Give some examples of everyday vibrating objects. Which exhibit SHM, at 0rep9 i6n2 ,dnzc7pot least approxip0etdnzn2o 76r9 ,cpimately?

Is the acceleration of a simple harmonic oscillator ever zero? If so, wherv :712a1ioprm7av i zye?

Explain why the motioxmw6og tn rkd cc07 6193cdopvf: 2s*rzly1 i*n of a piston in an automobile engine is approximately simple harv d*lcw 1io kyn6oms3dxc pfc0*t76rz 1g:92rmonic.

Real springs have mass. Will the true period and frequency be larger orv)cl2b4ezwhe*m nz hh3re 8.1 smaller thanvh28m. 3leh)crw4n* ezb e1hz given by the equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a sus r uew2;p(*cimple harmonic oscillator (SHO)?

A 5.0-kg trout is attached 8 8d0yoyxfc *fto the hook of a vertical spring scale, and then is released. Describe the scaleo0*8f8 yxcfd y reading as a function of time.

If a pendulum clock is(wmqj2a0a0dmfxb(*e accurate at sea level, will it gain or lose time when taken to high al wfbx2(*0aedjmmq0a ( titude? Why?

A tire swing hanging from a branch reaches nearly to the grounmg9 :vjbd t1vg3s8/ br6m+ppld (Fig. 11–48). How cou8sj pb gvmv :mgd1p9 +t3br6/lld you estimate the height of the branch using only a stopwatch?

Why can you make water slosh ba1htu8m -4v zikuo ncrc: ;xo;+ck and forth in a pan only if you shake the pan at 18rvzixmoct uc;:h-;n 4 kuo+ a certain frequency?

Give several everyday wm)orfucn.s 3i ;n 8*nexamples of resonance.

Is a rattle in a car ever a resom l;nb2ks+vk5wxwrl60*+v wm nance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to h)5sy44.x kckt t,jcv the frequency of its source? Why or whyj.s4yx4 c5, kktvth c) not?

Explain the difference between the speed of a trans 5 im0-qt+x-;ezzwbcoverse wave traveling down a cord and the speed of a tiny piece of the cord 0xzq-wo5+t-b mz;i ec.

Why do the strings used for the lowest-fr qrs8 )baxn k2yy*)zh)equency notes on a piano normally have wire wrapped around kh)2s qx*)y)n zb a8yrthem?

What kind of waves do you think will travel down a horizontal metal rod 0rd80xnb m9;y2mnfokt mcy 4.if you strike its end (a) vertically from above and (b) horizontally 9;rnmnomd2xy y4cmb 00t8k f.parallel to its length?

Since the density of )w2kte/adq pafm.l xq;z0 ,2mair decreases with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound wav2l fxk0m m tzeqa).qa/2 ;,dpwes in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude asnys;6.xnl m,u they travel away from the xnln y ;.su,m6source.

Two linear waves have the same amplitude and speed, sq79wmu(fm x4and otherwise are identical, except one has half the wavelength of the othe m7wq4x9(sumf r. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of cycc,oi , h4az b)epv* glc2)*xord as in Fig. 11–33, the frequbc l4oa), ecg,y* c) zx2vh*ipency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segmekxoar cr/35u. nts, are there any places you could touch it wru /cx.35kroaith a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incident and a* 1ox0f/n.oms 6j vjbwy ;b7qreflected waves cancel at the nodes. Does this mean that7;sov*a jmwb f qb.yoj1nx06/ energy was destroyed? Explain.

If we knew that energy was being transro,n5 giduf,l,t- 5vqmitted from one place to another, how might we dvun f,rtlg o,d5q5-i ,etermine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with a:w,.t n8dnprr kh80d 4w v3ojgmplitude 0.18 m, what is the total distance it travelsh w3or84wkng 8 nd.:0j,drtp v in one period?    m

  An elastic cord is 65 cm long when a weight of 75 zksu gw )q5 ;(8wuen l2j3:rptN hangs from it but is 85 cm long when a weight of5 szteupg)n; :2wj( rukw8lq 3 180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when i)gak )jx5+3kr99u frqw xrru:ts 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the3:9jr5uk+r qx) wrxgk) faru9 frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangse8vyxts l;v 3e 0gl,8a from it. (a) What is the spring stiffn0;y slt8vg elve38,axess 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 vibrates with agl9ojbrz.dzpqx0nlid+n*1b 0 o(9 t1 frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs frbtnox n0p+l 9z o il(.djrq*1dgb9 z10om it?    Hz

Construct a Table indicating the ,mtfcoh +xr.. position x of the mass in Fig. 11–2 at times t = 0,forx tm c.,+h.t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 0.2fyi8v-6 b*)q3t3i pmxy*urz x5 g is caught in a spider’s web. The web vibrates predominately 6tiby*f3i )x-puvy8 r xmq*3zwith 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,tr fr7g-c usvzsco1/z j *senw21 )s:.88 Hz. When an additional 680)rnc-jr,c2st vs171gfezw*ssz uo: /-g mass is added to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at thmq-) yx m6dxh8e end of a spring vibrates 3.0 times per second with an amplitude o m)hydxqm8 6-xf 0.13 m. Determine
(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 fl9 5delsgu mk/-kji 02rom equilibrium is the speed of a SHO half the maximum valu g0lu-25kjm9i dkl e/se?$\approx$    A

