Give some examples of everyday v+kwzz fmc lt:3o3kv17 qyz19fibrating objects. Which exhibit SHM, at least apprfc3 wq1 mvk7 9ztz1zy+:o3fkl oximately?

Is the acceleration of a simple harmonic oscillator ever zero? If so, where?)u/n)23j 8clk mvnyz j

Explain why the motion of a piston in an automobile eng yb8. s4hrk;glxq3me1 ww2 gt9d2)iuqine is approximately simple hab92yk1semgl id 3 ;xu q)4r.2wthq8 wgrmonic.

Real springs have mass. Will the true period and frequency be larger)vz gb (v unw5/ondf05 or smaller than given by the equations for a mass oscillating on the end of an idealized massless spz vw v(u0/) 5o5nfbgdnring? Explain.

How could you double the maximum speed of a simple hah9s6f50q wu4 hm-:fjim2 izhgrmonic oscillator (SHO)?

A 5.0-kg trout is atp 9w.ly22p715knje duudj hi0tached to the hook of a vertical spring scale, and then is releaijk0p9ldun 1 ypd752ew . ujh2sed. Describe the scale reading as a function of time.

If a pendulum clock is accuai6rd 7qp 5z1m *hoh6arate at sea level, will it gain or lose time when taken to high od6mr7h *q6ia ah z1p5altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11pwc/o7ayoy hup 7xv )cz.o- ,cd-1v5r –48). How coul1c7-7r dy.o o/uchwvypav)z -x5 c,opd you estimate the height of the branch using only a stopwatch?

Why can you make water slosh baop w jp 8sg:pyae;8a3.ck and forth in a pan only if you shake the pan at a ces ppogjaw e.3 8a:y;p8rtain frequency?

Give several everyday exampz9:fnmf x .iymcm(ap2*sl a:/gj,x)p d q(f,iles of resonance.

Is a rattle in a car ever a rescx mtp59hiyxrwc ax-: ;)m-3fonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the freffp-b0 xfdse29h e k+kdv40.jmvzl ; 2quency of its source?p-0e d2h jf.b9df ;v2x40lfkskme+vz Why or why not?

Explain the difference between the speed of a transverse wave traveling down a8o vw qmaf0g)rg)c-l)v bl46e cord and the speed of a tiny piew )rm)ol4- lbvefag6 80qc gv)ce of the cord.

Why do the strings used for the lowest-frequency notes on a piano non7rkz*wb pc - n6r1o9trmally have wire wrapped arn7 cwb *ot- nr1rkpz96ound them?

What kind of waves do you think will travel down a horizontal metal rod if youjq)hvz/fn 755pr,p uu strike its end (a) vertically from above and (b) horiz7u) 5q/ pufhvpj5,znrontally parallel to its length?

Since the density of air de6f jn08rpl 0cffu50q ni*p0gqcreases with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of soundgqqc *j0p0i0 08f6fn lrn 5upf waves in air to vary with temperature?

Give two reasons why wbg1 n0:wjd)rcircular water waves decrease in amplitude as they travel away fronrw: b1 gj)wd0m the source.

Two linear waves have vat7 d 4peqq ; :iodmq25y0qo)wpn*l,the same amplitude and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits more deq27q54w *nloq0ppiq,oayv m )t;d:energy? By what factor?

When a sinusoidal wave crosses tg/(u isau ds;)ew2qh0he boundary between two sections of cord as in Fig. 11–33, the frequency does not change (althh0a ue2wq d)guiss(;/ough the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places you could toap (.oh 4tuphknm4j (w27.z jouch it with a knife b( onp4zj2t4 jhhpwo a.7(ku. mlade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incident arndn(m:m sh3qmqll4kg91y3v + 7it z9nd reflected waves cancel at the nodes. Does:ml zm+iv (m3qt37 rgy99nhkl d41 qsn this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one s;/4rwxayc22n pk v1ea r)dc 9place to another, how might we determine whether the energy was being carried by particles (matern 4srkreyxvc1p c)w9a2 a2d; /ial bodies) or by waves?

