M u s i c a n d M a t h e m a t i c s

1. 8 b from Risskov School presents Musicand Mathematics Tones in Glass

2. 12 tones in one octave • Spreading of the 12 tones by means of • The starting point is the concert pitch a • a has a frequency of 440 Hz • When you multiply with , you get the tone above • Divided by , you get the tone below

3. The frequencies of an octave

4. Conditions for tones in glass We have examined if the following has an impact on tones in glass: • Temperature • Connexion between quantity of water in the glass and the frequency • Other materials than water in the glass

5. Temperature Thesis: When the water gets warmer, the tone becomes deeper. Conclusion: Temperature has no influence

6. Quantity of water and the frequency Thesis: There is a connexion between quantity of water and frequency. Our researches showed: • Two different glasses with the same percen-tage of water in proportion to the volume of the glasses do not give the same tone. • You can not find more tones in the same glass simply by adding x ml water (or removing from) the glass. Conclusion: We were wrong!

7. Other materials than water Thesis: It makes a difference to put other materials than water in the glass. Vi made experiments with: • Pure water • 10% salt • 10% sugar • 10% oil The speed of one oscillation/wave in pure water The speed of one oscillation/wave in 10% salt

8. Other materials than water continued Water: • The speed of one oscillation/wave is 0,001 s • Number of oscillations per second (frequency): 1/0,001 s = 1000 Hz 10 % salt: • The speed of one oscillation/wave is 0,0012 s • Number of oscillations per second (frequency): 1/0,0012 s = 833,33 Hz

9. Other materials than water continued Percentage the ”salt-frequency” is less than the ”water-frequency”: (1000 Hz – 833,33 Hz)/1000 Hz · 100 = 16,7 %

10. Other materials than water continued Conclusion: • The numbers do show a difference in the tone. • You could not hear a difference in the tone. The ”oil-water” did sound different, though. • A very questionably experiment.

11. Found tones Method to find the frequency of the tones • The speed of one oscillation/wave (from one wave top to the next) – in this situation 1,8 ms • Frequency: 1/0,0018 s = 556,56 Hz • 556,56 Hz/2 = 278,28 Hz. It is the tone cis (275 Hz). 556,56 Hz is cis one octave higher. This is how we have found all our tones. Science Workshop-program. By the use of a microphone the program shows a tone’s speed of one oscillation/wave.

12. Found tones continued The speed of sound in air is 340 m/s The speed of sound in glass is 5000 m/s Wavelength = speed/frequency The tone cis in glass: 5000 m/s / 555 Hz = 9 m The tone cis in water: 340 m/s / 555 Hz = 0,61 m

13. Found tones continued Percentage the wavelength in glass is bigger than the wavelength in air (the tone cis): (9 m – 0,61 m)/0,61 m · 100 = 1375 %

14. Conclusion • You can spread the 12 tones in one octave by means of . • Temperature of water in the glass has no influence on the tone. • There is no connexion between quantity of water and frequency. • Mathematical there was a difference in the frequencies, when the material is different from water. But you could not hear it (a very questionably experiment).

15. Conclusion continued • We found our own method to find the frequencies of the tones by the use of Science Workshop. Our starting point was one oscillation’s speed. • The tone cis’ wavelength in glass is 1375% bigger than the wavelength in air. • We think it is a fine instrument, and you can be very good at playing it. In Denmark we have professionals.