A First Course in Physics · Ch. XVII, §§ 448–458 · Chapter 17: Nature and Transmission of Sound
52. The nature of sound: waves, wave length and pitch
Goal: Your student can explain how sound passes from particle to particle as condensations and rarefactions, use wave length = speed ÷ vibrations per second, explain loudness falling off with distance, and explain pitch and the Doppler effect.
You'll need
- The book, open to these pages
- A Slinky or long spring (for longitudinal waves) and a rope (for transverse waves)
- A row of 5 coins or marbles on a table (or a Newton's cradle)
- A playing card and a bicycle wheel (to make pitch), or a comb
- A notebook and pencil
- A calculator (optional, for the problems)
What's in the book
How a pulse passes from particle to particle (the row of steel balls); loudness and the inverse square law; speaking tubes; trains of waves and wave length; l = v/n; condensations and rarefactions; water-wave analogy; longitudinal and transverse waves; musical sounds and noises (the siren disk); pitch; Doppler's principle. Nine problems follow.
The lesson, step by step
Hook question
SayWhen I talk to you, does the air from my mouth travel across the room to your ear?
Read together
Read §§ 448–458. The key relation:
wave length is equal to velocity divided by the number of vibrations per second
Try it: passing on a push
Line up coins touching in a row on a smooth table and flick one coin into the end: the far coin shoots off while the rest barely move (Fig. 367). The motion travels, the particles don't. Then stretch a Slinky on the floor and push one end sharply: a squeezed region (condensation) runs along it, followed by a stretched region (rarefaction). Shake a rope sideways for comparison: that wave is transverse (§ 455).
Explain the idea
Each vibration of the source sends out one condensation and one rarefaction. If a fork vibrates 110 times a second and sound goes 1100 ft per second, the waves are 10 ft apart (§ 451). Wave length = speed ÷ vibrations per second. Twice as far from a source, sound spreads over four times the area, so it is one fourth as loud (§ 449).
Try it: pitch and the Doppler effect
Hold a card against the spokes of a turning bicycle wheel (or run a fingernail along a comb, slowly then fast). Faster means more taps per second: higher pitch (§ 457). Listen to a car or ambulance passing: the pitch drops as it goes by (§ 458).
What we know now: today vibrations per second are called hertz (Hz). The Doppler effect is used in radar speed guns, weather radar and by astronomers (you will meet it again for light in Chapter XXI).
Say it back
Your student explains, with the Slinky, the difference between longitudinal and transverse waves.
Problems
Work problems 1–9 on book page 353.
Afterwards
Listen for the Doppler shift in passing cars, trains or motorcycles.
Answers to the book's problems
1. The talker's voice vibrates the parchment, which pulls on the thread; the thread passes the vibrations to the other parchment, which sets the air there vibrating. 2. In a dense medium more matter is set in motion, so more energy reaches the ear. 3. 4 times as loud (half the distance). 4. It gathers sound waves over a large opening and funnels them into the ear. 5. About 1.34 m (343.2 ÷ 256). 6. About 3 cm (343.2 m/s indoors, 334.2 m/s outdoors; each divided by 300). 7. The saw slows down as it cuts, so fewer teeth strike per second. 8. About 323 pulses a second (the train covers 88 ft. a second, which holds about 23 wave lengths of 3.77 ft.). 9. Sounds of all pitches travel at the same speed.
Worked out for this site from the scan. If a number in your copy differs, trust the book.