Assignment_4_Brief_Answers_09 - L = 10 5 m Length for C 9...

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Physics 2214 Assignment 4 Brief Answers 1. The displacements have amplitde s 0 = 0 . 0115 nm. 2. (a) The wave speed is v = 190 . 5 m / s. (b) The next two modes have frequency f 2 = 300 Hz and f 3 = 450 Hz. (c) The ﬁrst three allowed modes now have frequency f 0 1 = 187 . 5 Hz, f 0 2 = 375 Hz, and f 0 3 = 562 . 5 Hz. (d) The ﬁrst three allowed modes now have frequency f 0 1 = 750 Hz, f 0 2 = 1500 Hz, and f 0 3 = 2250 Hz. 3. (a) The standing wave frequencies are f n = n c 2 L . (b) i. 7 modes will be excited. ii. The length must be L = 0 . 15 m. 4. (a) The ﬁrst three modes look like: x s m ( x ) A 0 - A L x s m ( x ) A 0 - A L 1

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x s m ( x ) A 0 - A L (b) The ﬁrst three modes with arrows indicating direction: x s m ( x ) A 0 - A L x s m ( x ) A 0 - A L x s m ( x ) A 0 - A L (c) n + 1 adjacent regions. 2
(d) n + 1 degrees of freedom. 6. (a) Length for C 0 , both open: L = 5 . 25 m. Length for C 9 , both open: L = 0 . 0102 m. Length for C 0 , one open, one closed:

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Unformatted text preview: L = 10 . 5 m. Length for C 9 , one open, one closed: L = 0 . 0204 m. (b) i. Linear frequency scale Note Number f (Hz) 24 48 72 96 2000 4000 6000 8000 ii. Logarithmic frequency scale Note Number f (Hz) 24 48 72 96 10 1 10 2 10 3 10 4 (c) Pipe lengths vary exponentially. (d) Pitch varies as pitch ∝ log f 7. (a) Magnitude and phase of k th mode given by | A k | = 1 k p (1-. 04 k 2 ) 2 + 0 . 0001 k 2 F mω 2 and φ k = tan-1 ±-. 2 k 20(1-. 04 k 2 ) ² . (c) The curve in red is (i), the drive. The curve in blue is (ii), the response. 3 t F ( t ), y ( t ) 2 π/ω-A A 4...
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Assignment_4_Brief_Answers_09 - L = 10 5 m Length for C 9...

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