There are two types of progressive wave, transverse waves, and longitudinal waves.
Transverse waves
In transverse waves, oscillations/vibrations are perpendicular to the direction of energy transfer. They can be in any orientation - up and down, side to side, etc - provided that they occur at right angles to the direction of energy transfer. The peak/trough is where the oscillating particles have maximum displacement from their equilibrium positions. Examples of transverse waves include water waves/electromagnetic waves/waves on a stretched string (e.g a guitar string)/S- waves (produced in earthquakes).
Longitudinal waves
In longitudinal waves, oscillations are parallel to the direction of energy transfer. When they travel through a medium they crease a series of compressions and rarefactions. Examples include sound waves and P-waves (produced in earthquakes). Since the displacement of particles occurs in the same plane as the direction of energy transfer you may be wondering how the restoring forces work. Well lets take sound for an example. Air particles are displaced and bounce off their neighbors - this provides the restoring force. As the wave moves region of higher pressure (compressions) and regions of lower pressure (rarefactions). again, the particles are still oscillating around their equilibrium positions.
Key terms
Okay so there are quite a few key terms we have to commit to memory for this topic - but we will use them loads so i'm sure you'll remember them soon enough:
- Displacement - the distance from the equilibrium position in a particular direction
- Amplitude - the maximum displacement from the equilibrium position
- Wavelength - minimum distance between two points in phase on adjacent waves
- Period (of oscillation) - the time taken for one oscillation/the time taken for a wave to move one whole wavelength past a given point
- Frequency - the number of wavelengths passing a given point per unit time
- Wave speed - the distance travelled by the wave per unit time
NOTE: wavespeed has the unit v, but if we're talking about electromagnetic waves then it has the unit c (for the speed of light, 3 x 10^8 ms^-1).
The wave equations
We can see from the definition above that the frequency of a wave and its period of oscillation are reciprocals of eachother. From this we can form an equation that relates the frequency of a wave to its period:
f = 1 / T
We also know that if a wave has a frequency of say 10Hz, then there are 10 complete oscillations each second. Say we have a wavelength of 1m, this means that the wave has travelled 10m in each second meaning its speed must be 10ms^-1. this means that for a certain frequency the wave has trvelled a distance of f x λ (frequency x wavelength) per second which is equal to the wavelength. From this information we can form another important equation...
V = f λ
Graphical representations
So, like in forces and motion, we can show the displacement of the particles of a wave against the distance along the wave on a displacement-distance graph (this can be called a wave profile). The wave profile can be used to determine the wavelength and amplitude of both longitudinal and transverse waves. The wave profile of a transverse and longitudinal wave will look the same (well, the same shape anyway (sinusoidal), not necessarily the same numbers) because it is a measure of the displacement and distance of the wave/particles NOT how the wave looks.
Phase difference describes the difference in displacements of particles along a wave (or on different waves). One complete cycle is 360° (2π radians). If particles reach their maximum positive (or negative)displacements at the same time they are in phase and their phase difference is zero. Similarly, if one particle reaches its maximum positive displacement at the same time another reaches its maximum negative displacement the particles are in antiphase and their phase difference is 180° (π radians). There is an equation that we can use to determine phase difference:
ϕ = (x/λ) x 360°
We can also use displacement-time graphs to show how the displacement of a given particle varies with time (duh). They look the same for transverse and longitudinal waves. These types of wave can be used to determine the period (and therefore frequency) of a wave.
Oscilloscope experiment
So we need to know techniques and procedures used to use an oscilloscope to determine frequency. Basically, using the set up below we can see that using a microphone produces a trace on the oscilloscope screen. Each horizontal square on the screen represents a certain time interval known as the timebase. This is set to a certain ms cm^-1 (e.g 10 ms cm^-1) - this means that each square represents a time interval of 10 mc cm^-1. The up/down squares represent the y sensitivity which is measured in V cm^-1. E.g a setting of 10 V cm^-1 means that each square will represent a pd. of 10V. Using the timebase we can do f = 1/T to determine the frequency.
Reflection, refraction, polarisation, and diffraction.
Reflection: this occurs when a wave changes direction at a boundary between two different media but remains in he original medium. The law of reflection states that whenever waves are reflected the angle of incidence is equal to the angle of reflection. When waves are reflected their frequency and wavelength do not change.
Refraction: this occurs when a wave changes direction as ti changes speed when it passes from one medium to another. There is always some refection off the surface (partial reflection).If a wave slows down as it enters the medium it will refract toward the normal, if it speeds up it will refract away from the normal. Sound waves speed up when they enter a denser medium whereas electromagnetic waves usually slow down. Since the speed of the waves changes and frequency is constant, this means that wavelength also changes as V = f λ. water waves can also be refracted - when a water wave enters a shallower bit of water is slows down and it's wavelength gets shorter.
Diffraction: this is the spreading out of a wave as it passes through a gap/travels around an obstacle. ALL waves can be diffracted and the speed, wavelength, and frequency are all constant (they do not change). The effects of diffraction are most significant when the gap the wave travels through is the same as the waves wavelength.
Polarisation: this means that the particles oscillate in one plane only. We cannot polarise longitudinal waves as their oscillations already act in one plane only (the direction of energy transfer). If a wave is plane polarised its oscillations occur in one plane only (e.g some sunglasses contain polarising filters so you can only see in one plan only). Partial polarisation can also occur (this happens when transverse waves reflect off a surface). This means that more waves oscillate in one particular plane compared to others/another but they wave is not completely plane polarised.
Most naturally occurring electromagnetic waves are unpolarised. we can polarised them using polarising filters (each filter only allows waves with a particular orientation of oscillations through). We need to know how to observe polarising effects with microwaves and light:
- Unpolarised microwaves can be polarised by placing a metal grille in front of the transmitter (in between the transmitter and the receiver).
- If you take two pieces of polaroid filter and place them together (at right angled orientations to each other) you can nicely see the effect of polarisation. Unpolarised light travels through the first filter and becomes plane polarised. It cannot pass through the second filter as the second filter is not in the same plane as the first (it is 90° sideways). This means that the intensity of the light transmitted drops - no light is in fact transmitted through the second filter and the intensity falls to zero.
NOTE: think we need to know what wave fronts are, they are just lines joining all the points on a wave that are in phase
Intensity
This nicely leads me on to intensity. The intensity of a progressive wave is the radiant power passing through a surface per unit area. It has the units W m^-2 and is calculates with the following equation:
I = P/A
where A is the cross sectional area of the surface, P is the radiant power passing through the surface, and I is the intensity of the wave at the surface.
for a point source the radiant power will spread out uniformly in all directions (e.g over the surface of a sphere). This makes the equation I = P / (4πr²). From this we can see that intensity has an inverse square relationship with the distance from the source.
Intensity drops as the energy becomes more spread out and the wave height (amplitude) decreases. Decreased amplitude means a reduced average speed of the oscillating particles. For example, if you were to half th amplitude you would have particles that oscillate with half the speed which means a quarter of the kinetic energy and energy is proportional to intensity so intensity is proportional to amplitude squared...
intensity ∝ (amplitude)²
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