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There are two main boxes illustrated. The box at the top is smaller and contains a figure with an X axis and a Y axis. The X axis extends from minus ten to plus ten and is labelled t (for time) with units of milliseconds. The Y axis extends from minus one to plus one and is labelled V (for voltage) with units of volts. Plotted on these axes is a sine wave. On first opening the activity, there are four full cycles of the sine wave illustrated and the amplitude is 0.5 volts.

To the right of the box containing this figure there are three sliding scales.

The first sliding scale is labelled ‘Frequency’ and on opening the activity the value is displayed as 200 hertz. The slider enables values from 100 hertz up to 1000 hertz to be selected, in increments of 10.

The second sliding scale is labelled ‘Amplitude’ and on opening the activity the value is displayed as 0.50. The slider enables values from 0.10 up to 1.00 to be selected, in increments of 0.01.

The third sliding scale is labelled ‘Phase’ and on opening the activity the value is displayed as 0 (and, below this in brackets, ‘0 degrees’). The slider enables values from minus two pi (or minus 360 degrees) up to plus two pi (or plus 360 degrees) to be selected, in increments of pi over eight (or 22.5 degrees).

The larger box is positioned below the first box and the sliding scales. This comprises two elements. On the right-hand side there is a figure comprising an X axis extending from 0 to just over 10, labelled t (for time) with units of milliseconds, and a Y axis extending from minus one to plus one, labelled V (for voltage) with units of volts. On opening the activity, there is nothing plotted on this figure. To the left of these axes there is a dotted circle. There is a horizontal dotted line through the centre of the circle that is aligned with the X axis in the figure to its right. The centre of the circle is labelled zero and the radius of the circle is equal to 0.5.

Below this box there are two buttons, one labelled ‘Generate’ and one labelled ‘Reset’. Clicking on the ‘Generate’ button starts an animation in the bottom box. Once the ‘Generate’ button has been clicked, the name changes to ‘Stop’; if this is clicked again, it pauses the animation.

Without changing any of the initial sliding scales at first, clicking on ‘Generate’ has two effects. Firstly, on the circle, a horizontal line appears from the centre of the circle to the right-hand edge of the circle (that is, the length of the line is the radius of the circle). This line rotates in an anti-clockwise direction about the centre of the circle. The length of the line is labelled ‘a’. The distance between the endpoint of this line and the dotted line across the centre of the circle (which changes as the line rotates) is labelled ‘y’.

The second effect is that as the line rotates, the point on the outer edge of the circle maps onto the axes to the right of the circle, and traces out a waveform. The two are linked by a dotted line to show how the variation of the line marked ‘y’ on the circle traces out a waveform on the axes that is the shape of a sine wave. This continues until just over two and a half cycles of the sine wave have been traced out, and then the line stops.

The sliding scales can be used to change the value of the properties of the sine wave illustrated in the top box. Once the properties have been changed, pressing ‘Generate’ will start the animation again but with the new values set by the sliding scales. Pressing the ‘Reset’ button at any time will return to the original settings (frequency to 200 hertz, amplitude to 0.5 and phase to zero) and remove the rotating line and traced waveform from the bottom box.

Changing the value of the frequency using the appropriate sliding scale has the following effects:

In the top box, increasing the frequency will have the effect of showing more cycles of the waveform. Likewise, decreasing the frequency means that fewer cycles will be shown. In the bottom box, increasing the frequency means that the rotating line in the circle rotates quicker. This also means that more cycles are traced out on the axes to the right of the circle as the line completes more rotations within the time frame indicated on the figure. Likewise, lowering the frequency means the line rotates more slowly and fewer cycles are illustrated on the axes. At a maximum frequency of 1000 hertz, ten cycles are illustrated within 10 milliseconds. At a minimum frequency of 100 hertz, one cycle is illustrated within 10 milliseconds.

Changing the value of the amplitude using the appropriate sliding scale has the following effects:

In the top box, increasing the amplitude will increase the peak value of the waveform illustrated. Likewise, decreasing the amplitude will decrease the peak value of the waveform. In the bottom box, increasing the amplitude means that the radius of the circle – and therefore the length of the rotating line in the circle, ‘a’ – increases. This also means that the peak value of the waveform that is traced out increases. Likewise, decreasing the amplitude means that the radius of the circle, and therefore the length of the rotating line in the circle (a) decreases. At a maximum amplitude of one, the length of the rotating line is one and the peak value of the sine wave that is traced out is one.

Changing the value of the phase using the appropriate sliding scale has the following effects:

In the top box, increasing or decreasing the phase will shift the waveform with respect to time. A positive phase value shifts the waveform to the left (an advance in time relative to a phase of zero). A negative phase value shifts the waveform to the right (a delay in time relative to a phase of zero). In the bottom box, a change in the value of phase means that the rotating line starts from a different position. For example, for a value of pi over two (or 90 degrees), the line starts in an upright (or vertical) position, so extends from the centre to the top point of the dotted circle. For a value of minus pi over two (or minus 90 degrees), the line starts in a position that extends from the centre to the bottom point of the dotted circle. The effect this has on the waveform that is traced out is that the waveform also has a different starting point. Again, for an example of plus pi over two, where the rotating line starts at the top, and y is at a maximum value, the waveform also starts at its maximum value. At a value of two pi (or 360 degrees), the line has in effect rotated around the whole circle and the result, both in terms of the rotating line and the waveform that is traced out, is the same as when the phase is zero.

 1.1 Periodic signals