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Topic 5:
Topic 5:
Waves and Particle Nature of Light
Definitions:
Amplitude | A waves maximum displacement from the equilibrium position. |
|---|---|
Frequency (f) | The number of complete oscillations passing through a point per second. |
Period (T) | The time taken for one full oscillation. |
Speed (v) | The distance travelled by the wave per unit time. |
Wavelength (𝛌) | The length of one whole oscillation.Eg: the distance between successive peaks/troughs. |
Wave Equation:
The speed (v) of wave is equal to the wave’s frequency multiplied by its wavelength
Longitudinal Waves:
In longitudinal waves the oscillation of particles is parallel to the direction of energy transfer.
These are made up of compressions and rarefactions and can’t travel in a vacuum.
Sound is an example of a longitudinal wave, and they can be demonstrated by pushing a slinky horizontally.
Stage | Rarefaction | Compression |
|---|---|---|
Pressure | Decreased | Increased |
Displacement of particles | Neighbouring particles move away from each other | Neighbouring particles move towards a point |
Transverse Waves:
In transverse waves the oscillation of particles (or fields) is parallel to the direction of energy transfer.
All electromagnetic (EM) waves are transverse and travel at
in a vacuum.
Transverse waves can be demonstrated by shaking a slinky vertically or through the waves seen on a string, when its attached to a signal generator.
Graphs of Transverse and Longitudinal Waves:
There are two types of graphs which can be used to represent waves:
Displacement-distance graphs - these show how the displacement of a particle varies with the distance of wave travel and can be used to measure wavelength.
For a transverse wave, the displacement-distance graph will look very similar to the actual wave, whereas for a longitudinal wave the graph will look very different from the wave.
Displacement-time graphs - these show how the displacement of a particle varies with time and can be used to measure the period of a wave.
Further Definitions:
Phase | The position of a certain point on a wave cycle. This can be measured in radians, degrees or fractions of a cycle. |
|---|---|
Phase difference | How much a particle/wave lags behind another particle/wave. This can be measured in radians, degrees or fractions of a cycle. |
Path Difference | The difference in the distance travelled by two waves. |
Superposition | Where the displacements of tho waves are combined as they pass each other, the resultant displacement is the vector sum of each wave’s displacement. |
Coherence | A coherent light source has the same frequency and wavelength and a fixed phase difference. |
Wavefront | A wavefront is a surface which is used to represent the points of a wave which have the same phase. |
As an example of a wavefront, consider a rock being dropped into a pond, the peak of a each ripple formed can be considered as a wavefront. This is shown in the diagram.
There are two types of interference that can occur during superposition and they are:
Constructive interference: this occurs when two waves are in phase and so their displacements are added.
Destructive interference: this occurs when the waves are completely out of phase and so their displacements are subtracted.
The image to the left shows the interference of two waves (which are pictured below the resultant wave). On the left is constructive interference and on the right is destructive interference.
Phase difference and path difference:
Two waves are in phase if they are both at the same point of the wave cycle, meaning they have the same frequency and wavelength (are coherent) and their phase difference is an integer multiple of 360° (2𝝅 radians). The waves do not need to have the same amplitude only the same frequency and wavelength.
Two waves are completely out of phase when they have the same frequency and wavelength (are coherent) and their phase difference is an odd integer multiple of 180 degrees (𝝅 radians).
The phase difference (in radians) of two waves with the same frequency and their path differences are related as shown below:
Where is the path difference,
is the wavelength of the waves and
is their phase difference.
Below is an example question where you have to use the above relation.
Two waves have a path difference of 6m and both have a wave length of 2m, what is the difference of these two waves?
Firstly rearrange the above relation so that the phase difference is the subject.
Then, substitute in the given values
And so, their phase difference is 6 . As 6
is a multiple of
, the waves must be in phase.
Stationary waves
A stationary wave (also known as a standing wave) is formed from the superposition of 2 progressive waves, travelling in opposite directions in the same plane, with the same frequency, wavelength and amplitude.
No energy is transferred by a stationary wave
Where the waves meet:
-> In Phase: constructive interference occurs so antinodes are formed, which are regions of maximum displacement.
-> Completely out of phase: destructive interference occurs and nodes are formed, which are regions of no displacement.
A string fixed at one end, and fixed to a driving oscillator at the other gives you a good example of the formation of a stationary wave:
A wave travelling down the string from the oscillator will be reflected at the fixed end of the string and travel back along the string causing superposition of the two waves. Because the waves have the same wavelength, frequency and amplitude, a stationary wave is formed
Standing waves can also be represented on displacement-distance graphs like the one on the right.
NoteStudied by 13063 peopleNoteStudied by 44164 peopleNoteStudied by 124 peopleNoteStudied by 21 peopleNoteStudied by 4 peopleNoteStudied by 18 people