Class Code:

node25

Wave Physics

~ July 16th 2021: Lesson 3 ~

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Daryna and Edward

Review + Questions

• Crest, trough (transverse), rarefactions, compressions (longitudinal) are most common parts of waves
• Frequency = number of crests that pass a point in unit time
• Period = number of seconds per wave
• Velocity of a wave: v = fλ
• Waves are shaped as a sinusoidal graph
• Position of wave dependent on time = Amplitude × sin((2π × frequency × time) + phase constant)

Activity

• https://www.physicsclassroom.com/Physics-Interactives/Waves-and-Sound/Wave-Addition/Wave-Addition-Interactive
• use the 'construct' and 'destruct' buttons and observe what happens to the resultant wave
• click 'bar' to see the amplitude of each individual and the resultant waves
• come up with a definition for two constructive waves and two destructive waves
• double the frequency of one wave, see what happens
• experiment with the shapes of the waves to see how they interfere with each other
• change the transverse waves to longitudinal and see if and how the observations above change

Overlying question: what happens when two individual waves traveling through the same medium interact with one another?

Superposition Principle

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Resultant amplitude of 2 propagating waves is the vector sum of the individual amplitudes of the wave

Constructive interference: 2 maxima’s of a wave add together

Destructive interference: the maxima’s of the waves are 180% out of phase

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Superposition Principle

• Superposition principle still true in higher dimensions
• Wave interference used to understand other outcomes of wave behaviors
• Waves entering different phases
• Reflection
• Huygens Principle

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Waves in 2D + 3D Space

1D: wave on string

2D: ripples on water

3D: electromagnetic waves

• Phi = wave function
• K = wave number
• Omega = angular frequency
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x, t depends on single Cartesian coordinate; x, y, t on two; x, y, z, t on three

ψ(x, y, t) = A sin(k_xx) sin(k_yy) cos(ωt + φ)

Reflection

Reflection occurs when waves hit an obstacle and bounce off:

Specular Reflection = Smooth surface (mirror)

Diffuse Reflection = Rough surface

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Angle of incidence = Angle of reflection

Refraction

Refraction occurs when a wave changes speed:

Going from faster to slower speed, angle from normal decreases (more vertical)j

Opposite happens from slower to faster speed

Snell’s law: v₁ = velocity in air, v₂ = velocity in water

Diffraction

Diffraction occurs when a wave bends around an obstacle:

Huygens’ Principle: Every point on a wavefront is a source of waves itself.

Wavefront = all points at the same phase (e.g. all the crests of a wave)

Doppler Effect

Doppler Effect is change in frequency when source or receiver is moving:

When source and receiver are getting closer, higher frequency.

Opposite when source and receiver traveling away

Ex. Sound from a vehicle moving towards you is higher than when moving away.