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'Universe without Color' Chapter 1 Theory Section

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'Universe without Color' Chapter 1 Theory Section

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The DP physics theory behind 'What if electromagnetic waves only had one wavelength?'

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In the real world, simple harmonic motion may be interupted by external forces. For example, air resistance damps a pendulum.

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A force that is caused by density differences and gravity

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A stable position in a SHM system where the object will not move. For example, the lowest point in a pendulum is the equilibrium point.

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The distance between the peaks and equilibrium. The distance between peaks and troughs is 2a.

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Energy carried by a massive moving object, such as a car.

*Edit: Inertia refers to the behavior described in Newton's first law, where a resting object will not move, and a moving object will move at a constant velocity in a constant direction, unless another force acts on it.

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Use the instructions from today’s slides carefully (What? So what? Now what?)

Musical Instruments and Wave Behavior

What - Musical instruments uses longitudinal waves (Wind and brass instruments) or transverse waves (string instruments) to create standing waves. All instruments are driven damped oscillators, since there is always someone blowing/plucking/bowing on one end, and that the vibrations are converted to sound and emitted.

So What - Musical instruments are very important in our lives because much of the human culture is based on music. In early times when electronics didn't exist, the only way for people to create music is through these systems.

Now What -

1. What does over damping sound like on a string?

2. How does plucking or bowing drive the oscillation?

3. What happens if you drive an oscillation away from its natural frequency?

Question 1 (Paper 1a - Multiple Choice)

A flute can be modeled as a pipe open at both ends. The fundamental frequency produced by the flute is 440 Hz when the air temperature is 20°C. What is the approximate length of the flute?

A. 0.20 m
B. 0.39 m
C. 0.78 m
D. 1.32 m

Question 2 (Paper 2 - Extended Response)

A guitar string is fixed at both ends and vibrates in its second harmonic mode. The string has a length of 0.65 m and produces a note with frequency 392 Hz (G4).

(a) Sketch the standing wave pattern on the string for this mode. [2]

(b) Derive an expression for the frequency of the nth harmonic of a string fixed at both ends in terms of tension T, linear mass density μ, and length L. [4]

(c) Using your expression, calculate the tension in the string if it has a linear mass density of 6.3×10^−4 kg/m. [3]

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A process in which energy is converted and released

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Simple Harmonic vs Damped Harmonic oscillations

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Simple Harmonic vs Damped Harmonic oscillations

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Simple:

-Yes, only the restoring force exists.

-No dissapative forces

-Amplitude remains constant

-0.5kx^2*

-Total energy remains constant

-Energy is not lost

-Displacement/Time is a regular wave

-ma+kx=0 *

-Not a lol of real world examples.

Damped:

-No, because there are dissapative forces.

-There are dissapative forces like friction

-Amplitude decreases over time

-0.5kx^2, but ET decreases over time

-Energy decreases over time

-Energy is converted into heat, sound, etc.

-Displacement/Time shows a wave with amplitude decreasing over time

-ma+kx+bv=0, where b is the damping coefficient *

-Examples include shock absorbers and mass dampers

* Needs reviewing

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*Use school account

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Travelling waves transfer energy, while standing waves don't.

Travelling waves oscillate at every point, while standing waves have nodes andn antinodes.

Travelling waves travel, while standing waves are trapped between 2 boundaries.

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Research Questions:

How does changing the difference in frequency affect the frequency of the wave caused by constructive and destructive interference?

How do harmonics affect the amplitude, provided the energy remains the same?

How does pipe width affect the resonance frequency if the length stays constant?

Reflection:

I think the tuning forks were the most interesting, because of their resonating behavior as well as your abillity to tune them using a weight. One thing that surprised me was the constructive destructive interference experiment that I did with the two tuning forks, with one tuned slightly lower than the other. I was not expecting the oscillation to be so obvious. The research question that I am the most interested in is the first one that I wrote.

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Standing waves inside the microwave has nodes, which are cold spots. Having a rotating plate causes the food to get heated more evenly.

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These waves don't need a medium. Examples include EM waves.

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Phase angle refers to a measure of how much the wave moved, or how much a wave is out of phase compared to another wave. It is measured in radians. For example, if Wave 1's peaks coincide with Wave 2's troughs, their phase angle is pi rads.

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Wavefronts is a way to show wave behavior, where a line is drawn over the peaks of the waves to from parallel lines. Wavefronts can show waves travelling.

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A phenomenon where a material allows a ray to travel through.

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In short, nope. In order for light to change color, energy must be added or subtracted. Moreover, we percieve light based on frequency, and frequency doesn't change when velocity decreases.

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1. The double slit experiment. Construcive and destructive interference sounds very interesting.

2. Total internal reflection.

3. Refraction and reflection.

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A wave source (light, electron gun, etc) is placed in front of a plate with a thin slit. Behind the first plate sits a second plate with 2 slits. If a photographic plate is placed behind the second plate, an interference pattern can be observed.

Constructive interference happens when 2 waves intersect and double up, while destructive interference happens when two opposite waves (peak and trough) meets and cancels each other out.

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C3 HL Diffraction Formative WORKED SOLUTIONS

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Single Slit Diffraction (Common Misconceptions)

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Single Slit Diffraction (Common Misconceptions)

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Double Slit Diffraction (Common Misconceptions)

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Double Slit Diffraction (Common Misconceptions)

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Single and Double Slit WHAT IF Questions

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Single and Double Slit WHAT IF Questions

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fringe spacing (s) vs distance along the screen (y)

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fringe spacing (s) vs distance along the screen (y)

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The max n value can be found by substituting theta=90.

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Between two principal maxima, there are n-1 minima and n-2 secondary maxima. N refers to the number of slits in a diffraction grating.

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Longer wavelengths diffract more, and higher n numbers also diffract more.

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Data Analysis Task (Connecting C5 with E5: Fusion & Stars)

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Data Analysis Task (Connecting C5 with E5: Fusion & Stars)

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When a wave emitting object moves towards or away from an observer, the waves stretch or compress.

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Which component of relative velocity do we consider?

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Which component of relative velocity do we consider?

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Component of the relative velocity parallel to the line of sight.

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d Sin(Theta) is the formula for the path difference.

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R: Nucleus radius

R0: Radius of a singular nucleon (fermi radius)

V: Volume of nucleus

Rho: Density (constant)

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How can energy conservation be used to derive the borh energy levels?

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How can energy conservation be used to derive the borh energy levels?

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Intensity (I) measures the energy radiation per unit of area using Watts per square meters. I equals P/A

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Specific Latent Heat refers to the amount of energy needed to melt/freeze or boil/condense a substance without changing the temperature. The melt/freeze value is known as Lfusion, and the boil/condense value is known as Lvaporization.

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The Solar Constant is the intensity of the sun's rays, recived at Earth's location.

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Emissivity measures how an object radiates radiation, and albedo measures how well an object reflects radiation.

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Kirchhoff's law states that the total current (incoming and outgoing current) in a parallel circuit is equal to all the parallel loads added together.

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Due to the binding energy of nucleons, a free nucleon is more massive than a bound one.

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The exact binding energy of the nucleus can be calculated by using this formula. Take mass as the change in mass between free and bound particles.

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The strong force is only attractive at really short ranges, and some particles may be out of range in large nuclei. Therefore, more neutrons are needed as force carriers, since they don't repel each other like protons.

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Isothermal vs Adiabetic processes on PV diagram

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Isothermal vs Adiabetic processes on PV diagram

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Isothermal:Slow, P -> 1/V

Adiabetic: Really quick, smaller change in V

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As a cup of latte is mixed, its coffee particles (corticles) and milk particles (marticles) get mixed more evenly. The macro state remains the same, as the numbers of corticles and marticles don't change. However, the number of micro states increase, as the particles get arranged in different ways.

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Electric fields behave a bit like gravitational fields, but it can be negative if the net charge is negative. Gravitational fields, on the other hand, is always positive under normal circumstances.

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In a uniformly charged sphere, the field strength at the center is always 0, as the forces balance out.

However, the charge inside the sphere but not in the center behaves differently. In a non-conducting sphere, the field strength increases as you get closer to the surface. In a conductive sphere, the field strength is always 0 inside the sphere.