Waves

Introduction

To start with I want to ask you a question "What happens in an isolated system which is a collection of oscillating objects?"

Comment your answers below.

Waves represent transport of energy and the pattern of distribution has information of its propagation from one point to another. All communication essentially depends on transmission of signals via waves.

Likewise speech means production of sound waves in air and hearing amounts to their detection. And our daily life communication involves different kinds of waves . For example when we are talking somebody through mobile phone sound waves are first converted into an electrical signal which in turn will generate an electromagnetic wave that is transmitted and received and opposite process happens to convert them back to sound waves which is heard by the person.

So waves are very essential part of every human being and almost every living creature.

Transverse and Longitudinal Waves 

We have seen that motion of mechanical waves involves oscillations of constituents of the medium. If the constituents of the medium oscillate perpendicular to the direction of wave propagation, we call the wave a transverse wave. If they oscillate along the direction of wave propagation, we call the wave a longitudinal wave.

Displacement Relation In A Progressive Wave

Let us take a transverse wave so that if the position of the constituents of the medium is denoted by x, the displacement from the equilibrium position is denoted by y. A periodic travelling wave is then described by:

y(x,y)=asin(kx-wt+¢)                        [1.1]

The term ¢ in the argument of sine function indicates that we are considering a linear combination of sine and cosine functions:

 

y(x,t) = Asine(kx-wt) + Bcos(kx-wt)          [1.2]

 Then from equations [1.1] and [1.2],

a=√A^2+B^2 and ¢=tan-1(B/A).

Amplitude and phase

Let 'a' represents the maximum displacement of the constituents of the medium from their equilibrium position then 'a' is called Amplitude of the wave.

The quantity (kx-wt+¢) appearing as the argument of the sine function in Eq.[1.1] is called the phase of the wave.

Given the amplitude a, the phase determines the displacement (and velocity) of the wave at any position and at any instant. Clearly ¢ is the phase at x=0 and t=0. Hence ¢ is called the initial phase angle.