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Progressive waves
Transverse and longitudinal waves
Determination of frequency and wavelength
Stationary waves


Play with the 2 Wave Superposition Model. Test what you've learned by exploring the amplitudes, wave velocities, frequencies, wavelengths.

As a pedagogical tool, "modeling pedagogy: key in your own equation like A*sin(2*pi/λ(x-v*t) form" .

for ease of keying in, select from the dropdown menu is also possible before adding on through the input fields of f(x) and g(x).

The One-Dimensional Wave Function Superposition JavaScript Model shows how the superposition principle gives rise to wave phenomena such as standing waves and beats. Users enter real-valued wave functions and observe both the time dependent functions and their superposition. This model uses the JavaScript mathematical function parser.

Sample Learning Goals

(a) show an understanding and use the terms displacement, amplitude, phase difference, period,
frequency, wavelength and speed
(b) deduce, from the definitions of speed, frequency and wavelength, the equation v = fλ
(c) recall and use the equation v = fλ
(f) analyse and interpret graphical representations of transverse and longitudinal waves
(a) explain and use the principle of superposition in simple applications



For Teachers


Software Requirements


Android iOS Windows MacOS
with best with Chrome Chrome Chrome Chrome
support full-screen? Yes. Chrome/Opera No. Firefox/ Samsung Internet Not yet Yes Yes
cannot work on some mobile browser that don't understand JavaScript such as.....
cannot work on Internet Explorer 9 and below



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  1. Physlet Sound Illustrations Package Physlet Physics Chapter 18

Other Resources

  1. version by Andrew Duffy
  2. version by Andrew Duffy
  3. version by Andrew Duffy
  4. JavaScript version by Andrew Duffy
  5. Java version Superposition of Two Waves (with different phases,same amplitude,frequency) by Fu-Kwun Hwang
  6. Java version Superposition of two waves (same frequency, different amplitude, phase/dir ) by Fu-Kwun Hwang
  8. by ukukuku 

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