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class code: SPS21 teacher: Mr. Elert
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Physics A: Problem Set 14: Standing waves and resonance

recommended reading

High Marks: 4:32–4:35
Barron's Let's Review: 11.8 Standing waves, 11.9 Resonance
physics.info: Standing waves, Resonance
Wikipedia: Standing wave, Resonance, Broughton Suspension Bridge, Angers Bridge, Tacoma Narrows Bridge (1940)
HyperPhysics: Standing waves, Resonance
Mythbusters: Breakstep bridge minimyth
Mr. Machado: 07 Inteference and Standing Waves, 10 Resonance, 12 Semi-Closed Tubes and Standing Waves, 13 Open Tubes and Standing Waves

sample problem

  1. Tuning forks
    note pitch (Hz)
    C4 256
    D4 288
    E4 320
    F4 341
    G4 384
    A4 427
    B4 480
    C5 512
    D5 576
    E5 640
    F5 682
    G5 768
    A 1.00 m vertical tube is partially submerged in water. The height of the tube above the water can be adjusted to any value from 0 m (the tube is completely submerged) to 1 m (the bottom of the tube is just touching the top of the water). A vibrating tuning fork is held just over the open top end of the tube. Pick one of the notes from the table on the right and answer the following questions.
    1. Determine the wavelength of the sound emitted from the tuning fork in air at room temperature (vsound = 343 m/s).
    2. How long is ¼, ½, ¾, 1¼, 1½, 1¾ of the wavelength you calculated in part a.?
    3. At what heights will resonance occur? (Just highlight the answers from part b. that satisfy this condition.)

    To see a similar experiment using a shorter tube and, more importantly, to hear what resonance sounds like watch the video below.

    youtu.be/YpCA9CVsVos

homework

  1. A common form of hearing loss is associated with resonance in the ear canal. When this happens, there is reduced sensitivity to sounds around 4,000 Hz (since this frequency is consistently louder than all the others).
    1. Determine the wavelength of a 4,000 Hz sound wave in the human ear canal. (Assume that the speed of sound is about 348 m/s.)
    2. Determine the length of the ear canal in the average human. (Recall that the ear canal starts at the opening in the outer ear and ends at the eardrum.)
  2. Why do marching soldiers "break step" when they come to a bridge? Why don't they continue marching?