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Electromagnetic Wave
Electromagnetic waves are created by a fusion of electric and magnetic fields. The light you see, the colours around you are visible because of electromagnetic waves.
One interesting property here is that unlike mechanical waves, electromagnetic waves do not need a medium to travel. All electromagnetic waves travel through a vacuum at the same speed, 299,792,458 ms-1.
Following are the different types of electromagnetic waves:
- Microwaves
- X-ray
- Radio waves
- Ultraviolet waves
Graphing a Wave
When drawing a wave or looking at a wave on a graph, we draw the wave as a snapshot in time. The vertical axis is the amplitude of the wave while the horizontal axis can be either distance or time.
In this picture you can see that the highest point on the graph of the wave is called the crest and the lowest point is called the trough. The line through the center of the wave is the resting position of the medium if there was no wave passing through. We can determine a number of wave properties or characteristics from the graph.
Characteristics of Waves
- All waves have speed which depends on the nature of disturbance.
- All waves have wavelength (distance between two successive points in a wave ).Represented by the symbol λ and is measured in metres.
- All waves have frequency ‘f’ which is the number of waves passing a point in one second. It is measured in cycles per second or hertz (Hz).
The period of a wave is the time required for a complete wave to pass a given point.
Therefore T = 1 / f or f = 1 / T (period is measured in seconds).
The speed ‘v’ is given as; v = λ / T, since f = 1 / T then
v = (1 / T) × λ = f λ or v = f λ. This is the wave equation.
- All waves have amplitude which is the maximum displacement of the particles of the medium as the wave passes.
- Amplitude
The amplitude of a wave is a measure of the displacement of the wave from its rest position. The amplitude is shown on the graph below.
Amplitude is generally calculated by looking on a graph of a wave and measuring the height of the wave from the resting position.
The amplitude is a measure of the strength or intensity of the wave. For example, when looking at a sound wave, the amplitude will measure the loudness of the sound. The energy of the wave also varies in direct proportion to the amplitude of the wave.
Wavelength
The wavelength of a wave is the distance between two corresponding points on back-to-back cycles of a wave. This can be measured between two crests of a wave or two troughs of a wave. The wavelength is usually represented in physics by the Greek letter lambda (λ).
Frequency and Period
The frequency of a wave is the number of times per second that the wave cycles. Frequency is measured in Hertz or cycles per second. The frequency is often represented by the lower case “f.”
The period of the wave is the time between wave crests. The period is measured in time units such as seconds. The period is usually represented by the upper case “T.”
The period and frequency are closely related to each other. The period equals 1 over the frequency and the frequency is equal to one over the period. They are reciprocals of each other as shown in the following formulas.
period = 1/frequency
or
T = 1/f
frequency = 1/period
or
f = 1/T
Speed or Velocity of a Wave
Another important property of a wave is the speed of propagation. This is how fast the disturbance of the wave is moving. The speed of mechanical waves depends on the medium that the wave is traveling through. For example, sound will travel at a different speed in water than in air.
The velocity of a wave is usually represented by the letter “v.” The velocity can be calculated by multiplying the frequency by the wavelength.
velocity = frequency X wavelength
or
v = f X λ
Examples
- A rope is displaced at a frequency of 3 Hz. If the distance between two successive crests of the wave train is 0.8 m, calculate the speed of the waves along the rope.
Solution
v = f λ = 3 × 0.8 = 2.4 m Hz = 2.4 m/s.
- The figure below illustrates part of the displacement-time graph of a wave travelling across water at a particular place with a velocity of 2 ms-1. Calculate the wave’s;
- a) Amplitude
- b) Frequency (f)
- c) Wavelength (λ)
Solution
- a) From the graph, maximum displacement (a) = 0.4 cm
- b) From the graph, period T = time for one cycle = 0.20 seconds
So f = 1 / T = 1 / 0.20 = 5 Hz.
