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?