**Stationary / Standing Waves**When two similar waves travel in opposite directions they can superpose to form stationary wave. This usually happens when one wave is a reflection of the other. Stationary waves occur by resonance only at the natural frequencies of vibration of a medium.

**Formation of stationary wave**

Here,

At time t =0, the progressive waves travelling to the left and right are in phase. The waves combine constructively, giving amplitude twice that of each wave.

After a time equal to one quarter of a period (t = T/4). Consequently, the two waves are in antiphase. The waves combine destructively, giving zero displacement.

After time equal to one half of a period (t=T/2), the two waves are back in phase again and combine constructively.

After a time equal to three quarters of a period (t=3T/4), the waves are in antiphase.

After time equal to one whole period (t=T), the waves combine constructively.

The separation between two adjacent nodes or two adjacent antinodes = λ/2

Separation between adjacent node and antinode = λ/4

**Wavelength and speed of sound**

**Harmonics**

As we increase the frequency of the vibration generator we will see standing waves being set up.

The first will occur when the generator is vibrating at the fundamental frequency, f_{0}, of the string.

**First Harmonics**

It has 2 nodes and 1 antinode.

f = f_{0 } λ= 2L

**Second Harmonic**

It has 3 nodes and 2 antinodes.

f = 2f_{0 } λ= L

**Third Harmonic**

It has 4 nodes and 3 antinodes.

f = 3f_{0} λ = 2/3 L

**Fourth Harmonic**

It has 5 nodes and 4 antinodes.

f = 4f_{0} λ = ½ L