![]() ![]() ![]() Does the frequency depend linearly on whole tones from the base? Why or why not? (d) Find values for the parameters in an exponentially growing function which takes in a mimber of whole tones k away from the base, and returns the frequency of the note: (k)= (-2/ for which f(0) = 110 and f(6) = 880. If our base ( whole tones from the base) is an A (110 Hz), then the third" is a C# (551.37 Hz) and the fifth" is an E (659.25 Hz). For example, a "third" is 2 whole tones from the base a "fifth" is 3.5 whole tones from the base. (c) Notes are often thought of as some fixed position away from a base. Label your axes, and mark the times of the first few periode appropriately. What is the period of a 140 Hxxignal (this is referred to in music as "A4")? What about the period of an 880 Hz signal (referred to as "A5")? What about a signal with frequency /? (b) Supposing two sinusoidal functions with frequencies 110 Hx and 880 Hx are played at the same volume (no their amplitudes are both 1) with no phase shift and were average, draw each function separately, then draw them together on the same graph. (1) When listening to musie, our ears understand two sounds to be the same pitch (but different "octaves") if the frequencies are a factor of two apart. For instance, a 10 Hx signal goes through 10 cycles in one second, so its period is 1/10 second: T-6 T = 10 cond) cycles le (1 seconds (1 cycle) = Gove ) (1 cycle) = a second. The frequency is inversely related to the period of the signal. ![]() For example, 1 Hz corresponds to one cycle per second, and the period is also l second. Be careful with the volume if you are wearing headphones! A "pure tone in music can be expressed in in herty, which is in units of cycles per second strictly, the units are only "inverse seconds" and "cycles are neglected). If you'd like, use a tone generator (for example, ) or a keyboard to play the noter/frequencies mentioned. This problem is an application of the notions exponential growth and sinusoidal functions to music. ![]()
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