Physics M4C12 Waves 2

State the principle of superposition

• When two waves meet at a point, the resultant displacement at that point is equal to the vector sum of the displacements of the individual waves

What is constructive interferernce?

What is destructive interference?

• When two waves in phase superpose, resultant displacement with increased amplitude (‘maxima’)

• When two waves 180* out of phase (in antiphase) superpose, resultant displacement with decreased amplitude (‘minima’)

  • NB: Fully destructive int. only happens at exactly 180* out of phase, not just any ‘out of phase’ waves

What happens to intensity when:
Constructive interference?
Destructive interference?

• Constructive: intensity proportional to amplitude², Intensity increases (quadruples when fully constructive)

  • Sounds get louder, light is brighter

• Destructive: intensity proportional to amplitude², Intensity decreases

  • Sounds get quieter, light is dimmer

  • If two waves with same amplitude destructively interfere, displacement is 0 and intensity is 0

Define coherence

Frequency of coherent waves?

• Waves are coherent if they have a constant/fixed phase difference

• Therefore they will have the same frequency

Define path difference

Will waves arrive in phase or out of phase?

• Difference in distance travelled by two waves in terms of wavelength

• If n(lambda), will arrive in phase, constructive int., maximum amplitude

• If half wavelengths , will arrive out of phase,d estructive int., minimum ampltiude

Young’s double slit equation?

Requirements?

How to measure fringe spacing accurately?

• x = (lambda)D / a

• Coherent, monochromatic - achieved using a colour filter

• Measure distacne between 10 fringes, divide by 9

Energy in stationary waves vs progressive waves?

Amplitude in stationary waves vs progressive waves?

How are they formed?

Requirements?

• Do not transfer energy along direction of travel

• Amplitude is constant across all points in progressive waves, amplitude varies across a stationary wave

• When two progressive waves with same frequency and similar amplitude travel in opposite directions along the direction of travel

• Opposite direction, same (lambda) and frequency, similar amplitude

What are nodes?

What are antinodes?

• Areas on stationary wave of destructive interference, where displacement is 0

• Areas on stationary wave of constructive interference, where amplitude is at its maximum

Phase differences along stationary wave

• In between adjacent nodes, all points are in phase (p.d. of 2π)

  • All reach max their displacement at the same time

  • However max amplitude is still at the antinode

• If odd number of nodes between them, they are in antiphase (p.d. of π)

Wavelength in a stationary wave

• Distance between adjacent nodes is half the wavelength of the progressive waves that form the stationary wave

What are harmonics?

What is fundamental frequency?

• Specific frequencies of waves that create stationary waves

• Minimum frequencies a statioanry wave can exist at

Harmonics with 2 nodes?

Harmonics with 2 antinodes?

Harmonics with 1 node and an anti node?

Where can stationary waves form in air column?

• In a tube with a node and antinode at each end - Only at odd number multples of fundamental frequency

• In a tube with 2 antinodes at both ends - All integer multiples of fundamental frequency

• NOT a tube 2 nodes at both ends

  • Because antinode would be inside the tube