542_Physics ProblemsTechnical Physics

# 542_Physics ProblemsTechnical Physics - 544 P18.60...

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544 Superposition and Standing Waves P18.60 v = × = 48 0 2 00 4 80 10 141 3 . . . a fa f m s d NN m = 1 00 . ; λ = 2 00 . m ; f v = = λ 70 7 . Hz λ a a v f = = = 343 70 7 4 85 m s Hz m . . P18.61 Call L the depth of the well and v the speed of sound. Then for some integer n L n n v f n = = = 2 1 4 2 1 4 2 1 343 4 51 5 1 1 1 a f a f a fb g e j λ m s s . and for the next resonance L n n v f n = + = + = + 2 1 1 4 2 1 4 2 1 343 4 60 0 2 2 1 a f a f a fb g e j λ m s s . Thus, 2 1 343 4 51 5 2 1 343 4 60 0 1 1 n n = + a fb g e j a fb g e j m s s m s s . . and we require an integer solution to 2 1 60 0 2 1 51 5 n n + = . . The equation gives n = = 111 5 17 6 56 . . , so the best fitting integer is n = 7. Then L = = 2 7 1 343 4 51 5 21 6 1 a f b g e j m s s m . . and L = + = 2 7 1 343 4 60 0 21 4 1 a f b g e j m s s m . . suggest the best value for the depth of the well is
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