Standing Waves and Harmonics

• Standing waves occur when two waves with equal amplitude and frequency are travelling in opposing directions towards each other, oscillating up and down in a fixed pattern
• Standing Wave Example: shaking a rope at the right frequency creating a wave that interferes with its reflecting wave, forming a larger frequency standing wave. Now not appearing to be traveling along the rope, hence "stationary"
• NODE: the point of complete destructive interference, remaining motionless
• ANTINODES: the points of complete constructive interference, oscillating with maximum amplitude
• Standing waves are only produced when at resonant frequency
• Harmonics are which resonant frequency is being produced
• Fundamental frequency is the simplest (lowest) of vibration, consisting in one antinode
• Overtone refers to a higher level harmony
• General Formula for same ends:

  $l=$$n(λ/2)$

  $λ=$$2l/n$
• Formulas for f, v, l relationship in harmonies:

  $f=$$(nv/2l)$

  $f=$$nf₁$
• Resonant frequency depends on the tension and mass per unit of length such as a guitar string producing deeper notes on thicker strings