Simple Nature - Light and Matter

can be constructed as a superposition of sine waves with frequenciesf, 2f, 3f, . . . In this sense, sine waves are the basic, pure buildingblocks of all waves. (Fourier’s result so surprised the mathematicalcommunity of France that he was ridiculed the first time he publiclypresented his theorem.)However, what definition to use is really a matter of convenience.Our sense of hearing perceives any two sounds having the sameperiod as possessing the same pitch, regardless of whether they aresine waves or not. This is undoubtedly because our ear-brain systemevolved to be able to interpret human speech and animal noises,which are periodic but not sinusoidal. Our eyes, on the other hand,judge a color as pure (belonging to the rainbow set of colors) onlyif it is a sine wave.Discussion QuestionsA Suppose we superimpose two sine waves with equal amplitudesbut slightly different frequencies, as shown in the figure. What will thesuperposition look like? What would this sound like if they were soundwaves?v / Discussion question A.w / The pattern of waves madeby a point source moving to theright across the water. Notethe shorter wavelength of theforward-emitted waves andthe longer wavelength of thebackward-going ones.6.1.5 The Doppler effectFigure 7.2.8 shows the wave pattern made by the tip of a vibratingrod which is moving across the water. If the rod had beenvibrating in one place, we would have seen the familiar pattern ofconcentric circles, all centered on the same point. But since thesource of the waves is moving, the wavelength is shortened on oneside and lengthened on the other. This is known as the Dopplereffect.Note that the velocity of the waves is a fixed property of themedium, so for example the forward-going waves do not get an extraboost in speed as would a material object like a bullet being shotforward from an airplane.We can also infer a change in frequency. Since the velocity isconstant, the equation v = fλ tells us that the change in wavelengthmust be matched by an opposite change in frequency: higherfrequency for the waves emitted forward, and lower for the onesemitted backward. The frequency Doppler effect is the reason for354 Chapter 6 Waves