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Water waves and superposition

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课程笔记

Water Waves

  • Water waves are formed in a ripple tank using a motor-driven dipper that vibrates up and down.
  • Each vibration of the dipper creates a water wave that travels outward.
  • Waves transfer energy without transferring matter.
  • Water waves are a type of transverse wave.

Transverse Waves

  • In a transverse wave, the vibration is perpendicular to the direction of wave travel.
  • For water waves, the dipper moves up and down while the wave moves outward horizontally.
  • Examples of transverse waves include water waves, light waves, and waves on a string.

Superposition

  • Superposition occurs when two waves pass through each other and overlap.
  • The displacement of a particle in a wave is its distance from the rest position.
  • During superposition, the displacements of the individual waves add together.

Constructive Interference

  • When two peaks (crests) arrive at the same place at the same time, they add together.
  • The amplitude of the combined wave is greater than each individual wave.
  • This is called constructive interference.

Destructive Interference

  • When a peak and a trough arrive at the same place at the same time, they cancel out.
  • The amplitude of the combined wave is less than each individual wave.
  • This is called destructive interference.

General Rule for Superposition

  • If displacements have the same sign (both positive or both negative), they add.
  • If displacements have opposite signs, they subtract.
  • The result is the net displacement at each point.

Constructive interference: two waves with same displacement sign add to produce a larger amplitude.

Constructive interferencewave 1wave 2combined (bigger)

Destructive interference: a peak and trough cancel, resulting in zero displacement.

Destructive interferencewave 1wave 2 (inverted)cancel → zero

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练习题

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  1. 1.Which of the following is a transverse wave?

    Easy
    • AWater wave
    • BSound wave
    • CLongitudinal wave
    • DP-wave
  2. 2.Water waves transfer energy without transferring what?

    Easy
    • AMatter
    • BAmplitude
    • CFrequency
    • DWavelength
  3. 3.In a transverse wave, the vibration is ________ to the direction of wave travel.

    Easy
    • Aperpendicular
    • Bparallel
    • Copposite
    • Dat 45°
  4. 4.What is superposition?

    Easy
    • AWhen two waves pass through each other and their displacements add
    • BWhen a wave reflects off a barrier
    • CWhen a wave changes speed
    • DWhen a wave diffracts
  5. 5.When a peak of one wave meets a peak of another wave at the same place and time, what happens to the amplitude?

    Easy
    • AIt increases
    • BIt decreases
    • CIt stays the same
    • DIt becomes zero
  6. 6.When a peak of one wave meets a trough of another wave at the same place and time, what happens to the amplitude?

    Easy
    • AIt decreases
    • BIt increases
    • CIt stays the same
    • DIt doubles
  7. 7.In the ripple tank, what causes the water waves to form?

    Easy
    • AA motor connected to a dipper vibrating up and down
    • BA fan blowing across the water surface
    • CHeating the water
    • DPouring water slowly
  8. 8.If two waves have displacements of +3 cm and -3 cm at the same point, what is the resultant displacement?

    Medium
    • A0 cm
    • B6 cm
    • C-6 cm
    • D3 cm

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