A reference frequency of 10 kHz is applied to the horizontal input of a conventional cathode ray oscilloscope. When a test frequency is applied to the vertical input, the following stable Lissajous pattern is obtained. What is the test frequency applied?

Concept:

When a Lissajous pattern is formed on a Cathode Ray Oscilloscope (CRO), the ratio of frequencies of the vertical and horizontal signals can be determined from the pattern.

The general formula is:

\( \frac{f_y}{f_x} = \frac{\text{Number of vertical tangencies}}{\text{Number of horizontal tangencies}} \)

Given:

Reference frequency (horizontal) \( f_x = 10~kHz \)

Lissajous pattern shows 2 vertical loops and 1 horizontal loop ⇒ \( \frac{f_y}{f_x} = \frac{2}{1} \)

Calculation:

\( f_y = 2 \cdot f_x = 2 \cdot 10~kHz = 20~kHz \)

Answer:

Option 3) 20 kHz