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How do you subtract vectors Reverse the subtracted vector and add This is because A B A ( B) Figure 2-10a shows two vectors, A, 4 cm long pointing east, and B, 1 cm long also pointing east Figure 2-10b shows B, which is 1 cm long pointing west Figure 2-10b shows the resultant of A and B It is 3 cm long pointing east To determine the length and direction of the displacement vector, d df di, draw di , which is di reversed Then draw df and copy di with its tail at df s tip Add df and di In the example of the runner, his displacement is df di 250 m 50 m 200 m He moved to the right of the tree To completely describe an object s displacement, you must indicate the distance it traveled and the direction it moved Thus, displacement, a vector, is not identical to distance, a scalar; it is distance and direction What would happen if you chose a different coordinate system; that is, if you measured the position of the runner from another location Look at Figure 2-9, and suppose you change the right side of the d-axis to be zero While the vectors drawn to represent each position change, the length and direction of the displacement vector does not, as shown in Figures 2-11a and b The displacement, d, in the time interval from 10 s to 50 s does not change Because displacement is the same in any coordinate system, you frequently will use displacement when studying the motion of an object The displacement vector is always drawn with its flat end, or tail, at the earlier position, and its point, or tip, at the later position



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Waves transfer energy without transferring matter In transverse waves, the displacement of the medium is perpendicular to the direction of wave motion In longitudinal waves, the displacement is parallel to the direction of wave motion Frequency is the number of cycles per second and is related to period by: f

(p 388)

interference (p 388) node (p 389) antinode (p 389) standing wave (p 389) wave front (p 390) ray (p 390) normal (p 391) law of reflection (p 391) refraction (p 391)

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When a wave crosses a boundary between two media, it is partially transmitted and partially reflected The principle of superposition states that the displacement of a medium resulting from two or more waves is the algebraic sum of the displacements of the individual waves Interference occurs when two or more waves move through a medium at the same time When two-dimensional waves are reflected from boundaries, the angles of incidence and reflection are equal The change in direction of waves at the boundary between two different media is called refraction

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The half-wavelength dipole is too long for some applications where real estate is at a premium The solution for many operators is to use a coil-loaded shortened dipole such as shown in Fig 6-13 A shortened dipole (ie, one which is less than a halfwavelength) is capacitive reactance There is no reason why the loading coil cannot be any point along the radiator, but in Figs 6-13A and 6-13B they are placed at 0 percent and 50 percent of the element length, respectively The reason for this procedure is that it makes the calculation of coil inductances easier, and it also represents the most common practice Figure 6-13C shows a table of inductive reactances as a function of the percentage of a half-wavelength, represented by the shortened radiator It is likely that the percentage figure will be imposed on you by the situation, but the general rule is to pick the largest figure consistent with the available space For example, sup-

the position of a point on the rope before the pulse arrives compare to the point s position after the pulse has passed (142)

periodic wave (142)

class Oofla { } class Yazell implements Whomper { } class Floordum { } interface Whomper { } class Grobnet extends Yazell, Floordum { List<Oofla> o; }

wave velocity (142)

one end of a spring from side to side How does the frequency of your hand compare with the frequency of the wave (142)

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2-6 Wave polarization is determined by the direction of the electric field lines of force: (A) vertical polarized electromagnetic wave; (B) horizontally polarized wave

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