Wave, Motion and Sound - Part I

If you throw a piece of stone in a pond, you will see ripples forming on the water. The ripples will extend outwards. The kinetic energy of the stone is transferred to the molecules of water, which oscillate up and down. The molecules make a periodic up and down motion, without being permanently displaced from their mean position. The energy is transferred from one molecule to the other via their intra molecular bonds.  There are two types of waves, longitudinal and transverse waves. The distinction comes in the way in which the energy is transferred as the wave passes. Sound is measured by its speed, intensity and frequency; speed is measured in m/s, intensity is measured in decibel units (db) and frequency is measured in hertz (Hz).

What we will study in this chapter :
1. Types of waves and wave characteristics
2. Sound waves
3. Differences between sound waves and light waves

1. Types of waves and wave characteristics
Before we consider the types of waves, let us first see how a wave is generated and how the energy is transferred.

Consider the following diagram. A person is holding a string, which is attached, on one end. The person is jerking the string up and down at the other end.

The initial position of the particles is in a straight line. As the rope is swung up and down, the particles also start moving up and down but their position on the rope is not changing. The wave propagates perpendicular to the motion of the particle. The energy that is transferred from one particle to the other goes in the direction of the wave, but in a straight line only.

Thus points to be noted as regards propagation of waves is :

• The particles do not travel or leave their mean positions permanently. They vibrate about their mean positions, and stop after the wave has passed.

• The energy passes through the particles in a straight line.

There are two types of waves : 1) transverse waves and 2) longitudinal waves.

Transverse waves
The example above was that of a transverse wave.  Ripples formed on water when a stone is dropped are also an example of transverse wave. Vibrations of strings of a sitar or guitar are also examples of transverse waves.
(Light waves (or electromagnetic waves) are transverse waves too but the difference is that they do not need a material medium for transmission. This we will discuss in the last section.)

Thus a transverse wave is a wave in which the particles of the medium vibrate at right angles to the direction of propagation of the wave.

The diagram below shows the schematic of a transverse wave travelling in a medium, in the XY direction.

A transverse wave, as it passes through a medium, has a series of crests and troughs. A crest is an elevation or a hump in a transverse wave, that is above the line of mean position of the particles, in the medium. On the other hand, a trough is a depression or a hollow in a transverse wave, that is below the mean position of the particles in the medium.

A crest and a trough can be visually seen when you drop a stone in a pond and ripples are created. 

Longitudinal wave
A wave in which the particles of the medium vibrate back and forth in the direction of propagation of the wave, is known as a longitudinal wave.

The diagram below shows the schematic of a longitudinal wave travelling in a medium, in the XY direction.

The direction of vibration of the particles is in the same plane as in which the wave is propagating.  The particles vibrate back and forth, about their mean positions.

The examples of longitudinal waves are many. A wave travelling along a spring when it is pushed or pulled has compression and separation of spring coils.

The diagram above shows how a longitudinal wave travels along a spring. Areas around C are compressed and areas around R are rarified.  Thus instead of having crests and troughs as in a transverse wave, a longitudinal wave has compression and rarefaction.

The compression in a longitudinal wave can be described as that part of the wave where the particles of the medium through which the wave is travelling, is closer to one another than they are normally.  A rarefaction in a longitudinal wave is that part of the wave where the particles of the medium through which the wave is travelling, is farther apart to one another than they are normally.

Wave characteristics
A wave is a periodic cycle of a certain fixed pattern. A wave can be described by its wavelength, frequency, amplitude, time period, phase and wave velocity.

A wavelength of a transverse wave is the distance between consecutive crests or troughs. 

In case of a longitudinal wave, wavelength is defined as the distance between centres of consecutive compressions or consecutive rarefactions. It is denoted by and it has units of distance (meter, centimeter, etc).

All points on a wave, which have the same state of vibration, are said to be in phase with each other.  All points that are separated by n , where n = 1,2,3…., are said to be in phase.

Frequency of a wave is the number of vibrations a particle undergoes per second. It is denoted by f or . Its unit is inverse of time or s^-1 (or Hertz). Frequency gives the number of oscillations per second.

Time period is the time taken by a particle of the medium through which the wave is passing to do one cycle of vibration and return to its original position. T denotes the time period and its unit is second (s).
      T = 1/f = 1/

Amplitude of a wave is the maximum displacement of the particles in the medium when the wave passes, about their mean undisturbed positions.

x   or  v = x f

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