Stationary waves are produced when two waves of the same frequency moving in opposite directions superimpose. When the waves are 180 degrees out of phase, they cancel each other out, and when they are in phase, they add together. A stationary wave appears stationary and consists of nodes where there is no displacement and antinodes where displacement is at a maximum. In contrast, a progressive wave transfers energy as it moves in one direction with uniform pressure and density changes.

1. STATIONARY (STANDING) WAVES

2. When two waves of same frequency moving in opposite directions Superimpose we have stationary waves.

3. when the two waves are 180° out-of-phase with each other they cancel

5. when the the two waves are in-phase with each other they add together

9. COMPARISON OF STANDING WAVE WITH (PLANE) PROGRESSIVE WAVE

10. Appears to travel from one point to another. Consists of one wave moving in one direction. There is flow of energy. Consists of crests and troughs. Change in pressure and density is uniform. Appears to be stationary. Combination of two progressive waves moving in opposite directions. No transfer of energy takes place. Consists of nodes and antinodes. Change in pressure and density is not uniform. 1 2 3 4 5 Plane progressive wave Standing wave S.No.

11. NUMERICAL

12. Stationary waves are produced by the superposition of following waves Y 1 = 0.05Sin(5 π t- x) Y 2 =0.05Sin(5 π t+ x) Where x and y are in metres and t in secs. Find the displacement of a Particle Situated at a distance of x=1 m.

13. SOLUTION

14. Y= Y 1 + Y 2 =0.05Sin(5 π t- x) + 0.05Sin(5 π t+ x) =0.1CosxSin5 π t Now, Amplitude =0.1Cosx Or, Displacement= 0.1Cos1 (as x=1) =0.1Cos(180 ° / π ) =0.1Cos57.3 ° =0.054 m.

15. Thanks. LORD JESUS, the CREATOR of the universe bless you!