531_Physics ProblemsTechnical Physics

531_Physics ProblemsTechnical Physics - Chapter 18*P18.22...

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Chapter 18 533 *P18.22 The first string has linear density µ 1 3 3 1 56 10 2 37 10 = × = × . . kg 0.658 m kg m. The second, µ 2 3 3 6 75 10 7 11 10 = × = × . . kg 0.950 m kg m. The tension in both is T = = 6 93 67 9 . . kg 9.8 m s N 2 . The speed of waves in the first string is v T 1 1 3 67 9 169 = = × = µ . N 2.37 10 kg m m s and in the second v T 2 2 97 8 = = µ . m s . The two strings vibrate at the same frequency, according to n v L n v L 1 1 1 2 2 2 2 2 = n n 1 2 169 2 0 658 97 8 2 0 950 m s m m s m . . . a f a f = n n 2 1 2 50 5 2 = = . . Thus n 1 2 = and n 2 5 = are the number of antinodes on each string in the lowest resonance with a node at the junction. (b) The first string has 2 1 3 + = nodes and the second string 5 more nodes, for a total of 8, or 6 other than the vibrator and pulley. (a) The frequency is 2 169 2 0 658 257 m s m Hz b g a f . = . junction FIG. P18.22(b) *P18.23 For the E-string on a guitar vibrating as a whole, v f = = λ 330 64 0 Hz 2 cm a f . . When it is stopped at the first fret we have 2330 2 330
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