Mechanical Waves

Definition:
- Mechanical waves are energy disturbances that propagate through a medium (solid, liquid, or gas).
- These waves require particles of the medium to oscillate and therefore cannot travel through a vacuum.

Transverse Waves:
- In these waves, particle movement is perpendicular to the wave direction.
- Characterized by:
- Crests: High points of the wave.
- Troughs: Low points of the wave.
- Examples:
- Waves on a string: If one end of a rope is shaken, the wave travels sideways while particles of the rope move up and down.
- Water waves: On the water surface, particles move in an upward and downward motion as the wave travels horizontally.
Longitudinal Waves:
- In these waves, particle movement is parallel to the wave direction.
- Characterized by:
- Compressions: Regions where particles are close together.
- Rarefactions: Regions where particles are spread out.
- Examples:
- Sound waves: Vibrations in the air compress and expand air particles, creating regions of high and low pressure.
- Compression in springs: When a spring is pushed and released, the compression wave travels along the spring's length.

Wavelength (λ):
- The distance between two consecutive crests or compressions.
- Determines the spatial size of one full wave cycle.
Frequency (f):
- The number of wave cycles (oscillations) that pass a fixed point per second.
- Measurement unit: Hertz (Hz).
- High frequency implies more cycles per second, often correlating with higher energy.
Amplitude:
- The maximum displacement of particles from their equilibrium (rest) position.
- A larger amplitude corresponds to greater wave energy (e.g., louder sound in sound waves).
Wave Speed (v):
- The rate at which the wave travels through the medium.
- Formula: $v = f \times \lambda$
- Wave speed is the product of frequency and wavelength.
Period (T):
- The time required for one complete wave cycle.
- Relation to frequency: $T = \frac{1}{f}$
- Period (T) is measured in seconds.