Acknowledgements Except for third party materials and otherwise stated (see terms and conditions), this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 Licence Grateful acknowledgement is made to the following sources for permission to reproduce materia
7.1 The engineer and society Section 2 outlined some of the needs for engineering. Society relies on engineers to create solutions to the problems involved in meeting those needs. This is a good time to pause and point out that inevitably, in return for all this fun and power, engineers have a responsibility to society. The people who employ our services, directly or indirectly, have to have an assurance that we are working within certain social, safety and ethical boundaries. Particularly given the increasing tren
6 A problem with sensors The problem we will look at in this section concerns the analysis of the design of a component used in cars that are fitted with airbags. The airbag has to be inflated rapidly when an electronic circuit in the system decides that a serious collision is taking place. The crucial component in the electronics is the accelerometer, which therefore has to be extremely reliable. Motor manufacturers have turned to a technology called MEMS (micro-electromechanical systems) for these accelerometers, b
Learning outcomes After studying this course, you should be able to: understand the basic structural issues of the Forth Road Bridge give examples of how engineers are trying to alleviate the wear and tear on the bridge.
Introduction This unit focuses on the Forth Road Bridge that connects Edinburgh with Fife. This suspension bridge continues to face a number of problems regarding its deteriorating condition. The short video included in this unit illustrates some of the major structural issues facing bridges and examines some of the proposed changes to the use of the Forth Road Bridge to help increase its lifespan.
5.14 Response and damping You have learned so far in this chapter that when a musician plays an instrument, they force the primary vibrator to vibrate. If the primary vibrator is driven at one of its resonance frequencies, the normal mode of vibration corresponding to that resonance frequency will be excited. Now, in practice it is also true to say that even if the primary vibrator is driven at a frequency close to the resonance frequency, the normal mode will still be excited, but just to a lesser degree. In other wo
5.13.2 Circular membrane When a membrane that is stretched over a circular frame is struck, energy is supplied, which again causes the membrane to vibrate in a number of modes simultaneously. The first six modes in which the circular membrane can vibrate are shown in Figure 20. The diagrams comprise circles that are conce
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
5.11 Vibrating air column: standing waves in a conical tube The third configuration of air column that we shall consider is that enclosed by a conical tube. Figure 17 shows the normal modes of vibration for a conical tube plotted in terms of pressure. As you would expect, there is a pressure antinode at the closed tip of the cone and a pressure node at the open en
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
5.8 Vibrating air column: standing waves in a cylindrical tube open at both ends The frequencies at which standing waves can be set up in an air column enclosed by a cylindrical tube that is open at both ends can be determined quite easily. Because both ends are open to the atmosphere, the pressure at these positions always remains at atmospheric pressure. In other words, there is no fluctuation in the pressure at the open ends so they must be pressure nodes (think ‘no-deviation’ in pressure). So, as we saw with the string fixed at both ends, the length L of th
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):
5.3 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
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
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
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
Learning outcomes After studying this course, you should be able to: Explain correctly the meaning of the emboldened terms in the main text and use them correctly in context Identify whether a given sound source can be classed as a musical instrument and explain why (Activity 2) Identify the primary vibrator and any secondary vibrators in the most common types of instrument (Activity 3) Appreciate that, when a note is played, a musical in
