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WAVES AND OPTICS PHYSICS-C IV unit 2
Superposition of two perpendicular Harmonic Oscillations

Author of this note Mr
...
Prasad BSc from University of Calicut, MSc from
university of Delhi, and M
...
A from IGNOU Delhi
These notes were prepared during my teaching session for under graduate
students (11 Th and 12 Th class) of my school physics department

This note is helpful for under graduate students and junior level graduates

I declare that these notes are my original works based on my knowledge in
physics and the books mentioned below are the reference books I used for
preparing these notes

Table of contents
(1) Superposition of two perpendicular Harmonic Oscillations
(2) Lissajous Figures
(3) Lissajous Figures Definition
(4) Lissajous Figures Uses
(5) Measurement of Frequency using Lissajous figure

(6) Measurement of the Phase Difference using Lissajous figure

Reference Books
Vibrations and Waves, A
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French, 1stEdn
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Waves: Berkeley Physics Course, vol
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Fundamentals of Optics, F
...
Jenkins and H
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White, 1981,
McGraw-Hill
Principles of Optics, Max Born and Emil Wolf, 7th Edn
...

Optics, Ajoy Ghatak, 2008, Tata McGraw Hill
The Physics of Vibrations and Waves, H
...
Pain, 2013, John Wiley
and Sons
...
K
...

Fundamental of Optics, A
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R
...
R
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ChandPublications
Optics, Eugene Hecht, 4thEdn
...


Superposition of two perpendicular Harmonic Oscillations

Vibrations Having Equal Frequencies Assume that a molecule moves under the
synchronous influence of two simple harmonic vibrations of equivalent frequency,
one along the x axis, the other along the opposite y axis
When two mutually opposite simple harmonic movements of same frequency
amplitude and phase are superimposed the subsequent movement is uniform
circular movement
...

Lissajous Figures

The Lissajous figure is built utilizing a cathode ray oscilloscope (CRO)
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The Lissajous figure or the Lissajous design is built by the crossings point of two
sinusoidal curved axes of which are opposite to one another or kept up with at
right points to one another
...
Later in 1857,
Jules Antoine Lissajous researched it in more detail
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Lissajous Figures Definition
The meaning of a Lissajous figure can be characterized as one of an endless
number of curves framed by joining two simple oscillations that are opposite to
one another
...

The Lissajous figures oscilloscope permits you to plot one sine wave along the xaxis against another sine wave along the y-axis
...
The Lissajous figure shows the phase distinction between the two
signals and the connection between their frequencies
...
These examples rely upon the
amplitude, frequency, and phase difference of the sinusoidal sign applied to the
horizontal and vertical puzzles of the CRO
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The Lissajous figure is of high significance
in physical science to concentrate on the sinusoidal waves
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The uses of Lissajous figure are as per the following:

The Lissajous figures are used to determine the unknown frequency by comparing
it with the known frequency
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The Lissajous figure built will be shown on the CRO screen
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In this manner, apply the
sinusoidal sign, recurrence of which is known to the flat avoidance plates of CRO
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Assume fH and fV are the frequencies of sinusoidal signs, which are executed to
the horizontal and vertical redirection plates of CRO, individually
...
e
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/

⇒fV fH = nH

/ nV

From the above equation, the frequency of sinusoidal signal applied to the
vertical deflection plates of CRO can be drawn which is given below:

⇒fV = (nH

/ nV) fH⇒fV = (nH / nV) fH

Here, nH is the number of horizontal squares and nV is the number of vertical
...
Now, if
we substitute the value of nH and nV in the above equation we can determine the
unknown frequency of sinusoidal signal applied to the vertical deflection plates of
CRO
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Consequently, apply the sinusoidal signs with the identical
amplitude and frequency to both horizontal and vertical deflection plates of the
CRO

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