question_answer

State the principle of superposition of waves. Distinguish between conditions for the production of stationary waves and beats.                                                      

Answer:

                The principle of superposition states that when a number of waves travel through a medium simultaneously, the resultant displacement of any particle of the medium at any given time is equal to the algebraic sum of the displacements due to the individual waves. Mathematically, \[y={{y}_{1}}+{{y}_{2}}+{{y}_{3}}+.....+{{y}_{n}}\] (i) When two waves of same frequency moving with the same speed in the opposite directions in medium superpose an each other, they produce stationary waves. (ii) When two waves of slightly different frequencies moving with the same speed in the same direction in a medium superpose on each, they produce beats.