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
Author(s): The Open University

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
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

A feature of decibels is that adding two decibel values is equivalent to multiplying the ratios they represent. To see how this comes about, consider another context in which a decibel measurement is often used, that of signal amplification.

In Figure 28, the triangular symbol represents
Author(s): The Open University

For a variety of reasons, not least the very wide dynamic range of human hearing, the decibel (symbol dB) is often used as a unit for the amplitude of sound waves. The decibel is also used in other contexts, such as specifying the amplification of amplifiers or the degree to which a signal is affected by noise. In the context of sound, the use of the decibel as a unit captures something of the subjective impression of the way loudness changes with amplitude.

The decibel unit has
Author(s): The Open University

The nominal frequency range of human hearing is 20 Hz to 20 kHz, though most people cannot hear to 20 kHz. However, the pitches used in music correspond roughly to frequencies in the range from 20 Hz to 2.5 kHz. Generally, musical tones are not pure sine waves but are mixtures of sine waves with frequencies that can extend well beyond 2.5 kHz. However, although they are mixtures of sine waves, they are usually heard as having a single pitch.

The dynamic range of human hearing refers to
Author(s): The Open University

Amplitude refers to the size of a sine wave. It can be defined in various ways, but a standard definition is that it is the maximum value of a wave's departure from its average value. (The average value of a sine wave lies midway between its peaks and troughs.) The size of a sine wave is sometimes also expressed as a peak-to-peak amplitude, which is the vertical distance from peak to trough.

Root-mean-square (r.m.s.) amplitude is a way of specifying the size of a sine wave so that compa
Author(s): The Open University

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
Author(s): The Open University

The speed of sound in air, symbol v, is approximately constant at 340 metres per second. (You do not need to memorise this value.) As temperature increases, the speed increases slightly.

Speed, frequency and wavelength are related by the formula v = f Ã— Î». Other forms of this relationship are f = v/Î» and Î» = v/f. Because the speed is approximately constant, it follows that frequency and wavelength are inversely pr
Author(s): The Open University

Pressure in the air is related to how closely packed the molecules are. Other things being equal, more closely packed molecules are at a higher pressure than more dispersed molecules. Sound is associated with fluctuations of the air pressure caused by local disturbance. Fluctuations of pressure travel outwards away from the disturbance, carrying energy imparted by the disturbance.

A simple form of local disturbance to air pressure is a vibrating tuning fork. It generates a pressure wave
Author(s): The Open University

You saw in Section 2.3 that the prongs of the tuning fork vibrate cyclically. You also learned that a cycle of the prongs' vibration is a complete sequence of motion up to the point at which the motion starts to repeat itself. Another term for this repetitive kind of motion is periodic motion. The t
Author(s): The Open University

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
Author(s): The Open University

The sounds we hear generally consist of rapid fluctuations of air pressure in the atmosphere that surrounds us. Sound can also be transmitted through other media, for instance water, so not all sound consists of fluctuations in air pressure. However, for the purposes of this discussion I shall confine myself to sound in air.

These fluctuations in air pressure are caused by a local disturbance to the air pressure, which might be sudden and transient â€“ for example, when a paper bag is b
Author(s): The Open University

For much of the rest of this unit we shall be concerned with the properties of a type of sound wave that when represented as a graph has a characteristic shape known as a sine wave. Figure 1 shows you what a sine-wave graph looks like. For the moment you need not be concerned with what this grap
Author(s): The Open University

This unit contains material that is essential to learning about music technology. Here you will explore the concept of sound and be introduced to the physics behind travelling pressure waves as the physical manifestation of sound. You will also learn about the subjective perception of pitch and loudness, in particular their relationship to frequency and amplitude.

This unit is an adapted extract from the Open University courseAuthor(s): The Open University

Systems practice may be carried out individually or as part of a team. In doing action research â€“ which is a form of managing â€“ 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
Author(s): The Open University

It might be useful to re-read Box 4 before starting this section. In this example, the terms â€˜openâ€™ and â€˜closedâ€™ were used on several occasions. You have already encountered the term â€˜closed systemâ€™. You were told that human beings are closed systems in terms of inputs to
Author(s): The Open University

My focus in this section is on the M ball being juggled by a systems practitioner. My purpose is to enable you to appreciate the diversity of activities that might constitute managing. More specifically, I am concerned with the type of managing a systems practitioner might undertake. When you began Part 3, Section 4, I asked you to complete an activity (Author(s): The Open University

The capacity to put any systems approach into context is based on the ability of a practitioner to appreciate their own traditions of understanding and to make connections with the history of particular systems methods or methodologies, or to formulate their own. Above all, there is a need to learn from using them and to achieve outcomes that are agreed by those involved as worthwhile. This is a level of systems practice to which you can aspire.

At the beginning of Part 3, Section 5 I p
Author(s): The Open University

In the 1950s, Jay Forrester, a systems engineer at MIT, was commissioned by the US company Sprague Electric to study the extreme oscillations of their sales and establish a means to correct them. From previous experience, Forrester knew the essence of the problem stemmed from the oscillations present in situations that contain inertia effects, or delays and reverse effects, or feedback loops as basic structural characteristics.

Subsequently, in 1961, Forrester published his report on in
Author(s): The Open University