- 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. Electromagnet 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.
- What is a progressive wave?
It is a wave that moves continualy away from the source.
- 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.
- Diferentiate between electromagnetic and mechanical wave giving one example in each
- State two categories of waves.
- State two types of mechanical waves. State the difference between them.
- Give two examples of mechanical waves.
- 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.
- 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.
- 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.
- 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.
- Period,T- it’s the time taken by a particle to complete one oscillation. SI unit of period is the second(s)
- 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
- 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.
The figure below shows a displacement-time graph of a wave travelling at 2500cms-1
Determine for the wave:
A = maximum displacement from mean position
=3cm OR 0.03m in SIunits
b) Periodic time
T=(9-1) x 10s-3s
d) Wave length
- State the wave formula
- Sketch the variation of frequency with wavelength given that speed of the wave remains constant
- Name two types of progressive wave motion.
- 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.
- A water wave travels 2m in 5 seconds. If the frequency of the wave is 10Hz, calculate the:
- Speed of the wave
- Wave length of the wave
- The diagram below shows a displacement-time graph for a certain wave.
- How many oscillations are shown above?
- Calculate the frequency of the wave
- Calculate the periodic time of the wave
- Sketch the wave form of twice the frequency of the wave above.
- 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.
- 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:
- The wavelength
- Frequency of the vibrator.
- 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:
- The frequency
- The wavelength
- Calculate the wavelength of the KBC FM radio wave transmitted at a frequency of 95.6MHz
- 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)
- The figure below represents a displacement-time graph for a wave.
- Determine the frequency of the wave
- Sketch on the same axes the displacement-time graph of the wave of same frequency but 1800 out of phase and with smaller amplitude.