Doppler Effect (Sound)

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 moth)?

      

   2. How will the echo from an object moving away from the bat (like an escaping moth) compare to one from an object moving toward the bat (like a moth 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 simple ratios. For example, transposing up a perfect fifth means multiplying all the frequencies played by ³₂, transposing down a major sixth means dividing all the frequencies played by ⁵₃. 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
   11	98	54	43	32	53	158	21

   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 to finish this problem.

   ∆f	≈ ∓	∆v	= ∓	speed of source relative to observer
   f		c		speed of sound

   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?