The Physics
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Opus in profectus

Doppler Effect (Sound)

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Problems

practice

  1. Write something.
  2. Write something else.
  3. Write something different.
  4. Write something completely different.

numerical

  1. Bats use echolocation to visualize their world. They send out ultrasonic squeaks from their little bat mouths and then listen for the echos with their giant bat ears. The characteristics of the echo will vary depending on the characteristics of the object reflecting the squeak.
    1. How will the echo from a large object (like a tree trunk) compare to a small one (like a tasty insect)?
    2. How will the echo from an object moving away from the bat (like an escaping insect) compare to one from an object moving toward the bat (like an insect about to become lunch)?
  2. Musicians sometimes need to transpose compositions from one key to another. In the system known as just intonation the keys are related by very simple ratios. For example, transposing up a perfect fifth means multiplying all the frequencies played by 3/2, transposing down a major sixth means dividing all the frequencies played by 5/3. A few of the more common intervals are given in the table below.
    tonic major
    second
    major
    third
    perfect
    fourth
    perfect
    fifth
    major
    sixth
    major
    seventh
    octave
    1/1 9/8 5/4 4/3 3/2 5/3 15/8 2/1

    In a bizarre attempt to fuse music with physics, I have decided to load an orchestra onto a train of flatbed cars and drive them past an audience of musical-physics enthusiasts. My plan is to adjust the velocity of the train so that the musical-physics orchestra may play their repertoire in different keys without having to play any notes other than those that are written on the original score. Use this variation of the doppler effect equation…

    Δƒ  ≈ ±  v
    ƒ c
    Δƒ  ≈ ±  speed of source relative to observer
    ƒ speed of sound

    to finish this problem.

    1. By what interval would the orchestra be transposed if the train was driven…
      1. toward the audience at 25% of the speed of sound in air?
      2. away from the audience at 40% of the speed of sound in air?
    2. How fast and in what direction should the train be driven to
      1. raise the orchestra by a major second (also known as a whole tone)?
      2. lower the orchestra one octave?
    3. Is this a good idea?