Sine Wave Illustrator

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This animation illustrates the relationship between the amplitude of a sine wave and the radius and rotation of a circle.

As the circle rotates you'll note that the height of the opposite side of the right triangle created by the angle of rotation is identical to the amplitude of the sine wave at any moment of rotation. The height of the opposite side is the product of the sine of the angle of rotation and the length of the hypotenuse of the triangle. The length of the hypotenuse is equal to the radius of the circle.

You can observe sine waves in any combination of 10 different values of amplitude and 10 different wavelengths, with additional information relating to frequency and the value of the sine of the angle of rotation at any moment.

Pause the animation to note the value of the sine for any angle.

The formulae used in this program

The speed of sound constant (c):-
c = 343 metres per second

The wavelength scale (x):-
1 pixel = 1 metre

The amplitude scale (y) is arbitrary

The frequency is calculated as follows:-

f = c/l

where f is the frequency, c is the speed of sound and l is the wavelength.

The amplitude of the sinewave at any angle of rotation is calculated as follows:-

a = sin(Ø)

where a is the amplitude and sin(Ø) is the sine of the angle of rotation

q-trax multimedia
© Julian Ward-Davies 2004

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