What are the important effects which arises due to superposition of waves ?

Answer

### Step-by-Step Text Solution

1. **Understanding Superposition of Waves**:
- Superposition of waves occurs when two or more waves overlap in space. The resultant wave at any point is the sum of the displacements of the individual waves at that point.

2. **Interference of Waves**:
- When two waves of the same frequency and wavelength propagate in the same direction, they interfere with each other. This can lead to constructive interference, where the waves add together to form a larger wave, or destructive interference, where they cancel each other out.
- **Key Point**: Constructive interference occurs when the waves are in phase, while destructive interference occurs when they are out of phase.

3. **Formation of Stationary Waves**:
- If two waves of the same frequency and wavelength travel in opposite directions, they can create stationary waves (or standing waves). In this case, the waves interfere in such a way that certain points (nodes) remain stationary while others (antinodes) oscillate with maximum amplitude.
- **Key Point**: Stationary waves are characterized by fixed points of no displacement (nodes) and points of maximum displacement (antinodes).

4. **Creation of Beats**:
- When two waves of slightly different frequencies travel in the same direction, they produce a phenomenon known as beats. The beat frequency is equal to the absolute difference between the frequencies of the two waves.
- **Formula**: The number of beats heard per second is given by \( f_{beats} = |f_2 - f_1| \), where \( f_1 \) and \( f_2 \) are the frequencies of the two waves.
- **Key Point**: Beats result in a fluctuating sound intensity that can be heard when two similar sound waves interfere.

### Summary of Important Effects:
- **Interference**: Leads to constructive or destructive interference based on the phase relationship of the waves.
- **Stationary Waves**: Formed when two waves of the same frequency and wavelength travel in opposite directions, resulting in nodes and antinodes.
- **Beats**: Occur when two waves of slightly different frequencies interfere, producing a sound that fluctuates in intensity.