Wave Phenomena: Refraction, Diffraction, and Interference

Wave speed depends on the material properties of the medium. Different media (Medium 1 & Medium 2) have different wave speeds.
The symbol c is often used for wave speed, commonly associated with the speed of light but also used for sound.
If c1 > c2 (wave speed in Medium 1 is greater than in Medium 2), and the frequency f is fixed, then the wavelength lambda will be shorter in Medium 2.
- The relationship is given by the formula: \lambda = \frac{\text{wave speed}}{\text{frequency}}.
- A fixed frequency across media is argued for sensible boundary results over time.
- If wave speed v is smaller, wavelength lambda is smaller, leading to closer wavefronts.

Definition: Refraction is the change in wave propagation direction when a wave passes from one medium to another.
Cause: It occurs when adjacent media have different wave speeds.
Key Principle: The frequency f of the wave remains unchanged, but the wavelength lambda changes.
Mechanism of Bending: When a wavefront enters a slower medium, the portion of the wavefront that hits the boundary first slows down, while other parts still in the faster medium continue at their original speed. This differential slowing causes the wavefront to pivot or bend.
Snell's Law: This law describes the relationship between the angles of incidence and transmission (though not detailed in this transcript).

Temperature Gradient: The speed of sound in air depends on temperature. Variations in atmospheric temperature with elevation cause refraction effects.
- Temperature Inversion: Occurs when higher elevation air is warmer than ground-level air.
  - In this scenario, sound waves emanating upwards from a source near the ground will bend downwards.
  - Implication: People far away may hear sounds from a distant source more clearly, as sound traveling upwards is refracted back down towards the listener.
  - Historical Example: This effect reportedly impacted battles during the Civil War, allowing sounds of distant battles to be heard over surprisingly large distances.