Quiz1_Solution

# Quiz1_Solution - Quiz 1 Monday January 2“" 2009 PHY...

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Unformatted text preview: Quiz 1. Monday, January 2“", 2009 PHY 252 Name: SOL. UT I O N 0169*) = rooseﬂ‘zi't 1. A wave has the form n(x,t) = 1.2 x10‘8 cos(27r[3 X102t+ 0.872x:|) m. All numbers are in standard SI units. Determine: a. The direction of the waves motion. (+2: or —x?) {39 (1 point) b. The wave amplitude. (1 point) do: I-zxm 3M .=_ 11m“ c. The wave frequency. I ‘ (1 point) 5-: 300 H2. (1 514. :93.) d. The wavelength. (A. = , = I. '5. M (to (1 point) 0.8?2 e. The speed of propagation. (1 point) q, = 3cm == 300- _—_ 344MB c ssh-55s) 0.8?2. 5 3001.415 2. A piano tuner stretches a steel piano wire with a tension of F = 800 N. The wire is L: 0.400 m long and has a mass of m = 3.00 g. Given that the wave velocity is vp = N/FL/m ; a. What is the frequency of the fundamental mode? (1 point) “up = i9. =. 6171. _ ’A, = g??- M “=1 for the. :Suualameu‘faL K __ "U _ El? _l. = j. )1. fr! ﬂ 1 — m 2L h ml. 2. I\ __ I sooN 3 J. -— :1". ‘ Son'3ijoA-oom ‘2. _ 4—08 HZ+£W tl‘etfuualamenta-L. b. What is the number of the highest harmonic that could be heard by a person who is capable of hearing frequencies up to 10,000 Hz? (1 point) .5. ﬂ. < lo ac:on “L 2' \ I - F- r at. n s. 10,000”: Sm 2‘.= 1.7.; < “3:000 3:. 'n “ 408-212-932. I4 \< 9.4. _ 1“ Quiz 1. Monday, January 2“, 2009 PHY 252 3. The dispersion relation for waves on the surface of a deep body of water (such as a lake) is given by the equation 002 = gk + Z k3 p (k20) where g = 9.80 mls2 is the acceleration due to gravity, 3/: 0.072 N/m is the surface tension of water, and p=1,000 kg/m3 is the density of water. a. Write down an expression for the phase velocity vp for surface water waves as a function of g, k, yand p. (I point) 1. m1. : Lo —_. 3 +§_K P «=- K p = a 2: *- ‘VP (1? +"“) b. Sketch carefully the phase velocity vp as a function of wavevector k on the graph below, making sure that your plot shows the limiting behavior at low k and large k. There is no need to ﬁll in any values - I am looking for the shape of the curve. (1 point) we: v1, GRAVITY comma-ran X I A. —-K Long ’A. 9 ie 'ocean waves“ I SURFACE TEMSIOM X DOHIIUA’TEDJ usher-t 9L left-(ppm; c. Indicate on the graph where you expect; (1 point) i. Surface tension to dominate the wave motion. ii. Gravity to dominate the wave motion. = O I ‘ . 1 . - . ’UP [A a. Minimum when “UP 15 a. Minimum _0_L, .3. +- d_k K " ﬂu? Im'u =\/( F- P 9 3 _— Il- ,_ If - Kinda P I“ 0 \$ KM: J3; *) (A- 35.2. P Y" . in): I. M ...
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Quiz1_Solution - Quiz 1 Monday January 2“" 2009 PHY...

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