C C C D D E E F F G G G A A Frequency: 440 Hz

y= sin(440(2πx)) A Frequency: 261.63 Hz

y= sin(261.63(2πx)) C Frequency: 392 Hz

y= sin(392(2πx)) G Frequency: 349.23 Hz

y= sin(349.23(2πx)) F Frequency: 329.63 Hz

y= sin(329.63(2πx)) E Frequency: 293.66 Hz

y= sin(293.66(2πx)) D Sine Graphs in Music Sound Sound is produced by the vibrations of matter.

produced in waves

human ears can only pick up certain sounds

must fall between 20 and 20,000 Hz

that is between 20 and 20,000 vibrations per second! The frequency of a note determines how many hertz it is.

frequency is also referred to as the pitch of a sound

every note has a different frequency

the higher the pitch, the higher the note Hertz (Hz) is the unit that frequency is measured in.

cycles per second

measures how long it takes a sound wave to reach a certain point C C G G Sine graphs and Sound When you graph sound waves you can see that they resemble sine graphs.

Since they are sine graphs, you can graph the sounds and see how they compare.

We have demonstrated this by dissecting a song and graphing the individual notes it is made up of. Our Song The song we choose to look at was Twinkle Twinkle Little Star The first line of this song has 6 different notes in it, all of which

have different frequencies.

We found the graphs by using the equation: y= sin(f (2πx)) Where f equals the frequency of the note Background Music A A The Sine Graphs C G F F This is a continuous graph of the notes in the songs.

Notice how the graphs change based on the frequencies of the notes. The lowest note, C, has the least amount of cycles while the highest, A, has the most. E E D D Notice how similar the graphs of G and A are.

Frequency of G=392 Hz

Frequency of A= 440 Hz The graphs of F and E are very similar too.

Frequency of F=349.23 Hz

Frequency of E= 329.63 Hz The D and C graphs also look alike.

Frequency of D=293.66 Hz

Frequency of C= 261.63 Hz

All the notes were graphed using the equation y= sin(f (2πx))

Amplitude=1

Period=2π÷(2π×frequency)=frequency

No vertical shift

No horizontal shift All graphs are shown on the window...

X min=0

X max=.01

Y min=-2

Y max= 2 Because the period of each graph is the frequency, we had to use an extremely small window to present our data

Try using your calculator to make the graph of note A

Use the equation y= sin(440 (2πx))

Use these settings for your window

X min=0

X max=π

Y min=-2

Y max=2 Have you ever seen a picture of sound waves from a song and wondered what it meant?

All of those lines you see are actually a sequence of sine waves made by each note. You should get a graph that looks like the one below. Look familiar? From now on, whenever you see a picture of sound waves like that you will know that it was created using the basic principles of graphing a sinusoidal function. Activity!

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# Sine Graphs in Music

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