If a 100 Hz signal is fed to the horizontal input of an oscilloscope and a 150 Hz signal is fed to the vertical input, what type of pattern should be displayed on the screen?

This question tests your understanding of Lissajous figures, which are generated when two sine waves are applied simultaneously to the X (horizontal) and Y (vertical) inputs of an oscilloscope. The shape of the resulting pattern depends on the ratio of the two frequencies. The mathematical rule for Lissajous figures is that the ratio of the vertical frequency to the horizontal frequency equals the ratio of the number of horizontal tangency points (loops) to the number of vertical tangency points. Expressed as a formula: F_vertical / F_horizontal = Loops_horizontal / Loops_vertical. In this scenario, the vertical frequency is 150 Hz and the horizontal frequency is 100 Hz. The ratio is 150 / 100, which simplifies to 3 / 2. Therefore, the pattern will display 3 horizontal loops and 2 vertical loops. Distractors suggesting physical measurements in millimeters or unreduced loop counts fail to apply this ratio principle.