A First Course in Physics · Ch. XVIII, §§ 487–494 · Chapter 18: Properties of Musical Sounds
57. Organ pipes, wind instruments and the phonograph
Goal: Your student can explain how blown pipes make notes, why an open pipe sounds an octave higher than a closed pipe of the same length, which overtones each can make, and how wind instruments change pitch.
You'll need
- The book, open to these pages
- Drinking straws and scissors (straw pipes and a straw oboe)
- A bottle to blow across
- A recorder, whistle, or any wind instrument you have
- A notebook and pencil
- A calculator (optional, for the problems)
What's in the book
A tube blown across its mouth sounds the note it resonates to; closed pipes sound a wave length four times their length, open pipes twice; closed pipes give only the odd harmonics; how the air jet is set swinging by reflected pulses; organ pipes, flutes, whistles, reed instruments, bugles, cornets and trombones; Edison's phonograph. Seven problems follow.
The lesson, step by step
Hook question
SayAn organ has a separate pipe for every note. How does a flute play many notes with one tube?
Read together
Read §§ 487–494. The closed pipe:
when a current of air is suitably directed across the mouth of a closed pipe it will emit a note which has a wave length four times the length of the pipe.
Try it: pan pipes
Cut straws to several lengths, pinch or tape one end closed, and blow across the open ends: shorter, higher. Now open a closed one and blow again: it jumps up about an octave (§ 488). Blow harder on a bottle or recorder until the note jumps to an overtone (§ 489).
Try it: a straw reed
Flatten one end of a straw and cut it to a point, like a V. Put the point in your mouth and blow firmly: the flaps buzz like an oboe reed (§ 492). Snip the straw shorter while blowing and hear the pitch rise.
Explain the idea
The air jet flips in and out of the pipe, timed by pulses returning from the far end (§ 490). Closed pipe: wave length 4 × length, overtones 3, 5, 7… times. Open pipe: wave length 2 × length, overtones 2, 3, 4… times. Flutes shorten the tube by opening holes; bugles play only overtones; trombones slide to change the length (§§ 491–493).
What we know now: the phonograph (§ 494) led to records, then tapes, CDs and digital recordings; but every recording still ends at a vibrating speaker cone.
Say it back
Your student explains why the pitch rises as water is poured into a deep bottle (problem 7).
Problems
Work problems 1–7 on book page 387.
Afterwards
Play a few notes on a recorder or whistle and work out the pipe's sounding length from its pitch.
Answers to the book's problems
1. Inversely as the vibration numbers: 1, 8/9, 4/5, 3/4, 2/3, 3/5, 8/15, 1/2. 2. About 26.6 cm (E = 320; wave length 340 ÷ 320 = 1.06 m; one fourth of that). 3. No; it is higher in summer, because sound travels faster in warm air while the pipes stay nearly the same length. 4. G′, the octave above. 5. G′ (sol′), three times the vibrations of C. 6. By blowing differently the player brings out its several overtones. 7. The air column gets shorter, so its wave length is shorter and its note higher.
Worked out for this site from the scan. If a number in your copy differs, trust the book.