Graphing Sine Waves - Trigonometry Help - Game Tips:
- Sine waves are used to model many periodic and vibrational patterns in nature.
- The equation y = A sin (kT) represents a set of ordered pairs of the form (T,y).
- When graphed on a horizontal T-axis and vertical y-axis, the curve represented by y = A sin (kT)
is a Sine wave having vertical amplitude = |A| and horizontal wavelength = |2(Pi)/(k)|.
- In a vibrating string example, |A| is the maximum deflection of the string from rest position.
Wavelength refers to how long it takes for a pattern to repeat itself. Eg. a crest + a trough .
As 'k' gets larger in size, the wavelength gets shorter. Also Pi = 3.14159 approximately.
- The wave represented by y=5sin(3T) has amplitude 5 and approximate wavelength = 2(Pi)/3 = 2.1 units.
- The wave y= -10sin(T) has amplitude 10 and approximate wavelength = 2(Pi)/1 = 6.3 units.
- The simple basic sine wave y= sin(T) has amplitude 1 and approximate wavelength = 2(Pi)/1 = 6.3 units.
- It may take a minute to load the game at dial-up speeds.
- The game can be played using the mouse by itself or using the keyboard by itself.
- If the game doesn't respond to keyboard input, click inside the game area to reset the game's focus.
- Adjust the game's speed by pressing the + or - key repeatedly.