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In a radio or television transmitting antenna, electrons are moving back and forth at an extreme speed Their velocity is constantly changing as they speed up in one direction, slow down, reverse direction, speed up again, and so on Any change of velocity is acceleration When electrons move, a magnetic field is created When electrons accelerate, a changing magnetic field is produced An alternating magnetic (M) field gives rise to an alternating electric (E) field, and this generates another changing M field The process has come full circle Thus it repeats, the effects propagating through space at the speed of light The E and M fields expand alternately outward from the source in spherical wavefronts At any given point in space, the E flux is perpendicular to the M flux The direction of wave travel is perpendicular to both the E and M flux lines (Fig 26-14) The EM flux field can oscillate at any conceivable frequency, ranging from many years per cycle to quadrillions of cycles per second The sun has a magnetic field that oscillates with a 22-year cycle Radio waves oscillate at thousands, millions, or billions of cycles per second Infrared, visible light, ultraviolet, and X rays oscillate at many trillions of cycles per second All of these effects are electromagnetic fields, and as such, they all

Next, we check ( 2, 5) in the second original equation: 6x + 2y = 2 6 ( 2) + 2 ( 5) = 2 12 + ( 10) = 2 2=2 Finishing up, we check ( 3, 8) in the second original equation: 6x + 2y = 2 6 ( 3) + 2 ( 8) = 2 18 + ( 16) = 2 2=2

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Are you confused (or bemused)

have exactly the same form The difference is in their frequency The frequency of an electromagnetic wave is directly related to the wavelength in space

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Think back to the notion of multiplicity for the roots of certain quadratic, cubic, and higher-degree equations Do you wonder if the same concept applies to the solutions of two-by-two systems when at least one of the equations is of degree 2 or more Well, it does! If the equation we create by mixing has a root with multiplicity of 2 or more, the corresponding solution of the whole system has the same multiplicity You ll see this happen as you work out the last two practice exercises at the end of this chapter

R-S flip-flop inputs are labeled R (reset) and S (set) The outputs are Q and Q (Often, rather than Q, you will see Q , or perhaps Q with a line over it) The outputs are always in logically opposite states The symbol for an R-S flip-flop, also known as an asynchronous flipflop, is shown in Fig 26-3A The truth table (a specialized form of table denoting logic functions) for an R-S flip-flop is at Table 26-3A Synchronous flip-flop states change when triggered by the signal from a clock In static triggering, the outputs change state only when the clock signal is either high or low This type of circuit is sometimes called a gated flip-flop In positive-edge triggering, the outputs change state at the instant the clock pulse is positive-going The term edge triggering derives from the fact that the abrupt rise or fall of a pulse looks like the edge of a cliff (Fig 26-3B) In negative-edge triggering, the outputs change state at the instant the clock pulse is negativegoing Master/slave (M/S) flip-flop inputs are stored before the outputs are allowed to change state This device essentially consists of two R-S flip-flops in series The first flip-flop is called the master, and the second is called the slave The master flip-flop functions when the clock output is high, and the slave acts during the next low portion of the clock output This time delay prevents confusion between the input and output J-K flip-flop operation is similar to that of an R-S flip-flop, except that the J-K has a predictable output when the inputs are both 1 Table 26-3B shows the input and output states for this type of flip-flop The output changes only when a triggering pulse is received The symbol for a J-K flip-flop is shown in Fig 26-3C R-S-T flip-flop operation is similar to that of an R-S flip-flop, except that a high pulse at the T input causes the circuit to change state The T flip-flop has only one input Each time a high pulse appears at the T input, the output state is reversed.

Here s a challenge!

All electromagnetic fields have frequencies and wavelengths that are inversely related If fMHz is the frequency of a wave in megahertz, and Lft is the wavelength in feet, then Lft = 984/fMHz for waves in outer space or in the atmosphere of the earth If the wavelength is given as Lm in meters, then Lm = 300/fMHz The inverses of these formulas, for finding the frequency if the wavelength is known, are fMHZ = 984/Lft

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