Waves

Frontmatter

1. Introduction

Abstract

It is interesting to note that everybody who writes about waves begins by saying how difficult it is to produce a definition of what a wave is. We shall be no different in this introductory text.

Alan J. Davies

2. Vibrations

Abstract

We have seen, in the introduction in Chapter 1, that wave motion is associated with the oscillations of the individual particles which comprise the medium in which the wave propagates. The medium does, of course, contain many millions of particles and it would be a very ambitious task to try to describe a wave by considering the motion of every individual particle. However, there is much to be gained by becoming familiar with the properties of vibrations of a single particle. We shall consider the case of a particle of mass m attached to one end of a spring of stiffness k, the other end of which is fixed.

Alan J. Davies

3. Wave Motion

Abstract

Consider a very long string stretched along the x-axis, the string being at rest. Suppose that one end is held and given a sharp ‘flick’, setting it in motion. The disturbance set up by flicking the string will travel down the string. During the passage of the disturbance, each particle of the string remains at rest until the disturbance reaches it, at which instant the particle is displaced, returning to its original position once the disturbance has passed.

Alan J. Davies

4. Waves on Strings and Waves in Springs

Abstract

In Chapter 3, we discussed progressive and stationary waves by using the example of a wave on a string. In this section, we shall consider waves on strings in more detail. The two major assumptions are that the string is uniform with mass per unit length, ρ, and that the vibrations are sufficiently small so that the tension, T, remains constant.

Alan J. Davies

5. Sound Waves

Abstract

Sound waves are mechanical longitudinal waves that can be propagated in solids, liquids or gases. There is a very large range of frequencies over which such mechanical waves can be transmitted. The audible range is that range of frequencies which may be detected by the human ear. Mechanical waves in this range are called sound waves. The audible range is roughly between 20 Hz and 20 000 Hz. Waves with frequencies lower than the audible range are called infrasonic while those with frequencies above the audible range are called ultrasonic.

Alan J. Davies

6. General Properties of Waves

Abstract

We are all familiar with the characteristic change in the pitch of the sound of the siren of an emergency vehicle as it passes. This phenomenon is called the Doppler effect. We can explain the effect using the relationship between wave velocity and frequency given by equation (3.5). We assume that the velocity, c, of the wave is independent of the velocity of the source of the wave.

Alan J. Davies

Backmatter