  If a particle undergoes SHM with amplitude 0iu ib67o3kt-bsi2rlr5y e)f vb+to/ 0.18 m, what is the total distance it trrtyt-5oe6o /b ulv3)7 +fii sb20r ikbavels in one period?    m

  An elastic cord is 65 c8eebfrv. la7l*/ u)q km long when a weight of 75 N hangs from it but is 85 cm lonbk8 uf*ql/.ee lrav7)g when a weight of 180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compk i/m+k)ts2afwg/0 zz w6 vn-qress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a buatzwv -m/02+f gnqk )skwiz6 /mp, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (a) Whatp7y iz5r: tsy: is the spring stiff:rt 7:i5yypzs ness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibratesa wmr*vk6 ;qv9 with a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if* 6v9kqv amrw; only 0.38 kg hangs from it?    Hz

Construct a Table indilj6d v.- qygteig ( r2o/5min35xxgr:cating the position x of the mass in Fig. 11–2 at times t = 0,tr t55 6:x 3oggnm.l(d-v2/qexgiiry j = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web. The web vib:e:ft-6r bp il2 p-3xa)nv zyurates predominaxv-f urye-2t:pp63bzl)n ia: tely with a frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency of 0.88 Hz. When broc/nd ll7( 0an additional 680-g mass is added to m, the frequency is 0.orl0cd nb7( l/60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the enjyfv4(/nqk q;y5q 2zvd of a spring vibrates 3.0 times per second with an amplitude of 0.13 m. Determi( qq54yfj yn2vv/q kz;ne
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from eq- h,kkp xj1v- pnu17vguilibrium is the speed of a SHO half the maximum valuv pg17vk1j ,u-x ph-nke?$\approx$    A

A mass attached to the end of a spring is stretched a d(lin6u cptye )4pn8p;istance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0*sv 6vh; y+emxh93 gzp.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equil6ye3 +*x hzmh9s gvpv;ibrium position again?    s

  An object with mass 3.0 kg is attached tomobh/oyo3 :3 o a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic mo/om3: b yo3hootion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80w, :gh9 ovrryaveh 4i*lf :wo7t7;v(c .0 N to compress the spring of a toy popgun 0.200 m to “load” a 0.18av7hr i w;9l wo:hv :(ec,*fv7torgy40-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one end of qt. dp gse t3-nyg5-4ca spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with tc.g35- -qp tsndtg4ye he spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equatido9bvcpdmkjo m j01:fr+;0 )fh rhh*:on x = 0.45cos6.4t where x is in meters and t is in seconds. Determine ho1dr mdpf o+ch:r;hjv:fm)0 09bjk *
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of a SHO half KE and ha 1:9:c9+qvsf*g wgp qwp lf0swlf PE? ± 9+1ggp9s wsvq lf:q:p*cf 0 ww   A

  If one vibration has 7.0 times the env5rm6hm*q 3np 6 lcl*sergy of a second, but their frequencies and masses are tnmm6 rsl qlp v*c6h*53he same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring y53lj;2gud4n( cqkrv once every 0.65 sykndqg;(j5 2rv4c u 3l.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallel vertical springs, kfsdi( -c/jxdh3 sh-o9ah2m;each with spring stiffness constant k (Fig. 11–49). What will be thejahd- h2sh/ ic9;3d(mfo -xsk frequency of vibration?

  A 300-g mass vibrates according to ts4ne- 7eoja 5she equation x = 0.38sin6.5t where x is in meters and t is in7o eas jse45-n seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled ulhq :nga1 *,c -pz2m(avr3c oA and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizonsb 7,7za ,ydgeui)5kgt. .oa7 i hrpi.tal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Deii7tbu r,)7g.a.kho 5 si peygaz7,.dtermine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring ;oori 2qnq+7ag f,iv4fw7 up :stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 orqow4u ag i; qpnf77, 2i+vf:kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs,swzum ,m1mp 6zry- d;6 with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fh82 r o7h8xvyuixed horizontal spring whos82xy uhoh78vre spring stiffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high -6fw*el bqx9v biq1v 1 19akb0t (cfsibridge. After reaching his lowest point, ftbies60 qb-*1lvb1a q(9 9 cwk1ifv xhe oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exac0)jdv om + c8gml6n: 5z8pqbprtly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple penxu,fj2 e1vao :dulum be if it is to make exactly one swing per second? (That is, one complete vibration takes exacvo,1 2exfauj:tly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What 4kwhu 1o r9lx.is its period on Mars, where the acceleration of gravity is about 0.37 that on Ea hurk41lw9x .orth?    s

  What is the period of a v m .n2esft*u:dm5a 75ufjb (zsimple pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulum bob has a mass itpaw5 cjv06 1of 365 grams, and it is released at an angle of 12a 0c1tiv6 j5wp.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.993)h 0i*m*oz ppi( m*kiw0 m. If the clock loses half a minute per day, how should you adjust the length of the pendulum? wp( *i*omhkmi i)z0p* shortened by    mm.

