HW11_Solutions

HW11_Solutions - Homework Set 11 Chapter 15: 48. Adjacent...

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Unformatted text preview: Homework Set 11 Chapter 15: 48. Adjacent nodes are separated by a half-wavelength, as examination of Figure 15-26 will show. ( ) 1 node 2 96m s 0.11m 2 2 445Hz v v x f f ! ! = " # = = = = 49. Since 1 n f nf = , two successive overtones differ by the fundamental frequency, as shown below. ( ) 1 1 1 1 1 320Hz 240Hz 80Hz n n f f f n f nf f + ! = " = + " = = " = 57. The frequency is given by 1 . f v F ! ! = = The wavelength and the mass density do not change when the string is tightened. ( ) 2 2 2 2 2 1 1 1 1 1 1 1 294Hz 1.15 315Hz 1 F v F f F F f f f f F F F ! ! ! ! = = " = = " = = = 81. ( a ) The overtones are given by 1 , 2,3,4 n f nf n = = ( ) ( ) ( ) ( ) 2 3 2 3 G: 2 392Hz 784Hz 3 392Hz 1176Hz 1180Hz B: 2 494Hz 988Hz 3 440Hz 1482Hz 1480Hz f f f f = = = = ! = = = = ! ( b ) If the two strings have the same length, they have the same wavelength. The frequency difference is then due to a difference in wave speed caused by different masses for the strings....
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HW11_Solutions - Homework Set 11 Chapter 15: 48. Adjacent...

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