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DP IB Physics: SL

Topic Questions

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4.5 Standing Waves

Question 1a

Marks: 3

Standing waves are sometimes referred to as stationary waves.

(a)
State three conditions which are required for the formation of a standing wave.
[3]
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    Question 1b

    Marks: 3

    Standing waves can be thought of as the opposite of progressive waves.

    (b)
    Use the text in the box to complete the sentences below, comparing the two types of wave.
    constant transfer do not
    store do different at different points

       
    (i)
    Standing waves ______ energy but progressive waves ______ energy.
    [1]
    (ii)
    The amplitude of a standing wave is ______ , whereas the amplitude of a progressive wave is ______ .
    [1]
    (iii)
    The crests of a standing wave ______ move along but simply oscillate up and down, while but the crests of a progressive wave ______ move along as the wave travels.
    [1]

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      Question 1c

      Marks: 2
      (c)
      A stationary wave is made up of nodes and anti-nodes. State the definitions of 
        
      (i)
      A node.
      [1]
        
      (ii)
      An antinode.
      [1]
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        Key Concepts
        Nodes & Antinodes

        Question 1d

        Marks: 4
        (d)
        The length L shows 2.5 full wavelengths of a standing wave in a column of air. 

        WE - Nodes and Antinodes question image(1)

        (i)
        Identify the points marked X and Y. 
        [2]

        (i)

        State the boundary conditions for the formation of this standing wave. 

        [2]

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          Question 2a

          Marks: 3

          Standing waves are formed when waves undergo superposition.

          (a)
          State the principle of superposition.
          [3]

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            Question 2b

            Marks: 2
            (b)
            Name two types of waves which can undergo superposition.
            [2]

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              Key Concepts
              Nodes & Antinodes

              Question 2c

              Marks: 2
              (c)
              Distinguish between constructive interference and destructive interference.
              [2]
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                Key Concepts
                Nodes & Antinodes

                Question 2d

                Marks: 2

                A standing wave representing the first harmonic is set up on a vibrating string.

                (d)
                State the number of nodes and anti-nodes which would appear on this wave.
                [2]

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                  Key Concepts
                  Harmonics

                  Question 3a

                  Marks: 2

                  A standing wave is set up in a column of air within a pipe of length L, which is open at one end.

                  4-5-3a-qun-wave-in-pipe-sl-sq-easy-phy

                  (a)
                  Giving your answer as a fraction of L, determine the wavelength, λ.
                  [2]
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                    Key Concepts
                    Nodes & Antinodes

                    Question 3b

                    Marks: 3
                    (b)
                    For the standing wave identify which points are in phase and which points are in anti-phase.
                    4-5-3b-qun-points-a-e-on-a-wave-sl-sq-easy-phy
                    [3]

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                      Key Concepts
                      Nodes & Antinodes

                      Question 3c

                      Marks: 3

                      The column of air is vibrated so that it oscillates at the third harmonic.

                      (c)
                      Sketch a diagram to show the shape of the wave produced in the pipe.
                      4-5-3c-qun-half-pipe-sl-sq-easy-phy
                      [3]
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                        Key Concepts
                        Harmonics

                        Question 3d

                        Marks: 2

                        The column of air oscillating at the seventh harmonic has length L and velocity, v.

                        (d)
                        In terms of L and v, determine the

                        (i)
                        Wavelength.
                        [1]
                        (ii)
                        Frequency.
                        [1]
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                          Key Concepts
                          Harmonics

                          Question 4a

                          Marks: 3
                          (a)
                          Describe three methods that can be used to identify that two points on a standing wave are in phase.

                          [3]

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                            Key Concepts
                            Nodes & Antinodes

                            Question 4b

                            Marks: 2
                            (b)
                            Describe the boundary conditions for a standing wave in a pipe of air which is open at one end and closed at the other.
                            [2]

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                              Key Concepts
                              Boundary Conditions

                              Question 4c

                              Marks: 3
                              (c)
                              For a pipe that is open at both ends

                                 

                              4-5-4c-qun-open-pipe-sl-sq-easy-phy

                              (i)
                              Sketch the first harmonic.
                                 [2]
                              (ii)
                              Write an expression for wavelength in terms of the length of the pipe, L.
                              [1]

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                                Key Concepts
                                Harmonics

                                Question 4d

                                Marks: 3
                                (d)
                                For a string which is fixed at both ends, sketch the third harmonic.
                                [3]

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                                  Question 5a

                                  Marks: 3

                                  The diagram shows three possible harmonics on a string fixed at each end. 

                                  4-5-5a-qun-three-harmonics-sl-sq-easy-phy

                                  (a)
                                  Identify the three harmonics.
                                  [3]
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                                    Key Concepts
                                    Harmonics

                                    Question 5b

                                    Marks: 3
                                    (b)
                                    For the harmonic shown, identify an expression for the wavelength.
                                    4-5-5b-qun-fourth-harmonic-sl-sq-easy-phy
                                    [3]

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                                      Question 5c

                                      Marks: 3

                                      The diagram shows two waves which are travelling in phase.

                                      4-5-5c-qun-two-waves-in-phase-sl-sq-easy-phy
                                      (c)
                                      Sketch the resultant wave, including labelling the axes with relevant quantities.
                                             
                                      [3]

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                                        Question 5d

                                        Marks: 2

                                        Stationary waves are formed when two waves travelling on the same line superpose.

                                        (d)
                                        Identify two conditions which must be true for superposition to occur.
                                        [2]

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