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# Wave Motion and Definitions

Extracts from this document...

Introduction

"A" Level Physics.                        Wave Motion and Definitions                2.2

2.2.1                What is a wave ?

Waves involve a disturbance from an equilibrium position and the propogation of that disturbance from one region of space to another. Eg a brick thrown into a pond.

(1)         Pond showing water in equilibrium position.

(2)        Pond showing a disturbance from an equilibrium position.

(ie brick thrown into pond)

(3)         Disturbance is propogated.

2.2.2                Wave Definitions

Progressive Wave

is one  that  carries  energy and momentum from one place to another, without there being a transfer of matter  (ie the  material  that  the wave is moving through eg the water in a water wave).

Stationnary Wave

is the superposition of two waves of equal wavelength travelling towards each other at the same speed. Unlike progressive waves there is no net transfer of momentum or energy by the wave (see later for details about superposition).

Mechanical Wave

is one in which  the  wave is carried by material substance eg water for water waves, air for sound waves or vibrating string or slinky !

ElectromagneticWaves

may travel through a vacuum and require no medium eg waves all the waves in the electromagnetic spectrum. The waves are caused by vibrations of electric and magnetic fields.

2.2.3                Wave Nomenclature

• Period               T
• Frequency            f
• amplitude            A
• displacement         x
• wavelength        λ

2.2.5                Wavespeed and the Wave Equation.

Tells us how fast the "energy" moves from one place to another by a progressive wave or how fast the wave is moving.

Speed         =         Frequency         x         Wavelength

v        =        f  λ

Hutchings: Q 11.1 and 11.2 p 164.

2.2.

Middle

Examples:

(1)        A red light of wavelength 600nm is incident on a double slit of slit separation 2mm. Calculate the spacing between the fringes on a screen placed 2m away

(a)        Describe what would happen to the fringe spacing if the slit spacing was reduced

(b)        Describe what would happen if yellow light were used instead.

(2)        Estimate the speed of sound produced by the signal generator Young’s double source experiment in the lab.

2.2.12                Standing or Stationnary Waves.

Explains why

• musical insturments give particular sounds.
• long organ pipes produce low sounds and small organ pipes produce high notes.
• how you get different notes out of a guitar string
• aerials have particular lengths
• people like singing in the bath   !!

So what is a stationnary wave ?

STATIONARY or STANDING WAVES result from the SUPERPOSITION or INTERFERENCE of 2 wavetrains which have the same amplitude, frequency and wavelength but travelling in opposite directions with the same speed. This occurs at particular frequencies only.

What does this mean ?

• Two waves of same speed and frequency travel towards each other
• They meet and interfere
• At particular frequencies the wave appears to have stood still ie a stationnnary wave has been produced In this condition we say that accoustic RESONANCE has occured.

Important:                   Unlike Progressive waves there is no net transfer of momentum or energy by a stationary wave.

2.2.13                 Standing wave problems.

Conclusion

1  ) to a less dense material of absolute refractive index (n2)

n1 sin θ1        =        n2sinθ2

n1                =        sinθ2

n2                        sin θ1

μ                =         sinθ2

sin θ1

but   θ2 =  90 ° hence sinθ2  =  1

μ                =             1

sin θc

μ                =             1

sin θc

2.2.25                Application of the critical angle in optical fibres.

An optical  fibre consists of a graded (graded means that the density is not uniform) central core of glass which is surrounded by an outer cladding of material with a lower refractive index of refraction. As you can see from the diagram below most of the light is totally internally reflected down the fibre.

Advantages of using optical fibres

1. The raw material is very cheap (glass is made from sand !)
1. There is virtually no interference for communications sent this way.
1. The signal gets sent at the speed of light reducing signal delay.
1. Its vitually impossibly to “tap” into an optical transmission
1. Approx 20 000 more messages can be sent through 1 fibre compared to a similar copper cable which can only take one message at any time.
1. The signal is sent digitally down the cable reducing signal distortion.

Questions.

(1)        Calculate the angle of refraction for a ray of light moving from water to glass if the angle of incidence in the water is 30°. n for water is 1.33,  n for air is 1.0003.

(2)        Calculate the angle of incidence if the angle of refraction of a ray of light moving from glass to air is 40°. Take n for glass to be 1.58.

(3)        Calculate the critcial angle of from glass (n=1.58) to the following materials

(i)        air   n = 1.0003        and

(ii)        turpentine   n  =- 1.47

GNK/ALEVEL/WAVES/WAVES/Y12PN10/JANUARY 1996

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