The Sound of Sine, Part 1

Wherever there is sound, there are vibrations[br][br]Wherever there are vibrations, there are cycles[br][br]Wherever there are cycles, sine is somewhere nearby!
Animated Sound Wave
When moving air particles stimulate our eardrum (or a microphone, like in the case of a cochlear implant), the resulting vibrations and changes in air pressure are reinterpreted into electrical signals that are sent through the auditory nerve to the brain. The brain then decodes those signals into what we perceive as sound.[br][br]This vibration of air particles can be visualized through the graph of a sine wave, representing the changes in pressure of the air particles. Below we'll play with some equations for sine and explore how transforming them affects the resulting sound![br]____________________________________________
1. Try playing with the "a" slider in the applet below. [br]This describes the wave's [b]amplitude.[/b][br][br][list][*]How does it transform the graph?[/*][*]How does it transform the sound you hear?[/*][/list]
2. Try shifting the "h" slider. [br]This describes the [b]period[/b] of the wave measured in [i]hertz (Hz)[/i]. [br]1 Hz = 1 cycle per second[br][br][list][*]How does it transform the graph?[/*][*]How does it transform the sound you hear?[br][/*][/list]
_______________________________________________[br][br]When musicians and programs create music electronically, they are manipulating the amplitude and period (in hertz) of the wave.[br][br]In the applet below, manipulate the slides to get the sine wave to pass through those points
3. What equation passed through the given points?
4. How do the values for [b]amplitude (a)[/b] and [b]period described in [i]hertz[/i] (h)[/b] in the equation you wrote connect to the graph?
5. If you wanted to graph a wave with an amplitude of 0.5 and a period of 300 hertz, what would your equation be?
6. Check to see if your equation from #5 matches using the applet below.
___________________________________________________________[br][br]Additional Resources - "Let's Learn About Waveforms"[br][br][url=https://pudding.cool/2018/02/waveforms/]https://pudding.cool/2018/02/waveforms/[br][br][br][/url]"Virtual Oscilloscope"[br][br][url=http://www.physics-chemistry-interactive-flash-animation.com/electricity_electromagnetism_interactive/oscilloscope_description_tutorial_sounds_frequency.htm]http://www.physics-chemistry-interactive-flash-animation.com/electricity_electromagnetism_interactive/oscilloscope_description_tutorial_sounds_frequency.htm[/url][br][br][br][br][br]
[size=50]Credits:[br]Sound wave image:[br]https://commons.wikimedia.org/wiki/File:Sound_wave.jpg[br]Sound wave animation:[br]http://mypages.iit.edu/~muehleisen/acs_demos/wave_animations/planewave.html [/size]

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