Superposition and Stationary Waves · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Waves that add up and stand still

Science · Waves, Light & Sound · ages 16-18
Name ______________________   Date ____________

  1. A displacement node in an ideal stationary wave has zero displacement at every time.

    Circle one:   True   False

  2. Two identical sinusoidal waves travel in the same direction and remain in phase in a linear medium. What is their resultant?

    • Amplitude doubles; wavelength stays fixed
    • Amplitude stays fixed; wavelength doubles
    • Amplitude becomes zero; wavelength stays fixed

  3. Where is an antinode between two neighbouring displacement nodes in an ideal stationary wave?

    • At either node, where displacement stays zero
    • Halfway between them, where amplitude is greatest
    • At every point, where amplitude is equally large

  4. A uniform 1.2 m string fixed at both ends oscillates in its second harmonic. Give the component-wave wavelength in metres.

    Answer: ______________

  5. Neighbouring displacement nodes in an ideal stationary wave are 0.3 m apart. What is the component-wave wavelength?

    • 0.6 m
    • 0.3 m
    • 0.15 m

  6. Two equal pulses of opposite shape overlap exactly in an ideal linear medium. Their displacements are +3 cm and −3 cm. What happens?

    • The total is +6 cm, and both pulses remain joined
    • The total is zero, then both pulses continue unchanged
    • The total is −6 cm, then neither pulse continues onward

  7. A uniform string fixed at both ends has length L and travelling-wave speed v. What is its second-harmonic frequency?

    • v/(2L)
    • v/(4L)
    • v/L

  8. A uniform 1.2 m string fixed at both ends oscillates in its third harmonic. Give the component-wave wavelength in metres.

    Answer: ______________

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Answer key

For grown-ups. Fold this page away before handing over the rest.

Waves that add up and stand still W1-mt_AIxA2TYGJN-s1

  1. True · At a displacement node, the component displacements cancel throughout the cycle.
  2. Amplitude doubles; wavelength stays fixed · The displacements add at every point. Matching crests double, while the distance between successive crests stays unchanged.
  3. Halfway between them, where amplitude is greatest · The amplitude grows from zero at a node to its greatest value halfway to the next node.
  4. 1.2 · The second harmonic fits two half-waves, or one wavelength, into the 1.2 m string.
  5. 0.6 m · A node-to-node gap is half a wavelength, so wavelength = 2 × 0.3 m = 0.6 m.
  6. The total is zero, then both pulses continue unchanged · During exact overlap, +3 cm + (−3 cm) = 0. The pulses then continue unchanged in the ideal linear model.
  7. v/L · For n = 2, f_n = nv/(2L) gives f_2 = 2v/(2L) = v/L.
  8. 0.8 · Three half-waves fit the string, so wavelength = 2 × 1.2 / 3 = 0.8 m.
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