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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: Izxm 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 ssh55s)
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'3ijoAoom ‘2. _ 4—08 HZ+£W tl‘etfuualamentaL. 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 “ 408212932. 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
commaran X
I A. —K Long ’A. 9 ie 'ocean waves“ I SURFACE
TEMSIOM X
DOHIIUA’TEDJ
ushert 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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 Spring '08
 Treacy
 Frequency, group velocity, phase velocity, Phase velocity Vp

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