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C.2 Wave Model

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2024/07/05 08:37
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C.2.1 Traveling waves, wave properties, transverse and longitudinal waves

Key Terms
Terminology
Definition
oscillating source
sources that generates waves in certain directions
electromagnetic waves
waves of the electromagnetic field which can travel through vacuum
medium
Matter that mechanical waves uses for passing through
crest
point on a wave that has the maximum value of upward displacement
Traveling waves
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continuous disturbance in a medium that travels in the direction of propagation
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Energy is transferred by waves, but matter is not transferred by waves
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Waves are generated by oscillating sources
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Oscillations can propagate through a medium or in vacuum, depending on the type of wave
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Direction of a wave is defined as the direction of the propagation of energy
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continuous waves → succession of individual oscillations, wave pulse → one oscillation
C.2.1-1 Graph showing the progression of travelling wave
Types of Waves (Transverse / Longitudinal)
Real life Examples
Transverse
Water ripples: ‘up and down’ motion of the floating object
Longitudinal
Sound waves
Light waves
Compression waves down a spring
Transverse waves
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crest: top of the wave; trough: bottom of the wave
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wavefronts: parts of the wave that are moving together; indication of wave pattern movement
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rays: indication of the direction of energy transfer
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Direction of particle oscillation is perpendicular to the direction of energy transfer
C.2.1-2 annotated graph of transverse wave
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Transverse mechanical waves cannot be propagated through fluids
Longitudinal waves
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Direction of particle oscillation is parallel to the direction of motion and direction of energy transfer
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Compression: point on the wave with high pressure with the particles being closer to each other
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Rarefaction: point on the wave with low pressure with the particles being further apart from each other
C.2.1-3 annotated graph of longitudinal wave
Wave equations
c=distancetime=λT∴1T=f,c=fλ velocity=frequency×wavelengthc = \frac{\textit{distance}}{\textit{time}} = \frac{\lambda}{T}\\ \therefore \frac{1}{T} = f, \quad c = f\lambda \\  \textit{velocity} = \textit{frequency} \times \textit{wavelength}
Wave Graphs
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There are two types of graphs that represents the wave
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can be represented by displacement - distance graph and displacement - time graph
Displacement - Distance Graph
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represents displacement of particles on the wave at a fixed time
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formed by distance traveled by wave and displacement of particles
C.2.1-4 Displacement- Distance wave graph with key terms annnotated
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can observe value of amplitude and wavelength from the graph
Displacement - Time Graph
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Represents variation of the displacement of one particle with time
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formed by time and displacement of particles
C.2.1-5 Displacement - time wave graph with key terms annotated
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can observe value of period and amplitude from the graph

C.2.2 The nature of electromagnetic waves

Electromagnetic Waves : wave that is generated by combined oscillation of an electric and a magnetic field
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Electric and magnetic field oscillate perpendicular to each other and to the direction of wave propagation
C.2.2-1 Diagram of electromagnetic wave
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All electromagnetic (EM) waves travel at the speed of
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c=3108ms-1 in vacuum
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EM waves are transverse waves
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EM waves form a continuous spectrum based on their frequency
C.2.2-2 alined diagram of waves in their wavelength
Wavelength of Electromagnetic Waves
Electromagnetic Wave
Wavelength (m)
radio wave
>10−3>10^{-3}
microwave
1⋅10−3 2.5⋅10−51\cdot10^{-3} ~ 2.5\cdot10^{-5}
infrared
2.5⋅10−5 7⋅10−72.5\cdot10^{-5} ~ 7\cdot10^{-7}
visible light
7⋅10−7 4⋅10−77\cdot10^{-7} ~ 4\cdot10^{-7}
ultraviolet
4⋅10−7 1⋅10−94\cdot10^{-7} ~ 1\cdot10^{-9}
X-ray
1⋅10−9 1⋅10−121\cdot10^{-9} ~ 1\cdot10^{-12}
gamma ray
<10−12<10^{-12}

C.2.3 The nature of sound waves

Sound Waves
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Sound waves travel at the speed of approximately 343.2ms-1 (in 20 degrees Celsius dry air).
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Sound waves are longitudinal waves, so requires a medium in which to propagate
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Since the sound wave is longitudinal wave, as the sound wave travels series of compression and rarefactions happens
C.2.3-1 Diagram of sound wave
Factors of Sound Waves
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Nature of material
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Density
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Temperature (c ∝ T for an ideal gas)
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Humidity (for air)