# 11 Wave Motion

## Velocity of a Wave – Simulation

Try using the values in this simulation to find the velocity of this wave! Let me have your answer in the comment section!

Update on 21 August 2018: The latest iteration of this App is found here:

## 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.

## 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 $$A = A_o \cos{\theta}$$ where $A_o$ is the original amplitude of the unpolarized wave incident on the filter and $\theta$ 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
$$A = A_o \cos{\theta_1} \cos{\theta_2}$$
where $\theta_i$ 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, the intensity of the light that passes through these two filters is given by

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

where I0 is the initial intensity and θ is the angle between the light’s initial polarization direction and the axis of the polarizer.

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.