Stationary wave?

A stationary wave, also known as a standing wave, is a wave pattern that appears to be standing still, with points of no motion called nodes and points of maximum motion called antinodes. This type of wave is formed by the interference of two waves of the same frequency and amplitude traveling in opposite directions. Stationary waves are commonly seen in musical instruments, such as guitar strings and organ pipes, as well as in various natural phenomena, such as ocean waves and seismic waves.

Stationary Wave

A stationary wave is a wave where the medium does not physically move or travel, but the disturbance remains in one location.

Characteristics:

- Fixed Points (Nodes): Points where the disturbance is always zero.
- Oscillating Points (Antinodes): Points where the disturbance has maximum amplitude.
- Superposition of Waves: Stationary waves result from the superposition of two waves traveling in opposite directions.
- Reflection: The waves reflect at the boundaries and interfere constructively and destructively, creating the stationary pattern.
- Resonance: Stationary waves can only exist if the wavelength matches the distance between the boundaries or if the boundary conditions are met.
- Applications:

- Vibrating strings (guitar, violin)
- Sound waves in organ pipes
- Electrostatic and electromagnetic waves in cavities
- Microwave ovens (microwaves inside are stationary waves)

Types:

- Standing Waves: Stationary waves that exist in one dimension (e.g., vibrating string)
- Traveling Waves: A special case of stationary waves where the distance between boundaries is very large compared to the wavelength.

Equation:

The equation for a stationary wave is:

```
y = A sin(kx - ωt) + A sin(kx + ωt)
```

where:

- A is the amplitude
- k is the wave number
- ω is the angular frequency
- t is time

The first term represents a wave traveling in the positive x direction, and the second term represents a wave traveling in the negative x direction.