The Sounds of Trig. One of the numerous applications of trigonometry includes the science of sound...
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Transcript of The Sounds of Trig. One of the numerous applications of trigonometry includes the science of sound...
The Sounds of Trig
• One of the numerous applications of trigonometry includes the science of sound
• In a nut shell, sound is the pushing of certain air molecules at different rates
• Specially, the air molecules travel in waves– The bigger the wave, the more audible the sound
is
Sine/Sound Waves
• As it turns out, we can model sound waves use the sine function, or as more commonly known, sine waves
• For acoustics (audible sound), sine waves, or sound waves, are written as:– y = A sin(2πft + φ)
• Using the equation, we can model different levels or types of sounds according to different parameters
• A = amplitude (0 to 30,000)• f = frequency (1 hertz to 100 hertz)• t = time (essentially, your “x” variable)• Φ = any phase shift you apply (between - 2π and
2π)
Exploration
• You and a few partners, take out your graphing calculators.
• For your quick assignment, I want you to explore what each variable does in terms of sound.
• 1) Change the Amplitude, 2 times• 2) Change the frequency, 2 times• 3) Apply any phase shift you want
• Basic parameters:• A = 100• f = 37• Φ = 0
• Then, start changing your own parameters• Write down the apparent changes it does to the graph;
make it steeper, more broad, wider, etc. • How would these changes apply to your perception of
sound, in your opinion?