A First Course in Physics · Ch. XVII, §§ 459–467 · Chapter 17: Nature and Transmission of Sound
53. Echoes, resonance and sounding-boards
Goal: Your student can explain echoes and the conditions for reflecting sound, explain why a closed pipe resonates at a quarter wave length and an open pipe at a half, and tell resonance from forced vibration.
You'll need
- The book, open to these pages
- A tall glass or plastic bottle, a jug of water and a tuning fork if you have one (or a phone tone-generator app)
- A paper-towel tube or a straw and scissors
- A seashell or a cup
- A notebook and pencil
- A calculator (optional, for the problems)
What's in the book
Echoes and multiple echoes; why rooms help a speaker; sound is reflected wherever it meets a medium of different density; the reflected pulse; sound foci and whispering galleries; resonance in a tube over water; closed pipes resonate at ¼ wave length, open pipes at ½; resonators; forced vibrations and sounding-boards. Five problems follow.
The lesson, step by step
Hook question
SayWhy does singing in the shower sound so good?
Read together
Read §§ 459–467. The rule for a closed tube:
the length of air column which gives the best response is approximately one fourth wave length.
Try it: a resonating bottle
Play a steady tone from a tone-generator app (try 512 Hz) or strike a tuning fork and hold it over the mouth of a tall bottle. Slowly pour in water: at one water level the sound swells loudly. Measure the air column from the water to the top and compare with ¼ of the wave length (343 m/s ÷ 512 ≈ 67 cm, so about 17 cm, a bit less because of the mouth). Blow across the bottle's mouth to hear its own note.
Try it: forced vibration
Strike a tuning fork (or a fork from the kitchen drawer, tapped on your knee) and listen; then press its handle onto a table top. Much louder: the table is forced to vibrate and moves more air (§ 467). A piano's sounding-board does the same.
Explain the idea
An echo is sound reflected where it meets a different medium (§ 460). In a closed pipe, the reflected wave must return in half a vibration, so the pipe is ¼ wave length (§ 464); in an open pipe the reflection at the open end is reversed, so it must be ½ wave length (§ 465). Hold a seashell or cup to your ear: it hums at its own resonant note (§ 466).
Say it back
Your student explains why an echo needs a wall at least about 50 ft away (§ 459).
Problems
Work problems 1–5 on book page 361.
Afterwards
Clap in different rooms, a stairwell and outdoors near a big building. Where do you hear an echo?
Answers to the book's problems
1. The people and their clothes break up and absorb the sound waves instead of reflecting them. 2. About 2530 ft. (4.5 × 1126 ÷ 2). 3. 280 vibrations per second if the pipe is closed at one end, as in Fig. 376 (1 ft. = ¼ wave length); 560 if it is open at both ends. 4. 340 m per second (34 cm is half a wave length, so the wave is 68 cm; 500 × 68 cm). 5. In an open pipe the reflection at the open end is reversed, so the wave must travel down and back a whole wave length; in a closed pipe only half.
Worked out for this site from the scan. If a number in your copy differs, trust the book.