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The reciprocal of the Period is the Frequency, f. Thus, f = 1/T. The frequency indicates how many cycles exist in one second. To honor one of the 19th century researchers in the field, instead of calling the unit “cycles per second”, we use hertz, named after Heinrich Hertz and abbreviated Hz.
Find the period, amplitude and frequency of y = 3sin2x and sketch a graph from 0 to 6p. This is a sine graph that has been stretched both vertically and horizontally. It will now reach up to 3 and down to -3. The frequency is 2 and so we will see the wave repeat twice over the interval from 0 to 2p.
Learning Objectives. Calculate the amplitude and period of a sine or cosine curve. Calculate the frequency of a sine or cosine wave. Graph transformations of sine and cosine waves involving changes in amplitude and period (frequency).
Frequency signals are usually sine waves, but can also be pulses or square waves. If the frequency signal is an oscillating sine wave, it might look like the one shown in Fig. 17.1.
5. The graph of y = sin x goes through one complete wave every 2π. The length of a wave is called the wavelength or the period. We will use the terms wavelength and period interchangibly. The wavelength can be found by measuring the x-distance between the top of one wave and the top of the next.
The period of sin and cos is length of one full cycle of the wave, which is 2ˇ. The frequency is the reciprocal of the period, so sin and cos have a frequency of 1=(2ˇ). The frequency is the number
There are three attributes to a sine wave: period, amplitude, and phase. We've just covered periodicity. The amplitude “represents the maximum displacement of the varying quantity from its average value” (pg. 39, textbook, John R. Pierce in The Science of Musical Sound). sineGraph4.pd