Derive a formula for the maximzc 9:i8vc+g tjum speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequenc8ejf68r,lf r e 8xsu:;futls+y of 2.5 Hz. At it is released from rest starting at an a6 us+el88:s fxlft;frr,ej8ungle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass thefrjfodr 0mhk:d 3)g)h f+8)ou bow of his anchored boat every 3.0 s. He measures the distance betw rh of)3)oduj 8dk)0fr:hgmf+een two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed of 343 m/0) xn3eqfk md3zfk m3/s How far apart are the wave c mq mnkz0/ffd33) k3xerests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kswstg( 3b(9 bkHz and 1600 kHz (kilohertz) and b 3bk(s9tw(gs travel with a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of lony. 2lk ewd iv6n9y1 zfk0prz3*gitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as dense as ( / brsimux 8n.xy-.)ticm3qythe other. In which rod will the speed of longitud./tnb smuc( x- r8x)3.yyiiq minal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If t29wdn-zohw1g:x44 v rhpd3t 1/mrlf hhe tension in the cord is 150 N, how long will it take a pulse x192wdd/n4otvl-wrghf h m3 r4z p1h: to travel from one support to the other?    s

  A ski gondola is connected to the zwmjyj;+ p/smyk.: /ytop of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into thek.m//pyj:s ;w zyj +my terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the surface of the w pu0v+9wdxr*sea. He hears the echo of the wave reflected from the ocean floor directly b 9dwr*0 +wxpuvelow 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at dv3latn) )skj- uentz/ to9,x ,ifferent speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbance took plac e,jkxt t- az/ns3 o9))tlv,une).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated by a sinusoiq c6+g 9ekkc6fmcqq;qqe40 )h dal transverse wave. Assuming a frequency of 0.50 H;6cc+fhg)eq cq qm6e9 qkqk04z (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of ( 04dlqgv lbu/an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from th(vubl0lq/ dg4e source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measurpdm+ejeme96;n: +m fryn x/x3ed to be /nxp nm6 f;e y+39xee: drj+mm$ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves r:dace a)8 vl/of the same frequency travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes o)l ra8eacv:d/ f the two waves?   

  Two waves traveling along a stretched string have thebfgg3m,/ j e ;y,w0a jvsx/e1y same frequency, but one transports three times the power of the other. What is the ratio of the amplitx g,a;v,y1/e /0w fmbesjy3gjudes of the two waves?   

  A bug on the surface of a e)9 mx6f gygh6tak1)o pond is observed to move up and down a total vertical dishk6) f 6otxa)mg9 eyg1tance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in mpdz-gr .l) l1Fig. 11–52 are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at-d 1)rzmgpll . the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its f+3ye i7w 7xi:+z4oq 0emlm gq f .c6ze*jn)mecundamental frequency, what are the frequencies of the first f+4m :g7oqiw m *e7zi ez).j nex6flcqyc0+em 3our harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency wiluah v- /z*(gckl it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the sgh v/(a-*kuzctring vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz9xhrvh +0//4ufsei s*t hifl4. Name at least three other frequencies xt4 h4svi+9ffrhu//0il s *ehat which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string hm iheg 88.ueduszia)39*p2 gis 92m/s If the frequency of standing waves is i9.pa8u2huh* 8 zg)e3gesdmi 475 Hz, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are e, (l-ur*/a lzq,zvyj280 Hz and 350 Hz, what is the frequency vql j-e *au yr,,z/l(zof the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. -q sz8oi2drl* The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundame-lz or* 8q2dsintal and first two overtones?    Hz

  A particular guitar string is supposed to vibra:t,vbr ksdj u+)py g13id 1*::qjikzk8ej2 djte at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three 18d1:bk +k q)djptd e3k :yg,jujj*:ris2v izfrequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz2r* d/25i f,okxgib vz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the ,i5/2x g ivb2rzk *doffrequency? decreased by    %

