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							 Tonga
																				Tonga									 
										 
										 
										 
											 
											 
			 
			 
			 
			 
			 
			
(b) Combining five cos waves: cos(4.75x) + cos(4.875x) + cos(5x) + cos(5.125x) + cos(5.25x).
(c) Combining seven cos waves: cos(4.8125x) + cos(4.875x) + cos(4.9375x) + cos(5x) + cos(5.0625x) +
cos(5.125x) + cos(5.1875x).
(d) An integral over a continuous range of wave numbers produces a single wave packet.
Now suppose we add five such waves together, as in Fig. 3.2(b). The result is that some beats
turn out to be much stronger than the others. If we repeat this process by adding seven waves
together, but now make them closer in wave number, we get Fig. 3.2(c), we find that most of the
beat notes tend to become very small, with the strong beat notes occurring increasingly far apart.