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MODULE 4.4: WAVES
By Suhayl Patel – SP RESOURCES
SUHAYL PATEL
NCS6
![](https://csdnimg.cn/release/download_crawler_static/89243186/bg2.jpg)
Suhayl Patel
WAVE MOTION: Part 1
1. Progressive Waves: is a transfer of energy, as a result of oscillations of the source
a. Progressive waves are produced by a series of vibrations or oscillations of electric
and magnetic fields. Progressive waves transfer energy from one place to another
without transferring any material. The transfer of energy is the same direction as the
direction of the wave is travelling. Since waves carry energy away, the source of the
wave loses energy.
2. Longitudinal Waves: A wave where displacement/oscillation (of particles) is parallel to the
direction of energy transfer.
a. Example: Sound waves
b. Longitudinal waves have areas of compression and rarefaction:
c. A compression is a region in a longitudinal wave where the particles are closest
together.
d. A rarefaction is a region in a longitudinal wave where the particles are furthest
apart.
3. Transverse Waves: A wave where displacement/oscillation (of particles) is perpendicular to
the direction of energy transfer.
a. Examples: surface water waves, waves on a string, electromagnetic waves.
4. Transverse waves can be represented on a graph in two different ways:
a. On a displacement – distance graph
i. This graph shows the displacement of many particles from
different points, at an instant in time, from their equilibrium
positions.
b. On a displacement – time graph
i. This graph shows the displacement of one particle from its
equilibrium position, measured at the same position but at
different times.
5. Displacement, x: distance moved from the equilibrium position by a point/particle on a
wave. Measured in metres (m).
6. Amplitude, A: Maximum displacement from the equilibrium position (caused by wave
motion). Measured in metres (m).
7. Wavelength, λ: distance between (neighbouring) identical points/points with same phase
(on the wave). Measured in metres (m).
8. Period, T: The time taken for a whole cycle/oscillation
to complete. Measured in seconds (s)
9. Phase difference: How far through a cycle one point is
compared to the other. The comparison is between
two points on the same wave of the same frequency,
or on the same wave. Measured in degrees or radians.
![](https://csdnimg.cn/release/download_crawler_static/89243186/bg3.jpg)
Suhayl Patel
10. Frequency, f: number of complete cycles passing a point per unit time/second. Measured in
Hertz (Hz)
11.
a. Where F is the frequency measured in Hertz.
b. Where T is the Period time measured in seconds
12. Hertz: 1 Hz = 1 s
-1
13. Speed of a wave: distance travelled by the wave per unit time
14.
a. Where v is speed measured in ms
-1
b. Where f is the frequency measured in Hz
c. Where λ is the wavelength measured in m
d. This is called the wave equation
15. Deriving the Wave Equation:
a. You can work out the wave equation by imaging how long it takes for the crest of a
wave to move across a distance of one wavelength. The distance travelled is λ. By
definition the time taken to travel one whole wavelength is the period of the wave
which is equal to 1/f
b.
16. Oscilloscopes:
a. A cathode ray oscilloscope measures voltage. It displays waves from a single
generator as a function of voltage over time.
b. The displayed wave is called a trace.
c. The vertical axis is in volts. The volts per division shown on this axis is controlled by
the gain dial.
d. The horizontal axis is in seconds. Also called the timebase. The seconds per division
is controlled by the timebase dial.
e. Different sources produce different traces.
i. An AC supply produces a wave similar to the sine/cosine wave.
ii. A microphone converts sound waves into electrical signals which can be
seen on an oscilloscope.
f. Calculating Frequency of a wave from an oscilloscope: The time period should be
calculated from an oscilloscope trace taking care to make any unit conversions so
time is in seconds. The frequency of a wave can be calculated using 1/T
17. The following can be calculated from a displacement – distance graph:
a. Amplitude
b. Wavelength
c. Displacement
d. Phase difference
![](https://csdnimg.cn/release/download_crawler_static/89243186/bg4.jpg)
Suhayl Patel
18. The following can be calculated from a displacement – time graph:
a. Frequency
b. Time period
c. Amplitude
19. Phase Difference:
a. Phase difference relates how far out of step the oscillations/displacements of two
particles along a wave, or between particles on different waves are.
b. A complete cycle is represented by 360
o
or 2π radians.
c. If particles reach their maximum positive displacement at the same time then they
are described as in phase. They have a difference of zero.
d. If two particles are separated by a distance of a whole wavelength, we say their
phase difference is 360
o
or 2π radians.
e. If they are two complete cycles out, the phase difference is 720
o
or 4π radians, and
so on.
f. Two particles are out of phase when one reaches its maximum positive
displacement as the same time as the other reached its maximum negative
displacement.
g. Particles out of phase have the phase difference of 180
o
or π radians.
20.
a. The phase difference between two points on a wave of wavelength separated
by a distance, is given by the above two formulae.
21. Reflection:
a. Reflection occurs when a wave changes direction at a boundary
between two different media, whilst remaining in the original
medium.
b. Law of reflection:
i. the angle of incidence = the angle of reflection
ii. Incident ray, reflected ray and normal all lie in the same
plane
c. Angles are measured to the normal
d. When waves are reflected, their wavelength and frequency remains unchanged.
22. Demonstrating reflection with a ripple tank:
a. Set up the ripple tank so that the oscillating paddle is creating regular waves with
straight, parallel wave fronts. Place a barrier in the tank at an angle to the wave
fronts.
b. The angle the incoming waves make with the normal to the barrier is the angle of
incidence.
c. After being reflected. The angle between the reflected waves and the normal to the
barrier is called the angle of reflection.
d. These two angles are always equal to each other.
![](https://csdnimg.cn/release/download_crawler_static/89243186/bg5.jpg)
Suhayl Patel
23. Refraction:
a. Refraction occurs when a wave changes direction as it changed speed, when it
passes from one medium to another.
b. Whenever a wave refracts there is always
some partial reflection.
c. If the ray bends towards the normal – it is
slowing down.
d. If the ray bends away from the normal – it is
speeding up.
e. E.M waves slow down when entering a denser
medium. Sound waves speed up when
entering a denser medium.
f. If a wave slows down its wavelength decreases, and if it speeds up the wavelength
increases. The frequency remains unchanged in both cases.
g. Laws of refraction:
i. Incident ray, refracted ray and normal all lie in the same plane
ii. The ratio of sini/sinr is constant
24. Diffraction:
a. The spreading out of wave-fronts after passing through or around an obstacle.
b. How much a wave diffracts depends on the relative sizes of the wavelength and the
gap or obstacle.
c. When a wave diffracts, its wavelength does not change.
d. Diffraction effects become significant when the wavelength is comparable to the gap
width.
e. All waves diffract. In order to see the diffraction of light, we need a much smaller
gap.
25. Demonstrating Diffraction with a ripple tank:
a. Ripple tanks are shallow tanks of water that you can
generate a wave in.
b. A constant wave can be produced by an oscillating paddle.
c. A barrier with a gap is then placed.
i. When the gap is a lot bigger than the wavelength,
then diffraction is unnoticeable.
ii. The amount of diffraction increases as the gap is
made smaller and smaller.
iii. Maximum diffraction occurs when the gap is the
same size as the wavelength.
iv. This proves diffraction as water waves are seen
outside the ‘geometrical shadow’ region produced
by the barrier, and therefore showing diffraction.
26. Polarisation:
a. The process of turning an un-polarised wave into a plane polarised wave.
b. Only transverse waves can be polarised.
c. Longitudinal waves cannot be polarised.
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