16 superposition and standing waves superposition of waves standing waves additional: superposition...

16 Superposition and Standing Waves

• Superposition of Waves• Standing Waves• Additional: Superposition of Standing

Waves, Harmonic Analysis & Synthesis

• Hk: 1, 29, 33, 47, 51.

Superposition Principle

Terminology

• Phase Difference: The fractional part of a period which represents the offset in peak positions of waves.

• Coherence: The existence of a correlation between the phases of two or more waves such that interference effects can be observed.

• Interference: The variation with distance or time of the amplitude of a wave which results from the superposition of two or more waves.

Interference

• Constructive Interference: Resultant amplitude is larger than either individual wave.

• Destructive Interference: Resultant amplitude is less than either individual wave.

Destructive Interference:Constructive Interference:

Examples

Phase Difference

Constructive Interference

Standing Waves

• Amplitude is zero at fixed ends• Nodes (other places with zero amplitude)• Anti-nodes (places with maximum

amplitude)

…a wave in which the amplitude at a given location does not vary with time.

Standing Wave Features:

Standing Wave: Both Ends Fixed

Standing Wave: One End Fixed, One End Free

fourier analysis

Summary

• Superposition results in interference• Interference can occur due to Path

Difference• Standing Waves, and conditions for• Harmonics and Fourier Analysis• /