The string doesn't just vibrate in one single mode; instead, it vibrates in a combination of several modes simultaneously. The displacement along the string is the superposition of the standing-wave patterns corresponding to those modes. For example, if the string vibrated only in the first and second modes, the displacement at a given instant of time might appear as shown in Author(s):
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
5.3 Vibrating string: standing waves on a string 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
5.2 Vibrating string: speed of wave propagation 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
4 Excitation 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 – in which case short-lived ‘staccato’ note
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 in this unit: This extract is taken from TA212. ©
Audio Materials
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
7.1 The subjective experience 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
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
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
4.2 Frequency, wavelength and the speed of sound The speed of sound has a joint relationship with both the wavelength and the frequency of the sound. To see why, recall that at the end of Section 2.5, in connection with the wave produced by a tuning fork, I said ‘in the time it has taken for the source to go through one cycle of oscillation, the wave h
5.9 Developing other systems methods There are many more methods that are regarded as systems approaches for managing complexity (e.g. Rosenhead, 1989a; Flood and Carson, 1988; Flood and Jackson, 1991; Mingers and Gill, 1997; Francois, 1997; Flood, 1999; Jackson, 2000). The systems practitioners responsible for developing these come from a varied background, but in the main their experiences are similar to those described for Checkland, Beer, Espejo and the T301 team. All wanted to be able either to take action that stakeholders
