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# The square wave challenge

The wave shown in Figure 26 approximates what is called a ‘square’ or ‘rectangular’ wave. The challenge is to design this wave using sine waves as components.

Figure 26 Approximation to a square wave

To make this wave using Interactive 3 (which you should still have open in a separate tab), start with two sine waves, the first having A = 0.7 and f = 400 Hz, and the second having A = 0.2 and f = 1200 Hz. This will give something similar to the wave shown in Figure 27, which is a good start.

Figure 27 Combination of two sine waves

To make the top and bottom smoother requires sine waves with other frequencies. To get another sine wave, click on the ‘add another sine wave’ button below the second sine wave. Set the frequency of this to f = 2000 Hz.

## SAQ 10

Suggest an appropriate value of A for the wave with frequency f = 2000 Hz.

### Answer

Setting A = 0.1 gives the wave shown in Figure 28. This is closer to what is desired.

Figure 28 Combination of three sine waves

To finish this challenge requires one more sine wave. Click again on the ‘add another sine wave’ button to get a fourth sine wave. Set its frequency to f = 2800 Hz.

## SAQ 11

Suggest an appropriate value of A for the wave with frequency f = 2800 Hz.

### Answer

Setting A = 0.05 gives the wave shown in Figure 29. This is even closer to the desired square wave.

Figure 29 Combination of four sine waves

You can now close the interactive.

In the square wave challenge, the shape of the wave was made closer to that required by adding higher frequencies with decreasing amplitudes. This is a general principle behind a very powerful theory for representing and processing signals.

◄Contents►Next: 4.6 From the time domain to the frequency domain

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