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As you learned in 14, the wavelength, , of a wave is a function of its speed in the medium in which it is traveling and its constant frequency, f Because light has wave properties, the same mathematical models used to describe waves in general can be used to describe light For light of a given frequency traveling through a vacuum, wavelength is a function of the speed of light, c, which can be written as 0 c/f The development of the laser in the 1960s provided new methods of measuring the speed of light The frequency of light can be counted with extreme precision using lasers and the time standard provided by atomic clocks Measurements of wavelengths of light, however, are much less precise Different colors of light have different frequencies and wavelengths, but in a vacuum, they all travel at c Because all wavelengths of light travel at the same speed in a vacuum, when you know the frequency of a light wave in a vacuum, you can calculate its wavelength, and vice versa Thus, using precise measurements of light frequency and light speed, you can calculate a precise value of light wavelength Relative motion and light What happens if a source of light is traveling toward you or you are moving toward the light source You learned in 15 that the frequency of a sound heard by the listener changes if either the source or the listener of the sound is moving The same is true for light However, when you consider the velocities of a source of sound and the observer, you are really considering each one s velocity relative to the medium through which the sound travels Because light waves are not vibrations of the particles of a mechanical medium, unlike sound waves, the Doppler effect of light can involve only the velocities of the source and the observer relative to each other The magnitude of the difference between the velocities of the source and observer is called the relative speed Remember that the only factors in the Doppler effect are the velocity components along the axis between the source and observer, as shown in Figure 16-19.



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Figure 16-19 The observer and the light source have different velocities (a) The magnitude of the vector subtraction of the velocity components along the axis between the source of light and the observer of the light is referred to as the relative speed along the axis between the source and observer, v (b) (Illustration not to scale)

The Doppler effect To study the Doppler effect for light, the problem can be simplified by considering axial relative speeds that are much less than the speed of light (v c) This simplification is used to develop the equation for the obseved light frequency, fobs, which is the frequency of light as seen by an observer Observed Light Frequency fobs f 1





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same manner as the horizontal dipole, but is mounted in the vertical plane In general, the section of the radiator that is closest to the ground should be connected to the shield end of the coaxial cable transmission line Like the horizontal dipole, the approximate length of the vertical dipole is calculated from Lft = where Lft is the length, in feet FMHz is the operating frequency, in megahertz Example Calculate the length of a half-wavelength vertical dipole for operation on a frequency of 14250 MHz in the 20-m amateur radio band 468 FMHz [72]

The observed frequency of light from a source is equal to the actual frequency of the light generated by the source, times the quantity 1 plus the relative speed along the axis between the source and the observer if they are moving toward each other, or 1 minus the relative speed if they are moving away from each other

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Because most observations of the Doppler effect for light have been made in the context of astronomy, the equation for the Doppler effect for light generally is written in terms of wavelength rather than frequency Using the relationship c/f and the v c simplification, the following equation can be used for the Doppler shift, , which is the difference between the observed wavelength of light and the actual wavelength

v c The difference between the observed wavelength of light and the actual wavelength of light generated by a source is equal to the actual wavelength of light generated by the source, times the relative speed of the source and observer, divided by the speed of light This quantity is positive if they are moving away from each other or negative if they are moving toward each other

Doppler Shift (

Answer (for Objective 15): B is correct The no-arg LaoTzu constructor invokes the other LaoTzu constructor (via "this"), and the second LaoTzu constructor chains to the Philosopher s constructor (via "super") A, C, D, E, and F are incorrect based on the above

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