Syllabus Edition

First teaching 2014

Last exams 2024

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Standing Waves (DP IB Physics: SL)

Exam Questions

3 hours42 questions
1
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1 mark

Identify the line which makes up a correct description of the conditions for superposition.

A. One wave travelling in water with a constant speed
B. Two waves  travelling in opposite directions with the same frequency
C. Two waves  travelling near each other with the same frequency
D. Three or more waves travelling in the same direction with different frequency and speed

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    2
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    1 mark

    For the two waves shown, identify the correct possible result after they superpose.

    4-5-q2-sl-easy-mcq-phy

    • 4-5-q2-option-a-sl-easy-mcq-phy

    • 4-5-q2-option-b-sl-easy-mcq-phy

    • 4-5-q2-option-c-sl-easy-mcq-phy

    • 4-5-q2-option-d-sl-easy-mcq-phy

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    3
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    1 mark

    Identify the pair of statements which both correctly describe properties of standing waves.

      • All points have the same amplitude in turn
      • Points which are one wavelength apart are in phase
      • Each point has a different amplitude
      • Points between nodes are in phase
      • All points have the same amplitude in turn
      • Points between nodes are in phase
      • Energy is moved from one point to another
      • The wave has nodes and antinodes

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    4
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    1 mark

    For the wave shown, how many nodes, and how many anti-nodes are present?

    4-5-q4-sl-easy-mcq-phy

      Nodes Anti-nodes
    A. 2 6
    B. 2 3
    C. 4 6
    D. 4 3

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      5
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      1 mark

      The diagram shows a stationary wave. Which line correctly identifies the labelled sections?

      4-5-q5-sl-easy-mcq-phy

        P Q R
      A. antinode node length of string
      B. node antinode wavelength
      C. node antinode frequency
      D. wavelength wavelength length of string

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        6
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        1 mark

        A stationary wave is formed in a pipe which is open at both ends.

        Which statement must be correct?

        • Nodes form at the ends of the wave.

        • Antinodes form at both ends of the wave.

        • Displacement is a maximum at the nodes.

        • Displacement is at a minimum at the antinodes.

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        7
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        1 mark

        A stationary wave forms on a string of length L. Which harmonic has a wavelength where λ = 2 over 3 L?

        • First harmonic.

        • Second harmonic.

        • Third harmonic.

        • Fourth harmonic.

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        8
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        1 mark

        Which diagram shows the first harmonic on a string?

        q9-qun

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          9
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          1 mark

          Which is the correct general equation for the wavelength of the nth harmonic in a pipe of length L which is open at one end?

          • f subscript n space equals space fraction numerator n v over denominator 2 L end fraction

          • lambda subscript n space equals space fraction numerator 2 L over denominator n end fraction

          • v space equals space f lambda

          • lambda subscript n space equals space fraction numerator 4 L over denominator n end fraction

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          1
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          1 mark

          Which one of the following options is not possible for longitudinal waves?

          • Polarisation

          • Interference  

          • Superposition

          • Diffraction

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          2
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          1 mark

          Which one of the following options is always true regarding the energy transferred along a standing wave and its amplitude?

           

          Energy transferred along the standing wave

          Amplitude of vibrations along the standing wave

          A.

          None

          Varies

          B.

          None

          Is constant

          C.

          Some energy transferred

          Varies

          D.

          Some energy transferred

          Is constant

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            3
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            1 mark

            An open pipe has sound waves sent through it causing it to have a standing wave of the third harmonic occurring within it. What is the nature of oscillations at the centre of the pipe (point X) and at its edge (point Y)?

             

            Point X

            Point Y

            A.

            A node

            A node

            B.

            A node

            An anti-node

            C.

            An anti-node

            A node

            D.

            An anti-node

            An anti-node

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              4
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              1 mark

              The fundamental frequency for a pipe which is closed at one end, but open at the other, is 380 Hz. What is the frequency of its third harmonic?

              • 127 Hz

              • 380 Hz  

              • 760 Hz

              • 1140 Hz

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              5
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              1 mark

              An open pipe has both ends clear and has a standing wave formed within it. Which of the following statements is always true for this standing wave?

              • The number of nodes added to the number of antinodes is an odd number

              • There is always a central anti-node in the wave

              • The number of nodes added to the number of antinodes is an even number

              • There is always a central node in the wave

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              6
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              1 mark

              A wave of a certain frequency is setup on a string with two fixed ends which act as nodes

              q16_standing-waves_ib-sl-physics-mcq

              If the frequency is doubled, but nothing else is changed, how many nodes will be on the string?

              • Two

              • Three

              • Five

              • Seven

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              7
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              1 mark

              Organs such as those found in churches often have many different kinds of pipes with both open and closed ends. For a single pipe that has a specific length, what is the ratio of the fundamental frequency with both ends open to the fundamental frequency with one end closed?

              • 1:2

              • 1:4

              • 2:1

              • 4:1

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              8
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              1 mark

              A pipe with a single closed end has a standing wave set up within it. If the length of the pipe is 2 m, which value below is closest to the wavelength of the seventh harmonic?

