| SimReal: Mathematics - Basic - Power / Root | |
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A study of power expression with base 2 and exponent as a fraction (category a/b). In the simulation window you see part of a piano. Mark the checkbox 'Tangent name' to see the name of the white tangent keys c, d, e, f, g, a, h, c. When we press on a tangent key, we hear a tone caused by the vibrations of the piano wire and the air surrounding the piano and that propagates further to our ears. Each tangent has a given frequence (the frequency is a measure how fast the piano wire is oscillating. When we press the piano tangent called 'a', the piano wire oscillates 440 per second and we say that the frequency is 440 Hz (Hertz). Press the piano key called 'a' and listen to this tone with a frequency of 440 Hz. In the simulation window you see a wave illustrating the oscillation. Click the pushbutton 'Start Simulation' to see the movement of this wave. At the left hand of the wave you see a point moving up and down with a given frequency. The definition of frequency is the number of oscillations per second. The time for one oscillation of this point is the same time it takes for a wave top to move the distance to the next top. To be able to see the oscillation, it's necessary to scale down the frequency. With higher frequency the point on the wave will oscillate faster and the the wave tops will be closer. The differences between the frequencies of the piano keys are as follows: The frequency factor between one piano key and the next is constant for the whole piano. The frequency factor in one octave is 2. That means the frequency f2 of high 'c' (to the right on the piano in the simulation window) divided by the frequency f2 of the low 'c' (to the left on the piano) is 2, f2 / f1 = 2. Theory about Power / Root and Piano Simulation of waves Simulation of one piano (harmonics) Theory about harmonics Simulation of Beat (no: Svevning) Simulation of two pianos (beat) Simulation of Doppler Effect Use of Beat and Doppler Effect in medicince |
