Section 3 review
The superposition principle describes what happens when multiple waves overlap. It states that the wave amplitude at any place and time is the sum of the amplitudes from each individual wave. Interference is one possible result of superposition. When the combined amplitude of two waves is larger than either of the individual waves, the interference is constructive. If the combined amplitude decreases, the interference is destructive. A standing wave occurs when a wave interferes with its own reflection; it is characterized by nodes (places where the amplitude remains zero) and antinodes (where the amplitude is largest). In wave physics, resonance refers to the fact that certain physical systems will only sustain standing waves with certain frequencies. Resonance allows objects such as guitar strings and organ pipes to produce distinct musical notes. Read the text aloud
superposition principle, constructive interference, destructive interference, node, antinode, mode, standing wave

Review problems and questions

  1. Is it possible for two waves to have individual amplitudes that are not zero while the sum of the two waves has an amplitude of zero? Explain. Read the text aloud Show
  1. Give three examples in which wave behaviors such as reflection, refraction, and absorption help doctors diagnose their patients’ medical conditions. Read the text aloud Show
Waves on a rope held at both ends
  1. Two friends stand on either end of a rope of length 2 m. One friend repeatedly shakes her end of the rope up and down by a few centimeters. By shaking the rope at different rates (frequencies), she generates all three of the standing-wave patterns shown here.
    1. In Pattern (i), what is the wavelength of the wave?
    2. Suppose that she completes one up-and-down hand motion in half a second (0.5 s) to generate Pattern (i). What are the period, frequency, and wave speed?
    3. Next, she generates Pattern (ii). What has doubled, the wavelength or the frequency?
    4. In Pattern (iii), how many wavelengths fit between the two ends of the rope?
    5. Which pattern represents the rope’s fundamental mode of vibration? Read the text aloud Show
  1. For each standing wave pattern shown in the figure above, how many nodes are present? How many antinodes? Read the text aloud Show
  1. For a standing wave on a stretched string, what is the relationship between the number of nodes and the number of antinodes? Read the text aloud Show

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