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Lissajous patterns on a CRO has ten vertical maximum values and eight horizontal maximum values. The frequency of the horizontal input is 1000 Hz. Determine the frequency of the vertical input?
1000 Hz
1344 Hz
800 Hz
1256 Hz
800 Hz
Lissajous patterns are used to determine unknown frequencies by comparing them with a known frequency. The ratio of the frequency of the vertical signal to the frequency of the horizontal signal is inversely proportional to the number of loops or maximum values intersected along the respective axes.
Lissajous patterns are used to determine unknown frequencies by comparing them with a known frequency. The ratio of the frequency of the vertical signal to the frequency of the horizontal signal is inversely proportional to the number of loops or maximum values intersected along the respective axes.
fhтАЛfvтАЛтАЛ=NvтАЛNhтАЛтАЛ тАФ Frequency ratio formula for Lissajous patterns
fvтАЛ=fhтАЛ├ЧNvтАЛNhтАЛтАЛ тАФ Solving for vertical input frequency
When sinusoidal signals are applied to X and Y input plates of a CRO, the electron beam traces a Lissajous figure. The relationship is governed by the ratio of the number of points of tangency on the vertical side (NvтАЛ) to the number of points of tangency on the horizontal side (NhтАЛ).
fvтАЛ is the frequency of the vertical input.
fhтАЛ is the frequency of the horizontal input.
NvтАЛ=10 (vertical max values).
NhтАЛ=8 (horizontal max values).
fhтАЛ=1000┬аHz.
Simple method for frequency comparison.
Does not require highly calibrated internal oscillators.
Requires stable signal sources.
Interpretation becomes difficult for complex frequency ratios.
Calibration of signal generators.
Measurement of unknown frequencies in laboratory circuits.
Calculation: fvтАЛ=1000├Ч108тАЛ=800┬аHz.
Option A is the frequency of the horizontal input, not the vertical.
Option B and D are derived from incorrect inversion of the ratios (10/8 or similar errors).
C is correct тАФ The vertical frequency is calculated as fvтАЛ=1000├Ч108тАЛ=800┬аHz.
Always remember the relationship fxтАЛfyтАЛтАЛ=Number┬аof┬аvertical┬аtangency┬аpointsNumber┬аof┬аhorizontal┬аtangency┬аpointsтАЛ. A mnemonic is that the frequency ratio is inversely proportional to the number of loops touched along that axis.
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