A 100-kHz signal is applied to the horizontal channel of an oscilloscope. A signal of unknown frequency is applied to the vertical channel. The resultant wave form has 5 loops displayed vertically and 2 loops horizontally. The unknown frequency is:

To find the unknown frequency using a Lissajous figure, you must use the ratio formula: (Vertical Frequency / Horizontal Frequency) = (Horizontal Loops / Vertical Loops). Notice that the loop counts are inversely proportional to their respective axis frequencies. In this problem, the horizontal frequency is given as 100 kHz. The display shows 2 horizontal loops (tangency points) and 5 vertical loops. Plugging this into the formula gives: Unknown Vertical Frequency = Horizontal Frequency * (Horizontal Loops / Vertical Loops). Calculating this yields: 100 kHz * (2 / 5) = 100 * 0.4 = 40 kHz. Therefore, the unknown frequency applied to the vertical channel is 40 kHz.