View our demonstration animations:

1. Sonify points on graph
   Notice that there is an increasing mapping between values of the function and frequencies.
   Also notice the use of hiss to indicate negative values.
    
2. Sonify a function, investigating limit
   What a student might do while investigating a limit:
        Play function sonification from the negative side.
        Play function sonification from the positive side.
        Play function sonification from both sides.
   Notice that in the both-side sonification, the left-hand limit is played through the left speaker, while the right-hand limit is played through the right speaker. Since this limit exists, the two sounds converge at the end of the clip.
    
3. Sonify a derivative, investigating critical points and extrema of function
   In this feature, a short tangent segment tracks along the graph of the function while the graph of the derivative is plotted simultaneously with the sound.
   Again notice the use of hiss to indicate negative values and also a ping to indicate a zero value of the derivative .
    
4. Sonify a definite integral, investigating net area under a graph
   In this feature, the area under the graph is shaded while the graph of the definite integral is plotted simultaneously with the sound.
   Notice that the sound pulses four times in synch with the horizontal axis tick marks.