problem16_71

University Physics with Modern Physics with Mastering Physics (11th Edition)

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16.71: a) . 1 1 1 1 2 1 2 1 S S L R - + - = + - = + - = c v c v f f v c v c f f c v c v b) For small x , the binomial theorem (see Appendix B) gives ( 29 , 2 1 1 2 1 x x - - ( 29 , 2 1 1 2 1 x x - + - so - - c v f c v f f 1 2 1 S 2 S L where the binomial theorem has been used to approximate ( 29 . 1 2 1 2 x x - - The above result may be obtained without resort to the binomial theorem by expressing R f in terms of S f as . ) ( 1 ) / ( 1 ) ( 1 ) ( 1 ) ( 1 ) ( 1 2 S S R c v c v f c v c v c v c v f f - - = - - + - = To first order in c v , the square root in the denominator is 1, and the previous result is
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Unformatted text preview: c) For an airplane, the approximation c v << is certainly valid, and solving the expression found in part (b) for , v , s m 8 . 56 Hz 10 2.43 Hz 46.0 ) s m 10 00 . 3 ( 8 8 S beat S R S = × × = =-= f f c f f f c v and the approximation c v << is seen to be valid. Note that in this case, the frequency difference is known to three figures, so the speed of the plane is known to three figures....
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