There is another quantity that corresponds to the period, and we might cal the period in space, but it is usually called the wavelength, symbolized X.The avelength is the distance occupied by one complete cycle. It is easy to see, then that the wavelength is 2T/k, because k times the wavelength would be the number of radians that the whole thing changes, being the product of the rate of change the radians per meter, times the number of meters, and we must make a 2T change for one cycle. So kA= 2T is exactly analogous to wto= 2T Now in our particular wave there is a definite relationship between the fre- quency and the wavelength, but the above definitions of k and w are actually quite general. That is, the wavelength and the frequency may not be related in the same way in other physical circumstances. However, in our circumstance the rate of change of phase with distance is easily determined, because if we call p=w(I-r/c)the phase, and differentiate(partially)with respect to distance the rate of change, ao/ar, is There are many ways to represent the same thing, such as (29.7) ck(296) A=2mc(29.8) ly is the wavelength equal to c times the period? That's very easy, of course ecause if we sit still and wait for one period to elapse, the waves, travelling at the eed c, will move a distance cfo, and will of course have moved over just one wavelengt In a physical situation other than that of light, k is not necessarily related to w) in this simple way. If we call the distance along an axis x then the formula for a cosine wave moving in a direction x with a wave number k and an angular fre- quency w will be written in general as cos(ot -kx). Now that we have introduced the idea of wavelength, we may say something more about the circumstances in which (29. 1)is a legitimate formula. We recall that the field is made up of several pieces, one of which varies inversely as r, another part which varies inversely as r, and others which vary even faster. It would be worth while to know in what circumstances the I/r part of the field is the most important part, and the other parts are relatively small. Naturally, the answer is if we go 'far enough'away, because terms which vary inversely as the square ultimately become negligible compared with the 1/rterm. How far is"far enough""?2 The answer is, qualitatively, that the other terms are of order x/r smaller than the 4x24 he field. Sometimes the region beyond a few wavelengths is alled the“ wave zone a=0 0 =T 29-4 Two dipole radiators Next let us discuss the mathematics involved in combining the effects of two Fig. 29-5. The intensities in various oscillators to find the net field at a given point. this is very easy in the few cases directions from two dipole oscillators idered in the previous chapter. We shall first describe the effects e-half wavelength apart. Left: in qualitatively, and then more quantitatively. Let us take the simple case, where the phase (a= O). Right: one- half period oscillators are situated with their centers in the same horizontal plane as the de- out of phase(a= t). tector. and the line of vibration is vertical Figure 29-5(a)represents the top view of two such oscillators, and in this particular example they are half a wavelength apart in a N-s direction, and are oscillating together in the same phase, which we call zero phase. Now we would like to know the intensity of the radiation in various directions. By the intensity we mean the amount of energy that the field carries past us per second, which is roportional to the square of the field averaged in time. So the thing to look at hen we want to know how bright the light is, is the square of the electric field, not the electric field itself. (The electric field tells the strength of the force felt by a