PRODUCTION AND PROPAGATION OF WAVES

 PRODUCTION AND PROPAGATION OF WAVES

A wave motion is a process of transferring a disturbance (in form of kinetic energy) from one point to another in a medium without any transfer of particles of the medium

A Wave is a disturbance that transfers energy between two points through vibrations (or oscillations) in a medium, without transferring matter between the two points.

A wave is defined as a disturbance which travels through a medium transferring energy from one point to another without causing any permanent displacement of the medium.
Example of waves

1. When you hold the end of a rope and a friend of yours wave the rope at the other end up and down, then a wavy movement appears. This is a movement of the rope and it transfers energy but NOT the rope.
 2. When you throw a stone on the surface of a calm pond, a circular ripple will appear and subsequently other smaller ripple will appear from the point of origin, these waves will eventually turn into a few big circles which then encompass smaller circular ripples in the middle. What happen is, the kinetic energy from the stone is transferred to the water in the form of ripples, which is an example of wave.

There are two types of waves:
1. Mechanical waves                           2. Electromagnetic waves

Mechanical waves are those waves that require a material medium for their propagation. Examples of such waves are water waves, sound waves on a rope or string.

Electromagnetic waves are waves that do not require a material medium for propagation. Examples are light waves, radio waves, x-rays and gamma rays.

PROGRESSIVE OR TRAVELLING WAVES

A Progressive or travelling waves is a wave that transfers energy in travelling or moving away from the source of the disturbance i.e. waves moves in the same direction.

There are two types of progressive waves

1. Transverse waves                                                                            2. Longitudinal waves

Transverse waves
Transverse wave is a wave in which direction of vibration is perpendicular to the direction of movement of wave.
Examples are : water waves, waves on a string, radio waves, light waves and electromagnetic waves.
Longitudinal waves
Longitudinal wave is a wave in which the direction of vibration is parallel to the direction of travel of the wave
Examples are: sound waves and waves on a slinky spring.(which consists of regions of rarefaction and compression).
STATIONARY OR STANDING WAVES

This is the combination two waves moving in opposite directions, each having the same amplitude and frequency. The phenomenon is the result of interference i.e when waves are superimposed, their energy are added together or cancelled out. Examples are plucking the spring of the guitar, two people shaking either end of a jump rope in sync, noticeable in musical instruments (flutes or guitar).

Condition necessary for the production of stationary wave in a medium

I.                     Two waves must be travelling in opposite directions.

II.                    Incident and reflected waves must have the same frequency or wavelength

III.                  Incident and reflected wave must have equal amplitude

IV.                  There must be a barrier

V.                   There must be superposition.

TERMS USED IN DESCRIBING WAVES



A pulse is a sudden increase in magnitude of a physical quantity, shortly followed by a rapid decrease.

Wavefront is a line that joins all the points vibrating in phase, such as a line passing through similar wave crests. It consists of crest and trough. Crest is the peaky part of the wave and trough is the lowest part of the wave.
Wavefront is perpendicular to the direction of wave movement.
A Cycle is a complete to- and fro- movement of a body when it has returned to its original position and is moving in the same original direction.

Phase: particle which are at the same vertical distances from their positions of rest and are moving in the same direction are said to be in the same phase.
Amplitude, a, is the maximum displacement from the resting position. It is measured in metre.

Wavelength, , This is the distance between two successive crests or successive trough of a wave. It is measured in metres.
Period, T, is the time taken to make one complete oscillation. It is measured in seconds. Period is also the time taken by the wave to travel one wavelength.

T = 1/f
Frequency, f, is the number of oscillations produced in one second. The S. I unit of frequency is the Hertz (Hz) which is one cycle or oscillation per second.

f = 1/T

Wave speed, v, This is the distance which the wave travels in one second. Its unit is metre-per –seconds (ms-1).

Phase difference,  , is a measure , in angular form, of the fraction of a cycle two particles in a wave or two waves are out of step by in their motion.  =

MECHANICAL RELATIONSHIP CONNECTING FREQUENCY (F) WAVELENGTH ( ), PERIOD (T) AND VELOCITY (V)

There is a very important relation between frequency (f) wavelength ( ), period (T) and velocity (v) of all waves. This is given by: v = f  i.e velocity = frequency x wavelength .

The above relation is easy to prove. The speed of a waves ,v, is given by

 Velocity ,v, =

A wave travels a whole wavelength ( ) in a time given by the period (T). v = .

Recall, f =1/T. hence v =  = f ,   = vT

Example

1.  A radio station broadcasts at a frequency of 600 KHz. If the speed of the light in air is 3 x108 ms-1. Calculate the wavelength of the radio wave.

Solution

f = 600KHz = 600x1000Hz, v =3 x108 ms-1,  =?

V= f  ;   = =  = 500m

Assignment

1.  A wave sent out from a source is reflected back to the source in 1.0x10-3s. if the velocity of the wave is 3x108 ms-1. The distance of the reflecting surface from the source is

2. In a ripple tank with a 20 Hz vibrator, the waves speed is 0.3 ms-1 until the waves reach a shallower region where the speed is 0.2ms-1 .

a. what is the wavelength in each of these parts of the tank?   b. Plane wave-fronts travelling from the deeper part make an angle of 60o with the boundary; at what angle to the boundary do they traveled in the shallower parts.

 

 

  

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