(a) General Waves Properties

Learning objectives

describe what is meant by wave motion as illustrated by vibration in ropes, springs and experiments using a ripple tank
show understanding that waves transfer energy without transferring matter
show an understanding and use the terms displacement, amplitude, period, frequency, wavelength and speed
state what is meant by the term wavefront
recall and apply the relationship velocity = frequency x wavelength to new situations or to solve related problems
compare transverse and longitudinal waves and give suitable examples of each

Introducing waves

Waves are everywhere around us; sound waves, visible light waves, radio waves, microwaves, water waves, stadium waves, earthquake waves, waves on a string, and slinky waves.

What are waves?

A wave may be thought of as a spreading of disturbance from one place to another.

The source of any wave is a vibration or oscillation.

For example, we can produce waves on a rope by fixing one end of a wall and moving the other end up and down. These up-and-down movements make up the vibrations or oscillations.

We can observe that rope waves travel sideways while the rope itself goes up and down. We say that the rope is the medium through which the rope waves move or propagate.

For example, when we drop a pebble into a pond of still water, a few circular ripples (disturbances) move outwards on the surface of the water. As these circular ripples spread out, energy is being carried with them.

We say that water is the medium through which the water waves move or propagate. The water molecules only move up and down while the water waves spread out.

Wave motion provides a mechanism for the transfer of energy from one point to another without the physical transfer of the medium (such as rope or water) between the two points.

Types of waves

There are two types of waves.

Transverse Wave

Transverse waves are waves that travel in a direction perpendicular to direction of vibration.

Transverse waves can be recognised by their crests and troughs.

Rope waves, water waves, light waves and electromagnetic waves are examples of transverse waves.

Longitudinal wave

Longitudinal waves are waves that travel in a direction parallel to direction of vibration.

Longitudinal waves can be recognised by their compressions and rarefactions.

Sound waves is an example of longitudinal waves.

Travelling waves

In Transverse Waves and Longitudinal Waves, there appears to be something moving or travelling with the waves which is actually the movement of disturbance which carries energy away from a source.

These waves have the following important features:

A travelling wave carries energy.
The medium or material through which a wave travels does not travel with the wave.
The particles of the medium which are displaced by the wave motion, vibrate about their rest positions but do not travel with the wave.
The shape of the wave stays the same as it travels through a medium but its amplitude gets smaller as the energy is lost or the waves spread out.
The speed of a wave is not affected by the shape of the waves or their amplitude but it is affected by the nature of the medium it travels through.

Properties of waves

Displacement-Distance Graph

Amplitude, a

Maximum displacement from the rest or mean position.

Unit: metre, m

Wavelength, λ

Shortest distance between any two points on a wave that are in phase.

Unit: metre, m

Phase

Two points moving in the same direction with the same speed and having the same displacement from the rest position.

Displacement-Time Graph

Although the graph looks like a transverse wave, it can be used to show the displacement of particles in both transverse and longitudinal waves.

The displacement can be the distance the particles are moved from their rest positions either at right angles to, or parallel to, the direction of travel of the wave motion.

Frequency, ƒ

Number of complete waves produced per second.

Determined by the source

Unit: Hertz, Hz

Period, T

Time taken to produce one complete wave.

Unit: second, s

T = 1/f

Wave Speed

Speed, v

Distance traveled by a wave in one second.

Unit: metres per second (m s^-1)

v = f λ

Speed of a wave is

1. independent of the shape or amplitude of the wave.

2. independent of its frequency or wavelength.

3. dependent on the nature of the material it travels through

Wavefront

An imaginary line on a wave that joins all points which have the same phase of vibration. (For example, a wavefront can be drawn by joining all crests of a wave. The direction of wave travel is always perpendicular to the wavefront.)

Water waves

The ripple tank is a very useful apparatus used to generate water waves and to demonstrate wave properties (such as reflection and refraction).

Structure of a ripple tank

The ripple tank consists of a shallow glass-bottomed tray, a light source (such as a lamp) directly above the tray and a white screen beneath the tray. The screen is used to capture the image of hte shadows formed when water waves transverse the tray.

Generating plane waves and circular waves

In a ripple tank, plane waves can be set up by using a straight dipper made up of either wood or plastic. Circular waves can be formed by using a spherical dipper made of plastic. When a straight dipper is placed in the water and vibrated by means of a motor, plane waves (or circular waves if a spherical dipper is used) are produced. These waves will be seen as bright and dark lines on the screen below the tray. These line show the positions of the crests and troughs of the waves.

Reflection of water water waves

Obeys laws of reflection .

No change of the speed for the reflected waves.

Refraction of water water waves

When water waves travels from a deeper to a shallower region, the wavelength becomes shorter in the shadow region.

Since frequency of the wave does not change, decrease in wavelength means decrease in speed.

If the angle of incidence is zero, the wave continues in the same direction.

If the angle of incidence is not zero, then the decrease in speed of the wave cause a change in the direction of travel of the waves when they cross the boundary. The waves bend towards the normal of the boundary.

Waves interference

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