              • 0.345 m

              • 0.782 m

              • 0.983 m

              • 1.14 m

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              9
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              1 mark

              A standing sound wave is set up in an open pipe (both ends open) and the frequency of the first harmonic is 400 Hz. What is the approximate length of this pipe? (Assume the speed of sound is 343 m/s).

              • 0.14 m

              • 0.43 m

              • 1.27 m

              • 4.81 m

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              10
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              1 mark

              A pipe of length L is open at one end and closed at the other end of the pipe. What is the frequency of the fifth harmonic? (Assume the speed of sound in air is 343 m s–1).

              • 150 ÷ L

              • 281 ÷ L

              • 429 ÷ L

              • 611 ÷ L

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              1
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              1 mark

              A standing wave is set up on a string with both ends fixed. The frequency of the first harmonic is 150 Hz. 

              Determine the approximate length of the string, L and for the second harmonic, the approximate distances between two successive nodes, N and two successive antinodes, A.

              The speed of sound is air = 340 m s−1 and the speed of sound on the string = 250 m s−1.

                L / m N / m A / m
              A. 1.10 0.55 0.55
              B. 1.10 0.24 0.55
              C. 0.84 0.42 0.42
              D. 0.84 0.42 0.56

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                2
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                1 mark

                A guitar string is stretched and fixed at each end so that the length is 75 cm. It is found to vibrate with resonant frequencies at 240 Hz and 360 Hz. There are no other resonant points between these two.

                4-5-sl-mcq-hard-q2-phy

                  What is the lowest resonant frequency which can oscillate on the guitar string?

                • 60 Hz

                • 120 Hz

                • 180 Hz

                • 240 Hz

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                3
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                1 mark

                A copper pipe of diameter 15 mm and length 45 cm is sealed closed at one end. A string is attached such that the copper pipe can be quickly spun around, causing the effect of a wind blowing across the open end at different frequencies.

                4-5-sl-mcq-hard-q3-phy

                What is the wavelength of the third harmonic?

                • 30 cm

                • 34 cm

                • 45 cm

                • 60 cm

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                4
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                1 mark

                A standing wave on a string between two fixed points sounds its second harmonic at frequency f.

                Which expression, where n is an integer, gives the frequencies of harmonics that have an antinode at the centre of the string?

                • 1 half n f

                • n f

                • 2 n f

                • left parenthesis 2 n space plus space 1 right parenthesis space f

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                5
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                1 mark

                A pipe of length L1 has one open end and one closed end. A second pipe, of length L2  is open at both ends. The frequency of the first harmonic of both pipes is the same. 

                What is the ratio L subscript 1 over L subscript 2?

                • 1 fourth

                • 1 half

                • 3 over 2

                • 2

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                6
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                1 mark

                A flute is a musical instrument with a typical length, L, of 67 cm. It has a hole in the lip plate at one end which the musician blows across, and is open at the other end. 

                The length of the air column is varied by opening and closing a series of keys along the side. The velocity of the air entering the lip plate is controlled by the musician.

                4-5-sl-mcq-hard-q6-phy

                To create a frequency f  the musician creates a wave with velocity v, holding down the keys such that the column of air is half the available length.

                If she wants to increase the frequency to three times the original pitch, which changes to would achieve this?

                  v L
                A. × 9 × 2
                B. × 3 × 1 half
                C. stays the same × 3
                D. × 1 half × 1 over 6

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                  7
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                  1 mark

                  A thin wire is held at tension with length L so that the speed of the waves on the string is equal to the speed of sound in air. At this tension the fundamental frequency of oscillation produces resonance in a pipe which is closed at one end.

                  4-5-sl-mcq-hard-q7_1-phy

                  Which of the pipes shown resonates?

                  4-5-sl-mcq-hard-q7_2-phy

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                    8
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                    1 mark

                    A very long, empty measuring cylinder of cross sectional area 2.5 × 10−3 m2 is set up so that water can be slowly run into it through a narrow, flexible tube.

                    4-5-sl-mcq-hard-q8-phy

                    A tuning fork is made to oscillate and held over the open end. A resonant frequency is heard early on in the experiment and then again after a further 5.5 × 10−3 m3 of water has run into the cylinder.

                    What is the wavelength of the wave produced by the tuning fork?

                    • 0.70 m

                    • 1.40 m

                    • 2.20 m

                    • 4.40 m

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                    9
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                    1 mark

                    A string is stretched to a length where  L = 300 cm. At this length and tension it has resonant frequencies at 360 Hz and subsequently at 420 Hz.

                    4-5-sl-mcq-hard-q7_1-phy

                    What is the speed of the standing waves on the string?

                    • 18 m s−1

                    • 36 m s−1

                    • 180 m s−1

                    • 360 m s−1

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                    10
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                    1 mark

                    Two microwave transmitters are set up to emit microwaves so that a stationary wave is created between them. The microwaves have a frequency of 300 MHz.

                    Which line correctly gives both the formula which represents the the distance between two adjacent nodes in the standing wave and the value for the distance?

                      Formula Distance
                    A. fraction numerator c over denominator 2 f end fraction 50 cm
                    B. fraction numerator f over denominator 2 c end fraction 2.0 m
                    C. fraction numerator c over denominator 2 f end fraction 5.0 m
                    D. fraction numerator f over denominator 2 c end fraction 20 cm

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