# Sine wave frequency and amplitude relationship

### Phase (waves) - Wikipedia

Calculate the amplitude and period of a sine or cosine curve. of sine and cosine waves involving changes in amplitude and period (frequency). .. you were given the frequency and asked to find the period using the following relationship. Where sine waves occur in nature - sound waves, mechanical motion, The amplitude of a sine wave is the maximum distance it ever reaches from zero. Since the In the bouncing weight above, the frequency is about one cycle per second. A seagull bobs up and down on a sinusoidal-shaped periodic ocean wave with a The Relationship between Wave Frequency, Period, Wavelength, and.

## Amplitude, Period, Phase Shift and Frequency

Time zones are also analogous to phase differences. A real-world example of a sonic phase difference occurs in the warble of a Native American flute.

The amplitude of different harmonic components of same long-held note on the flute come into dominance at different points in the phase cycle. The phase difference between the different harmonics can be observed on a spectrogram of the sound of a warbling flute. In time and frequency, the purpose of a phase comparison is generally to determine the frequency offset difference between wave cycles with respect to a reference.

The oscilloscope will display two sine waves, as shown in the graphic to the right. In the adjacent image, the top sine wave is the test frequencyand the bottom sine wave represents a signal from the reference.

### Phase, Frequency, Amplitude, and all that..

If the two frequencies were exactly the same, their phase relationship would not change and both would appear to be stationary on the oscilloscope display. Since the two frequencies are not exactly the same, the reference appears to be stationary and the test signal moves.

**Wave Amplitude**

By measuring the rate of motion of the test signal the offset between frequencies can be determined. Vertical lines have been drawn through the points where each sine wave passes through zero.

The bottom of the figure shows bars whose width represents the phase difference between the signals. In this case the phase difference is increasing, indicating that the test signal is lower in frequency than the reference.

We say that it has a period which we will denote by given by The height of the peaks and valleys in this function will be given by its amplitude. We are now ready to consider the effect of the phase-shift.

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In fact, we can make note of the fact that the graph of the function will cross the t axis when The first time that this happens is when which corresponds to a value of t given by Thus, the graph will be shifted so that it crosses the t axis at this value.

The shape of the curve does not change, only its position on the t axis. Superimposing sines and cosines Let us take a second look at the function we investigated above, and notice that when we apply the trigonometric identity we obtain is a constant, and therefore so isand assigning the names we have found that Thus, by using a trigonometric identity for the sums of angles, we have reduced a problem we needed to understand the question we started with, at the top of this page with a problem that we already know how to solve.

We have found that the sum of a sine and a cosine curve is actually equivalent to a sine with a phase shift. A bit of care is required, however, since in order for this conversion to work, it must be true that For your consideration: Describe the behaviour of the function Solution: We observe that the constants in front of the trigonometric functions have the values We would like to find the angle and the amplitude that fit with this pattern.

The ratio of the constants Thus, looking up the angle that has a value of we find that Thus the phase shift is.

We further calculate that which tells us that.