WAVES 1 - Form 2 Physics Notes

• Introduction
• Definition of a Wave
• Classification of Waves
  • Electromagnetic Waves
  • Mechanical Waves
  • Exercise
• Pulse
• Terms Associated with Waves
• The Wave Equation
• Revision Exercise

Introduction

• In this topic basic concepts about waves are studied.
• Knowledge about waves has been broadly applied in daily life e.g. in radio and television, mobilephones, remote control system, heat energy, radiation, etc.

Definition of a Wave

• A wave refers to the transmission of a disturbance.
• A wave therefore transmits energy from one point to another.

Classification of Waves

• Waves can be broadly classified as electromagnet or mechanical in nature.

1. Electromagnetic Waves

• These are waves which do not require material medium for transmission.
• Such waves can be propagated in vacuum.
• Examples of electromagnetic waves are Radio waves, Radiant heat e.g. from sun, light, Microwaves etc.
• NB:Electromagnetic waves are transverse in nature

2. Mechanical Waves

• These are waves which do require a material medium for transmission.
• Such waves cannot be propagated in vacuum.
• Examples of mechanical waves are water waves, sound waves, etc.

Classification of Mechanical Waves

a. Transverse waves

• These are waves in which displacement of medium particles is at right angle to the direction of propagation of the wave.
• Examples of transverse wave are water waves, waves on a rope swung up and down.
• Transverse waves travel as a series of crests and troughs.
  
• A crest is the highest point of a transverse wave while a trough is the lowest point of a transverse wave
• Formation of transverse wave can be illustrated by swinging a slinky spring or a rope fixed at one end up and down.

b. Longitudinal waves

• These are waves in which displacement of medium particles is parallel to the direction of propagation of the wave.
• Examples of longitudinal wave are Sound wave,waves on a slinky spring fixed at one end and vibrated to and fro etc.
• Longtudional waves consists of sections of rarefactions and compressions.
• Compressions are sections of high pressure in which particles are pushed closer together while rarefactions are sections of low pressure in which particles are pulled slightly further a part from one another.
• Pressure variation in a longtudional wave is what causes wave motion.
  
• Formation of longitudinal wave can be illustrated by vibrating a slinky spring fixed at one end to and fro along its length.

Examples

1. What is a progressive wave?
   It is a wave that moves continualy away from the source.
2. Explain why the amplitude of a progressive wave decreases gradually from the source.
   As the wave moves away from the source, the energy is spread over an increasingly large area.

Exercise

1. Diferentiate between electromagnetic and mechanical wave giving one example in each
2. State two categories of waves.
3. State two types of mechanical waves. State the difference between them.
4. Give two examples of mechanical waves.

Pulse

• A pulse is a single disturbance that is transimitted through a medium.
• It can be transverse or longtudional in nature.
• Generation of a pulse can be illustrated by jerking a rope fixed at one end just once.

Terms Associated with Waves

• Consider the transverse wave form and an oscillating pendulum bob shown below.
  

1. Oscillation– an oscillation is a complete to and fro motion. For example, in the above oscillating bob, a complete oscillation is D-E-F-E-D.
2. Amplitude,A - it is the maximum displacement of a particle from mean position. Its SI unit is the metre (m). For an oscillating pendulum bob above DE or EF is the amplitude.
3. Wavelength,λ– it is the distance between any two particles in a wave that are in phase. It is denoted by Greek letter lambda, λ. Its SI unit is the meter(m).
   
   Note: Particles in a wave are said to be in phase if they are oscillating in same direction and at the same level of displacement.
   
   Particles A and D, B and E are in phase. C and D are out of phase by 180⁰.
   
4. Period,T- it’s the time taken by a particle to complete one oscillation. SI unit of period is the second(s)
5. Frequency, f– it is the number of complete oscillations(full wavelengths) made by a particle in one second. SI unit of frequency is hertz(Hz).
   Relationship between Frequency and Period
   Frequency is the reciprocal of period i.e. f=^I/_T

6. Speed of the wave- It is the distance covered by a wave in one second.

The Wave Equation

• The wave equation relates Speed,V, Wavelength,λ and Frequency, f of a Wave
• Generally, speed = ^distance/_time
• For a distance of wavelength covered by a wave, time taken is equivalent to the period of the wave.
  
• This is called the wave speed equation
• From the wave equation, if speed of the wave is constant, frequency is inversely proportional to wavelength.
• This can be presented graphically as shown below.
  

Example

The figure below shows a displacement-time graph of a wave travelling at 2500cms^-1

Determine for the wave:

a) Amplitude

Solution

A = maximum displacement from mean position
=3cm OR 0.03m in SIunits

b) Periodic time

Solution

T=(9-1) x 10s^-3s

=8x10s^-3

c) Frequency

Solution

d) Wave length

Solution

Revision Exercise

1. State the wave formula
2. Sketch the variation of frequency with wavelength given that speed of the wave remains constant
3. Name two types of progressive wave motion.
4. A vibrator sends out 12 ripples per second across a ripple tank. The ripples are observed to be 5cm apart. Find the velocity of the ripples.
5. A water wave travels 2m in 5 seconds. If the frequency of the wave is 10Hz, calculate the:
   1. Speed of the wave
   2. Wave length of the wave
6. The diagram below shows a displacement-time graph for a certain wave.
   
   
   1. How many oscillations are shown above?
   2. Calculate the frequency of the wave
   3. Calculate the periodic time of the wave
7. Sketch the wave form of twice the frequency of the wave above.
8. Electromagnetic waves travels at a velocity of 3.0x10⁸ms^-1 in air, calculate the wavelength in air of radio waves transmitted at a frequency of 200MHz.
9. Wave ripples are caused to travel across the surface of a shallow tank by means of a suitable straight vibrator. The distance between successive crests is 6.0cm and the waves travel 50.4cm in 3.6 seconds. Calculate:
   1. The wavelength
   2. Velocity
   3. Frequency of the vibrator.
10. Water waves are observed as they pass a fixed point at a rate of 30 crests per minute. A particular wave crest takes 2 seconds to travel between two points 6m apart. Determine:
    1. The frequency
    2. The wavelength
11. Calculate the wavelength of the KBC FM radio wave transmitted at a frequency of 95.6MHz
12. The audible frequency range for a certain person is between 30Hz and 16500Hz. Determine the largest wavelength of sound in air the person can detect (speed of sound in air is 333m/s)
13. The figure below represents a displacement-time graph for a wave.
    
    
    1. Determine the frequency of the wave
    2. Sketch on the same axes the displacement-time graph of the wave of same frequency but 180⁰ out of phase and with smaller amplitude.