Transverse Vibration in a Stretched String

1. Wave Propagation: When a string is plucked or struck, it experiences a disturbance at a specific point. This disturbance travels along the length of the string, creating a wave.

2. Medium: The string acts as a medium for the wave to travel through. In this case, it's a one-dimensional medium (along the length of the string).

3. Transverse Wave: The vibration of the string is perpendicular to the direction of the wave's motion.

4. Equilibrium Position: When the string is at rest, it has an equilibrium position.

5. Amplitude: The maximum displacement of any point on the string from its equilibrium position is called the amplitude.

6. Frequency and Pitch: The frequency of the wave determines the pitch of the sound produced.

7. Wave Speed: The speed at which the wave travels along the string is determined by factors such as tension in the string and its linear density.

8. Nodes and Antinodes: Nodes are points on the string that remain stationary during vibration, experiencing minimal displacement. Antinodes are points of maximum displacement.

9. Harmonics: The fundamental frequency is the lowest frequency at which the string can vibrate.

10. Mathematical Representation: The wave equation, such as the one-dimensional wave equation, can be used to mathematically describe the motion of the string.

Overall, this is a broad topic with both theoretical and practical applications.

Mathematical representation of the wave equation:

\[ \frac{{\partial^2 y}}{{\partial t^2}} = v^2 \frac{{\partial^2 y}}{{\partial x^2}} \]