- Velocity = f λ hence λ = 2 / 5 = 0.4 m.
e
Electromagnetic waves are created by a fusion of electric and magnetic fields. The light you see, the colours around you are visible because of electromagnetic waves.
One interesting property here is that unlike mechanical waves, electromagnetic waves do not need a medium to travel. All electromagnetic waves travel through a vacuum at the same speed, 299,792,458 ms-1.
Following are the different types of electromagnetic waves:
- Microwaves
- X-ray
- Radio waves
- Ultraviolet waves
Graphing a Wave
When drawing a wave or looking at a wave on a graph, we draw the wave as a snapshot in time. The vertical axis is the amplitude of the wave while the horizontal axis can be either distance or time.
In this picture you can see that the highest point on the graph of the wave is called the crest and the lowest point is called the trough. The line through the center of the wave is the resting position of the medium if there was no wave passing through. We can determine a number of wave properties or characteristics from the graph.
Characteristics of Waves
- All waves have speed which depends on the nature of disturbance.
- All waves have wavelength (distance between two successive points in a wave ).Represented by the symbol λ and is measured in metres.
- All waves have frequency ‘f’ which is the number of waves passing a point in one second. It is measured in cycles per second or hertz (Hz).
The period of a wave is the time required for a complete wave to pass a given point.
Therefore T = 1 / f or f = 1 / T (period is measured in seconds).
The speed ‘v’ is given as; v = λ / T, since f = 1 / T then
v = (1 / T) × λ = f λ or v = f λ. This is the wave equation.
- All waves have amplitude which is the maximum displacement of the particles of the medium as the wave passes.
- Amplitude
The amplitude of a wave is a measure of the displacement of the wave from its rest position. The amplitude is shown on the graph below.Amplitude is generally calculated by looking on a graph of a wave and measuring the height of the wave from the resting position.
The amplitude is a measure of the strength or intensity of the wave. For example, when looking at a sound wave, the amplitude will measure the loudness of the sound. The energy of the wave also varies in direct proportion to the amplitude of the wave.
Wavelength
The wavelength of a wave is the distance between two corresponding points on back-to-back cycles of a wave. This can be measured between two crests of a wave or two troughs of a wave. The wavelength is usually represented in physics by the Greek letter lambda (λ).
Frequency and Period
The frequency of a wave is the number of times per second that the wave cycles. Frequency is measured in Hertz or cycles per second. The frequency is often represented by the lower case “f.”
The period of the wave is the time between wave crests. The period is measured in time units such as seconds. The period is usually represented by the upper case “T.”
The period and frequency are closely related to each other. The period equals 1 over the frequency and the frequency is equal to one over the period. They are reciprocals of each other as shown in the following formulas.
period = 1/frequency
or
T = 1/f
frequency = 1/period
or
f = 1/T
Speed or Velocity of a Wave
Another important property of a wave is the speed of propagation. This is how fast the disturbance of the wave is moving. The speed of mechanical waves depends on the medium that the wave is traveling through. For example, sound will travel at a different speed in water than in air.
The velocity of a wave is usually represented by the letter “v.” The velocity can be calculated by multiplying the frequency by the wavelength.
velocity = frequency X wavelength
or
v = f X λ
Examples
- A rope is displaced at a frequency of 3 Hz. If the distance between two successive crests of the wave train is 0.8 m, calculate the speed of the waves along the rope.
Solution
v = f λ = 3 × 0.8 = 2.4 m Hz = 2.4 m/s.
- The figure below illustrates part of the displacement-time graph of a wave travelling across water at a particular place with a velocity of 2 ms-1. Calculate the wave’s;
- a) Amplitude
- b) Frequency (f)
- c) Wavelength (λ)
Solution
- a) From the graph, maximum displacement (a) = 0.4 cm
- b) From the graph, period T = time for one cycle = 0.20 seconds
So f = 1 / T = 1 / 0.20 = 5 Hz.
- Velocity = f λ hence λ = 2 / 5 = 0.4 m.