Physics
Phase Angle
Phase angle refers to the measure of the relative position of two waveforms or oscillations. In physics, it is often used to describe the relationship between the displacement and velocity of a vibrating object. It is measured in degrees or radians and provides valuable information about the timing and alignment of different waveforms.
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eBook - PDF- Stanley A. Gelfand(Author)
- 2016(Publication Date)
- Thieme(Publisher)
The angle between the radius and the horizontal is called the Phase Angle ( θ ) and is a handy way to tell loca-tion going around the circle and on the sine wave. In other words, we consider one cycle (one “round trip” of oscillation) to be the same as going around a circle one time. Just as a circle has 360°, we also W ave propagation Oscillations of individual particle s Longitudinal representation Transverse representation Amplitud e Distance Wavelength Wavelength Fig. 1.6 Longitudinal and transverse representations of a sound wave. Wavelength (λ) is the distance covered by one replication (cycle) of a wave, and is most easily visualized as the distance from one peak to the next. Fig. 1.7 Sinusoidal motion (θ, Phase Angle; d, displacement). (Adapted from Gelfand 2010, courtesy of Informa.) 1 Acoustics and Sound Measurement 11 180° is covered in ½ second; 90° takes ¼ second; 270° takes ¾ second; etc. Hence, the Phase Angle also reflects the elapsed time from the onset of rota -tion. This is why the horizontal axis in Fig. 1.8 can be labeled in terms of phase. As such, the phase of the wave at each of the points indicated in Fig. 1.7 is 0° at a , 45° at b , 90° at c , 135° at d , 180° at e , 225° at f , 270° at g , 315° at h , and 360° at i , which is also 0° for the next cycle. Phase is often used to express relationships between two waves that are displaced relative to each other, as in Fig. 1.8 . Each frame in the figure shows two waves that are identical to each other except that they do not line up exactly along the hor-izontal (time) axis. The top panel shows two waves that are 45° apart. Here, the wave represented by the thicker line is at 45° at the same time that the other wave (shown by the thinner line) is at 0°. The phase displacement is highlighted by the shaded area and the dotted vertical guideline in the figure. This is analogous to two radii that are always 45° apart as they move around a circle.
eBook - PDF- Stanley A. Gelfand(Author)
- 2011(Publication Date)
- Thieme(Publisher)
1 1 Acoustics and Sound Measurement Recall that r rotates around the circle at a fixed speed. Hence, how fast r is moving will determine how many degrees are covered in a given amount of time. For example, if one com-plete cycle of rotation takes 1 second, then 360 ° is covered in 1 second; 180 ° is covered in � second; 90 ° takes � second; 270 ° takes � sec-ond, etc. Hence, the Phase Angle also reflects the elapsed time from the onset of rotation. This is why the horizontal axis in Fig. 1.6 can be labeled in terms of phase. As such, the phase of the wave at each of the points indicated in Fig. 1.6 is 0 ° at a , 45 ° at b , 90 ° at c , 135 ° at d , 180 ° at e , 225 ° at f , 270 ° at g , 315 ° at h , and 360 ° at i , which is also 0 ° for the next cycle. Phase is often used to express relationships between two waves that are displaced relative to each other, as in Fig. 1.7 . Waves a and b are identical except that they do not line up exactly along the horizontal (time) axis. Notice that wave b is displaced from wave a so that wave a is at 45 ° at the same time that b is at 0 ° (shown by the dotted vertical guideline in the figure). In other words, waves a and b are 45 ° apart or out-of-phase . Similarly, waves c and d are displaced from each another by 90 ° because wave c is at 90 ° when wave d is at 0 ° (at the dotted vertical guideline). Hence, c and d are 90 ° out-of-phase. Waves e and f are 180 ° out-of-phase. Here, wave e is at its 90 ° (positive) peak at the same time that wave f is at its 270 ° (negative) peak. The difference between them is 270 ° – 90 ° = 180 ° Notice that these two otherwise identical waves are exact mirror images of each other when they are 180 ° out-of-phase. Parameters of Sound Waves We already know that a cycle is one complete replication of a vibratory pattern. For example, two cycles are shown for each sine wave in the upper frame of Fig. 1.8 , and four cycles are shown for each sine wave in the lower frame.
eBook - PDF- Stanley A. Gelfand, Lauren Calandruccio(Authors)
- 2022(Publication Date)
- Thieme(Publisher)
As such, the phase of the wave at each of the points indicated in Fig. 1.7 is 0° at a, 45° at b, 90° at c, 135° at d, 180° at e, 225° at f, 270° at g, 315° at h, and 360° at i, which is also 0° for the next cycle. Phase is often used to express relationships be- tween two waves that are displaced relative to each other, as in Fig. 1.8. Each frame in the figure shows two waves that are identical to each other except that they do not line up exactly along the horizontal (time) axis. The top panel shows two waves that are 45° apart. Here, the wave represented by the thicker line is at 45° at the same time that the other wave (shown by the thinner line) is at 0°. The phase displacement is highlighted by the shaded area and the dotted vertical guideline in the figure. This is analogous to two radii that are always 45° apart as they move around a circle. In other words, these two waves are 45° apart or out- of-phase. The second panel shows the two waves dis- placed from each another by 90°, so that one wave is at 90° when other one is at 0°. Hence, these waves are 90° out-of-phase, analogous to two radii that are always 90° apart as they move around a circle. The third panel shows two waves that are 180° out-of- phase. Here, one wave is at its 90° (positive) peak Fig. 1.8 Each panel shows two waves that are identical in every way except they are displaced from one another in terms of phase, highlighted by the shaded areas and the dotted vertical guidelines. Analogous examples of two radii moving around a circle are shown to the left of the waveforms. Top panel: Two waves that are 45° out-of-phase, analo- gous to two radii that are always 45° apart as they move around a circle. Second panel: Waves that are 90° out-of- phase, analogous to two radii moving around a circle 90° apart. Third panel: Waves that are 180° out-of phase, analogous to two radii that are always 180° apart (pointing in opposite direc- tions) moving around a circle.
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