Acoustic Effects¶
About this lesson plan¶
This is a lesson plan for indented for realization during 2h lesson activities.
It has been developed during work in iCSE4school project based on lesson carried out in 2015-2017 at The Stefan Batory High School in Chorzów.
It was prepared by Adam Ogaza based on his lesson.
Attention!
In each of the “code” cells you can change any number, text or instruction. In order to return to the original version refresh the webpage. Sometimes the next code depends on variables defined from the previous one, so one has to execute cells in order of apperance.
Introduction¶
The main aims of this lesson are:
Explaining, what is echo and after-sound.
Demonstration of acoustic resonance.
Explaining the principle of operation of music instruments.
Explaining, what are beats,
Exercising in plotting diagrams in Python.
Exercising interaction and sliders in Python.
Exercising animations in SAGE
Circumstances taken into consideration:
Students have already basic knowledge of waves in general. In particular they know the equantion of wave, idea of standing wave and resonance.
It is the second students’ contact with animations in Python. They participated in one IT lesson devoted to this problem.
One should remember, that student don’t know higher mathematics, so presented IT solutions must not be too sophisticated.
Gradation of difficulty level is recommended. One should start with simple examples and gradually complicate them (for example by adding more parameters or varying constants)
All described below can be carried out during two hours: one in physics laboratory, the second in a class-room equiped with sufficient amount of computers
Theoretical part¶
Exercises in programming were preceded by a theoretical lecture about acoustic effects. This lecture was filmed and published in Polish but with English subtitles.
Main problems discussed in this lecture are the following:
Echo
After-sound
Acoustic resonance
Standing waves (especially in instruments)
Beats
I will not describe the details here, because all of them are visible in the film.
IT part¶
Main skills exercised during lesson:
Processes controlling with sliders.
Puting diagrams into motion.
Examining the motion of wave impulses.
Composition of vibrations.
Examining standing waves and beats.
The physical problems discussed in the code and diagrams below, are the following:
Beats - how does the shape of composite wave depend on component frequencies.
How to animate a wave impulse and its reflection.
Showing, that standing wave is really a result of interference betwee two waves travelling in opposite directions.
Beats
Easy example of plot with fixed frequencies and initial phase, which can be changed inside the code. Results of those changes can be observed on the plot.
More complex drawing including the parameters of functions and envelope. For simplicity the amplitudes are chosen to be equal.
A slider controlling the time shift. Enables moving the picture.
Controlling the frequency of second wave. One can onserve the dependence of pulsation period on the difference between frequencies of component waves.
Creation of graphics array for further animations.
Ready animation. We see the sequence of plots for different time arguments.
Another approach, making use of plots defined above
Animation showing the impact of second frequency on the pulsation period.
Reflection and standing waves
Standing wave as an interference of two waves travelling the opposite side. Students can manipulate all the parameters (it was an exercise).
In order to make the time evolution of the standing wave more apparent, an animation is very useful.It might also be instructive to display the travelling waves.The variable delay seems to be unnecessary and the argument x-vt is used instead of t-x/v so that no problem arises when v goes to zero.
Graphics array useful for a more detailed analysis.
Wave pulse and its reflection
Motion of wave impulse. I know, that so defined impulse is not physical because of differential discontinuity, but it is the first approach to such kind of animations. Students were informed of the physical doubts.
Two incoming wave impulses coming from opposite directions
Superposition of impuls and its reflection
Numerical wave reflection
Conclusions¶
Programming in Python became an interesting supplement of physics lesson. The benefit lies in the possibility of (more or less) easy visualisation of processes with the change of parameters. Thank this, the formulae presented during lectures are less abstract and everybody can single-handed check, how the result of interference depends on frequencies, direction of speed and so on.
Animations itself were a new challenge for students. In the previous version I asked student to develop somehow the code to create some new ideas. It failed, because the code was too difficult for them. All they are able to do is to manipulate the parameters.
Nevertheless, I judge this lesson high. Students were very interested and engaged. Their skills, both in physics and informatics, increased.
