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 3 156 10 237 10 = × . . kg 0.658 m kg m. The second, 2 3 3 675 10 711 10 = × . . kg 0.950 m kg m. The tension in both is T == 693 679 .. kg 9.8 m s N 2 . The speed of waves in the first string is v T 1 1 3 67 9 169 × = . N 2.37 10 kg m ms and in the second v T 2 2 97 8 . m s. The two strings vibrate at the same frequency, according to nv L L 11 1 22 2 = nn 12 169 20658 97 8 20950 m m . . . af = n n 2 1 250 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 2169 257 m Hz bg . = . junction FIG. P18.22(b) *P18.23 For the E-string on a guitar vibrating as a whole, vf λ 330 64 0 Hz 2 cm . . When it is stopped at the first fret we have 2330 2 330 2 64 0 12 Hz Hz cm Lv F .
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