  One end of a horizontal string is attach4vl 7c64,que z oa e-ewxey6k-ed to a small-amplitude mechanical 60-Hz vibrator4 , k67zvlca-weeu-y eexoq46. The string’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of tnh 1,k5fu cn;a-f.gzy he string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kghn;5gf -1f .a,ky zucn, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the right frequen.j jej+ tp2jdbhp7 01acy, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub 2 +t0 7jh bpjjejpa.1dis 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a 4 5s lt92 q f81co4q jwecz;w)hd4pvbrboundary within the Earth between two kinds of material. If it approaches the boundary at an incidentl1qr9;z eb44dw8t5 fovw cjhc ) 2s4pq angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an unl -a ,vb4gteqb7vx nd6j-a ,0kderwater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incide0,7 -tv,k6g-adjavxlne 4bqb nt wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm aibh-i6 r06sbu n 5j p4ooxs4g .8ou6jjnr when it hits a layer of cold, dense air. If the sound wave hi-s8ubn4x50 i6rh6s j j6gojopo4 .un bts the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary between two types of rock a 7da ko rto0.cprh7724pqwf3t t a 38r7 fprodp7kwt q 204oath.3c7 $^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m in diameter. Accordinmh krwn9w /*hj3 k-fk6g to the user’s manual, the dish has to be k k9fm knj/-*36wwhh rpointed in the direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 km/h travels across the Pac-,s xrd)hguqr)-me(wcta1 n z (cnc2,ific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how xcnu))e, c 1rwqs2nt- -m,r(a d(chgzmuch time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 55ag 8s vb3 if 2ogr:mk,g,ype,+0 kN/m Find the maximum compression of the bumper if the car, with mass8gfkgs3avye b g+,:iop,r m,2 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 mt0wb(yy .7ql.w )w jpm below, which stretches the net 1.1 m. Assume that the njbywy(qw) p.7tw0 . mlet behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placec: cn8gbi3tdb 09tqje) ::rgl d on the end of a freely hanging spring. The mass then falls 33 cm before it sn0:c 8 :g3tjbdi:l)c9qe btgrtops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed offyw ,3nak .6e/x1uzqosd i u)9 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of the spkof),xs e ad n193.yzqiu6 wu/ring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 0pqhxax8 kqlh,u / *v/cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of xq/,q 0/vk*8uaxl hphwaves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-rpm phonograph rova snw*/jl02 eoxj0i6 /xkc+ecord have a wavelength of 1.0n s+2j jxxolceoawk/*i6/0v 70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x is izr, qr-i02od bn meters and t in2 oz0drr i-b,q seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscilla.-hnorjdjw60b )haw,yf + pn) tes with frequency f. What is its frequency if it accelerates at 0.5njaw 6h+fy ).o, pb0n-w)dhrj0g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. g0i3m b ero7f/When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for a while. i 07f/ger3bm o
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are t*wjn2c7 c67 c gpx)jpquned to play at 392 Hz (G) and 440 Hz (A))7pqxccj 6n pjc*w 72g.
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stretched two-part cord of Figzhvlri3 ) (3uu. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavel)( hu3 u3lvzirength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a+c+ (n0 ailoj+0vljw k-wu/ sb frequency of 264 Hz, and the tip of each prong moves 1.8 mm to either side of center. Calculate ln oul/(0+ vc+0wjj-abws +ki
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of qr3k dzmz som: z**6e*jrc/5afrequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will k3e m/ odm:rqrc 6*zajzzs**5not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a ring trma.t2tsjktyzt-f, c - -0 vi.hat can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string w2.ratiyc0,.j tm-- stk t z-fvith one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-sl0dk(yurlsj )2xaxy2vs ka w9p ):y;+py6k,way swing takes 1.000 sd),x0j vrl+ p; a2x :spu(say l)62yywy9kksk .
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscilll1p o: 4cru*--z,s4v z uiexovate in the vertical direction or can swing as a pendulum of small amplitude, but notrl:4 s,vz oezic4 xuovup1--* both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

  A block with mass $M=5.0\mathrm{kg}$ rests on a frictionless table and is attached by a horizontal spring $\begin{pmatrix}k=130\mathrm{N/m}\end{pmatrix}$ to a wall. A second block, of mass $m=1.25\mathrm{kg}$ rests on top of M. The coefficient of static friction between the two blocks is 0.30. What is the maximum possible amplitude of oscillation such that m will not slip off M?    m

  A 10.0-m-long wire of mass 123 g is stretched under a tension of 255 N. m5f l lg1p6e zoz-hr7,A pulse is generated at one end, h1ez mplz-l7o,rf5g6 and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with spring stifxd8r(y)ug4z nfness constant k. A penny r)yd4nu (gzx8 of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel cr cojyt4c.tf81 ane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hc81 oj.yt ft4cint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which aluzoe6h, (/eqqz0 sh 8d7pm4ra so gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, esti zrd0eq m z8o ,phq7h4e/(uas6mate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz