## Phase Difference GeoGebra Apps

I created a series of GeoGebra apps for the JC topics of Waves and Superposition, mainly on the concept of Phase Difference. The sizes of these GeoGebra apps are optimised for embedding into SLS. When I have time, I will create detailed instructions on how to create such apps. Meanwhile, feel free to use them.

Instructions on how to embed the apps into SLS can be found at this staging environment of the SLS user guide.

Phase difference between two particles on a progressive wave. Move the particles along the wave to see the value.

Phase difference between two particles on a stationary wave. Move the particles along the wave to observe how their velocities are different or similar.

Observe velocity vectors of multiple particles on a progressive wave.

## Wavefront

In order to help students visualise a wavefront, a 3-D image is usually used to show the imaginary line joining particles in phase. I created the Geogebra apps below to allow students to change the wavefront and observe it move with time at a constant wave speed. There represent simplified versions of waves on a ripple tank with a linear and circular wavefront.

Rotating the first waveform, you can get the displacement-distance profile of a wave, which is basically the cross-section of a 3-D wave.

## Graphs of a Progressive Wave - Geogebra App

This simple Geogebra app allows students to observe the oscillation of a particle perpendicular to the direction of energy transfer.

## Geogebra Simulation for Particle on a Transverse Wave

I am once again exploring the use of Geogebra to create simulations for Physics. This is what I managed to put together. It serves to help students visualise how a particle in a transverse wave moves. The slider allows the user to pick any particle along the horizontal direction of the wave.

## Measuring speed of sound in air using Audacity

A physics demonstration on how to measure the speed of sound in air using Audacity, an open source audio recording software. There are Windows and Mac versions of this free software, and even a portable version that can run off a flash drive without needing to be installed on a computer (for school systems with stricter measures regarding installing of software).

The sound is reflected along a long hollow tube that somehow, existed in our school's laboratory. The two sound signals were picked up using a clip-on microphone attached to the open end of the tube and plugged into the laptop. I used my son's castanet which gives a crisp sound and hence, a simple waveform that will not have the echo overlapping with the generated sound. The timing at which the sound signals were first detected were read and subtracted to obtain the time taken for the wave to travel up and down the 237 cm tube.

The value of the speed of sound calculated is 356 m/s, which is a bit on the high side due to the temperature of 35°C and relative humidity of between 60-95% when the reading was carried out.

If you are interested, you can check out how the software can be used to determine the frequency of a tuning fork.

We are about to get students to conduct experiments to explore how tension, length and thickness of a guitar string affects its pitch (frequency). I might post some results here when there's time.

## Phase Difference Simulation I created this simulation for use later this semester with my IP4 classes, to illustrate the concept of phase difference between two oscillating particles.

## Polarization with 3 Filters

In what seems like a counter-intuitive demonstration, we can place a polarizing filter in between two other filters which do not transmit light in order to cause light to pass through again.

This is because each filter will permit the components of electric field vectors of the electromagnetic waves that are parallel to its axis of polarization according to the equation $A = A_o \cos{\alpha}$ where $A_o$ is the original amplitude of the unpolarized wave incident on the filter and $\alpha$ is the angle between the electric field vector and the axis of polarization. Each time the wave passes through a filter, it undergoes a reduction in amplitude according to the equation so that by the third filter, its resultant amplitude is
$A = A_o \cos{\alpha_1} \cos{\alpha_2}cos{\alpha_3}$
where $alpha_i$ is the angle between the axis of polarization of the ith filter and the electric field vector direction of the incident light on the ith filter.

According to Malus' law, which applies to two filters with an angle of $\theta$ between their axes of polarization, the resulting intensity for light that passes through 3 filters is given by
$I=I_o \cos^2{\theta_1}\cos^2{\theta_2}$
where $\theta_1$ is the angle between the axes of the first and second filters and $theta_2$ is the angle between the axes of the second and third filters.

## Polarization Using Sunglasses and a Computer Screen

Using a pair of polarizing sunglasses, you can demonstrate the effects of polarization together with a computer screen which is also polarizing. When the axes of polarization of the two polarizing screens are rotated, the brightness alternates between bright and dark.

Light coming from a computer screen is usually polarized. In the video below, when polarized light passes through another polarizer, the intensity of the light is given by Malus' law:

$I = I_o cos ^2{\theta}$

where $\theta$ is the angle between the two axes of polarization and $I_o$ is the original intensity of the unpolarized light.

Only the components of electric field vectors in electromagnetic radiation that are parallel to the axis of polarization of a polarizing filter will be permitted through. Those electric field components that are perpendicular to the polarization axis are blocked by the filter. Hence, the amplitude of a vector A that passes through is given by $A = A_o \cos{\theta}$. Since intensity is proportional to the square of amplitude ($I \propto {A^2}$), we have Malus' law.

The purpose of having polarizing filters in sunglasses and computer screens is to cut out glare due to light from other sources.