Ideas for Math

Distance and the speed of sound
The speed of sound is approximately 330 m/s
The speed of light is so fast that when we see lightening, we normally say that it happens right them, regardless of how far away it is.

1) If we see lightening, and it takes 8,5 seconds until we hear thunder - how far away did the lightening strike?
2) And if it takes 5 seconds from you see lightening until you hear thunder - what is the distance?

The speed of sound and echo
3) If you shout towards a mountain or big rock formation, you will hear an echo. How do you calculate the distance to the rock formation?
4) Use the Delay-program. Time the echoes, and calculate the distances as if you have heard the echoes in the real world.
5) If you know the distance to a rock formation, you can calculate the time of the echo, how?

The speed of sound and reverb
Reverb functions in much the same way as echoes. It is easy to hear with your eyes closed if the room is large or small. You can hear this on how long it takes from the sound to die out. The latter also depends on what is on walls and ceiling in the room. The article Sound and Physical Space provides good explanations for these things. Look at the different words that are linked in the text.

Sound is oscillations in the auditory range, which is 20 - 20 000 Hz. We know that Hz is a measure on frequency, so that the number of Hertz is the same as number of oscillations/secod. 60 Hz, for example, is 60 oscillations/second.

When we see waves in water, we can measure the wavelength from one top to the next, although it is a little difficult. We can also calculate the wavelength to the different sound frequencies.

6) How will you calculate the wavelength for the lowest frequency a human can hear? Hint: We know the speed of the sound, which is the same for all frequencies. The math is: speed of sound divided into number of oscillations/second.
7) Do the math for 100 Hz, 330 Hz, 4000 Hz.

Resonance, reverb
Wavelength is important in determining resonance, because all acoustical rooms from guitar bodies to cathedrals have physical dimensions that amplifes and weakens different frequencies.

Natural scale
Use the information in Spectra and Harmonics to calculate natural scales. (The components are evenly spaced from the fundamental.) Use the Additiv Synthesis-program to hear the results.