JEE Main & Advanced Physics Wave Mechanics Principle of Superposition

(1) The displacement at any time due to any number of waves meeting simultaneously at a point in a medium is the vector sum of the individual displacements due each one of the waves at that point at the same time.

(2) If \[\overrightarrow{{{y}_{1}}}\,,\overrightarrow{{{y}_{2}}},\overrightarrow{{{y}_{3}}}\].... are the displacements at a particular time at a particular position, due to individual waves, then the resultant displacement.

\[\overrightarrow{y\,}\,=\overrightarrow{{{y}_{1}}}+\overrightarrow{{{y}_{2}}}+\overrightarrow{{{y}_{3}}}\,+\,.....\]

(3) Important applications of superposition principle 

(i) Interference of waves  : Adding waves that differs in phase

(ii) Formation of stationary waves : Adding wave that differs in direction.

(iii) Formation of beats : Adding waves that differs in frequency.

(iv) Formation of Lissaju's figure : Adding two perpendicular simple harmonic motions. (See S.H.M. for more detail)