Question

How is Lissajous figures used to measure unknown frequency?

Answer 1

Lissajous figure will be displayed on the screen, when the sinusoidal signals are applied to both horizontal & vertical deflection plates of CRO. Hence, apply the sinusoidal signal, which has standard known frequency to the horizontal deflection plates of CRO. Similarly, apply the sinusoidal signal, whose frequency is unknown to the vertical deflection plates of CRO
Let, 𝑓𝐻and 𝑓𝑉 are the frequencies of sinusoidal signals, which are applied to the horizontal & vertical deflection plates of CRO respectively. The relationship between 𝑓𝐻 and 𝑓𝑉 can be mathematically represented as below.
`(fV)/(fH)=n_H/n_V`

From above relation, we will get the frequency of sinusoidal signal, which is applied to the vertical deflection plates of CRO as

`f_V=(n_H)/(n_V)f_H`
Where,
𝑛𝐻is the number of horizontal tangencies
𝑛𝑉 is the number of vertical tangencies

We can find the values of 𝑛𝐻 and 𝑛𝑉 from Lissajous figure. So, by substituting the values of 𝑛𝐻, 𝑛𝑉 and 𝑓𝐻 in Equation 1, we will get the value of 𝑓𝑉, i.e. the frequency of sinusoidal signal that is applied to the vertical deflection plates of CRO.