Tune the bottles
Tonight's idea
A sound has a frequency: the number of vibrations each second. Faster vibration means a higher note.
Blow across a bottle and you make the air at its neck bob in and out. The trapped air inside acts like a spring. Add water and there is less air to squeeze, so the air responds faster and the blown note rises.
Tap the same bottle gently and a different system rings: mostly the glass, joined to some of the water. More water adds moving mass and usually slows that ringing, so the tapped note falls.
For matching bottles: more water means blow higher, tap lower. Bottle shape, neck and material matter too, so compare like with like.
Watch one: reverse the ranking
These matching bottles contain one-quarter, one-half and three-quarters water. Predict the order before reading the labels.
The rankings reverse because blowing and tapping do not test the same vibration.
Your turn
- Four matching bottles contain 0, ¼, ½ and ¾ water. Put them in order from lowest to highest note when you blow across them. Which has the smallest air space?
- Now put the same four bottles in order from lowest to highest note when you tap them gently. Why is this order the reverse of your first answer?
- A simple straight tube 40 cm long plays a note. A similar tube half as long plays one octave higher, which means twice the frequency. (a) How long is the tube one octave higher? (b) How long is one that is two octaves higher? Why should you not use this rule for a bottle?
- Three frequencies in the ratio \(4:5:6\) make a simple chord. The lowest bottle is 200 Hz, or 200 vibrations each second. What frequencies should the other two bottles have? Explain how you used the ratio.
Stretch: a bottle is not a tube
For bottles with matching necks, a useful model says \(f^2 \times V\) stays constant, where \(f\) is the blown frequency and \(V\) is the air volume. If the air volume becomes one-quarter as large, what happens to the frequency? What if the air volume is only halved?
Answers
- From lowest to highest: 0, ¼, ½, ¾ water. The bottle with ¾ water has the smallest air space and the highest blown note.
- From lowest to highest: ¾, ½, ¼, 0 water. Blowing makes the trapped air resonate, but tapping makes the glass and some water vibrate. More water leaves less air, so the blown note rises; it also adds moving mass, so the tapped note usually falls.
- (a) \(40 \div 2 = 20\) cm. (b) Halve again: \(20 \div 2 = 10\) cm. A bottle is a chamber with a narrow neck, not a simple straight tube. Its neck and the volume of trapped air both matter.
- The ratio parts are 4, 5 and 6. \(200 \div 4 = 50\) Hz for one part. The frequencies are \(4 \times 50 = 200\) Hz, \(5 \times 50 = 250\) Hz and \(6 \times 50 = 300\) Hz.
Stretch. If \(V\) is divided by 4, then \(f^2\) must be multiplied by 4, so \(f\) is multiplied by 2. The note rises one octave. If \(V\) is only halved, \(f\) is multiplied by \(\sqrt{2}\), about 1.41, not by 2. This is why “half the air means twice the frequency” is the wrong rule for a bottle.