Wave Function Generated by Swinging a Ball on a String in a Circular Motion

Imagine that you are swinging a ball on a string. You swing it above your head in a horizontal plane in a circle. The figure labeled "View From Above" shows what the swinging string and ball looks like from above your head.

Now, imaging that a friend is standing a few feet away from you, watching the motion of the ball from your side. This view is shown in the figure labeled "View From Side". The ball is actually moving in a circular path, but to your friend looking at the ball from a side view, the ball appears to move from left to right and back again in a horizontal motion. This observer (your friend) sees the ball move to the right, slow down, slowly reverse direction, speed up as it moves to the left, then slow down again and reverse direction, speed up, and repeat this motion again and again.

If your friend (the observer) then graphs the horizontal positions of the moving ball, they will graph a sine wave as shown in the "View of Wave Function". The position of the ball is graphed on the y-axis, and the x-axis indicates the passing of time.

Using the sliders above, try changing the Period and the String Length, and note how these changes affect the other values shown above. In particular, note that:
  • Changing the Period changes both the wavelength and frequency, but not the wave speed.
  • As the frequency increases, the wavelength decreases, and vice versa.
  • Changing the String Length changes the amplitude of the wave, but not the frequency or wavelength.
  • The Peak Amplitude of the wave is equal to the String Length.