A mass attached to the end)r8bp *,qv zqt+93i.do. a hu eckdaoei/5 p/v of a spring is stretched a distance $x_0$ 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 0.315 m. qfm17 7 g(9bnbeen 2ilIf the spring is stretched an additional 0.130 m and released,2 1 7bn79iemqln fg(eb how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 k 0gfucewd rq r)54h+2*u fw)e)zaau .gg is attached to a spring with spring stiffness constant r+2ff 0agqezrdcw))uuu5 w4*haeg .) k = 280 N/m and is executing simple harmonic motion. 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 80.0 N t3.j8 ,0imgeq00mpgne ob tf*eo compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball le 80te 0fq ggpnje .bmo*,3m0eiave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attachedet*xnp +/t eg- to one end of a 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 the spring compressed, the mass experiences a maximum acceleratio*-egxptt/ e +nn 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 equation x = 0.45cos6.4t where x is ic89cwx6n*krma,r fs fy4l99 hn meters and t9n9 lx cc*y 9 ,fwrm46rfk8has is in seconds. Determine
(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 hal1 l +*+veofgsjf PE? ± g oefl ++j1v*s   A

  If one vibration has 7.0 timnd f,3(g)b mjyes the energy of a second, but their frequencies and masses are the same, whgjf )3d(n by,mat is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring once ev4v c:dr81d1ztwqe aa5ery 0.65 s. awq:dd45z cv1 ra 81et
(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 suppo t+okn-onh32ok/s 8tsrted by two identical parallel vertical springs, each with spring stiffness cons/2tt3nok ko-+ns8 hsotant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to ig2 s/e-z 9cyr,0zy xqthe equation x = 0.38sin6.5t where x is in meters and t is in seconds. Dexs-ge2yi qc,zzy 9 r0/termine
(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 -) k v3 3ywxq9ja7c mq 3li5;xju1quizof SHM, labeled A 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 raj9of +p)b p+n:vfa. on the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which giofjr pabnfpva:.+)9+ves the mass an initial speed of 2.96m/s Determine
(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 stiffness constan kt l,r2z97:qmby9ln9uk 3vkdt 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) wdq r9 zmb2t3k:9yn7lkku l,v9 ith 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, waer6e-mxgsm/q 4 +m yamw;0y.r1ew0q ith 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 bloyq59. bf.(r rj xc-ttnck attached to a fixed horizontal spring whose springt (.b.r5r ftxjycq9- n 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 aq,2gigd;1 ha : b3o qy4w0f hf9rdp5kl high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0bq,wy3idq5g pl g1h a f920h4;dr:kof 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 vibra , vm/:tu7q 5/jkpmu30qi nufftions in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simp1)mdnd5mqv 6 29fhm3w/ m/soz rjh2cnle pendulum be if it is to make exactly one swing per second? (That is, one complete vibration t/m2dmd9mj f6mh1n2 w hz5/ncs)r3q ovakes exactly 2.0 s.)    m

  A pendulum has a period o1kh ehd6miemzq3, s97f 0.80 s on Earth. What is its period on Mars, where the acceleration of h76 midez 13k9q,emshgravity is about 0.37 that on Earth?    s

  What is the period of a simple-ym 5nq1x +rho 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 of 365 eyi e)i*;hox 2grams, and it is ey;i oihx2* )ereleased at an angle of 12.0 $^{\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 0.9930 m. If the clock loses *)vaginbq6 a -half a minute per day, how should you adjust the length ofqin6*ava-g )b the pendulum? shortened by    mm.

Derive a formula for the ma3h;d 4tfv3 b bc0ilw(oximum 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 frequency of 2.5 Hz. At i xw. j3mwei:5gkc 25ort is released from rest starting at an imw5 5xe2okj r: 3gw.cangle 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 the bow of r-aunnnq*it;3is14g*;g x ujhis anchored boat every 3.0 s. He measures the distancenqxs ;ungiia- j*r4 ;1ut*3ng between 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 speed399qeb-gu y: 1 fezg)ddhnqm- of 343 m/s How fa19:3efzmqgbqhe9- gd-dn) u yr apart are the wave crests (compressions)?    m

  (a) AM radio signals h-cca3nuhq*uj+:j:fr w,9nlc, 5w yhoave frequencies between 550 kHz and 1600 kHz (kilohertz) and travel with a speed -9f, acuh,ln jwh o*3c+q:5r:ujcyn wof $ 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 l : bk sij3r33mxwvyq87ongitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but o,w91mnwt6 jngl+m )pu ne is twice as dense as the other. In which rod,g1ntmwmn)9l6 pjwu+ will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stre s6+q6bo nqd+htched between two supports 28 m apart. If the tension in the cord is dq q+hn6+bs6 o150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hil3iihl.aa/ng * l by a steel cable of length 620 m and diameter 1.5 cm. As the gon i3 h/aga*nli.dola comes to the end of its run, it bumps into the 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 q0-ox +mle0 /j:aeap hof his ship just below the surface of the sea. He hears the echo of the wave reflected from : eqaj/0ex0ah+plm o- the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speec e7; jpsjm*z*0b- jecds, and this difference helps in locating the earthquake “epicenter” (where the disturb*pj-jbz; 0c*m 7escejance took place).
(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 0iqwolp g6ju685l ic8kfe6 3b ( xaqu/sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually ina lq g/uie86xf03copu(biq86 l5k6j wclude 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 an e/eiwhpyn -e4s.dz1i08rvksn v5tj( 2arthquake P wave passing through td8jr 4we ni.(pk/n vsth2iyes5-1v 0zhe Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Ear rb)pxi*lh/i/e0 z fv/th is measured to be l)/*i ep0b /r/xivh fz$ 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 o gsukb38 md2e:f the same frequency travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the 83udgsekb:m2 amplitudes of the two waves?   

  Two waves traveling along a stretched srt( 2d)tdmg e.tring have the same frequency, but one transports three times the power of the other. What is the ratio of the amplitudes of the t 2rg.t) dtemd(wo waves?   

  A bug on the surface ov40ne*-n* af(orm:z rnf/nok f a pond is observed to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest kno04nz-n:(v/f**mrfnr a e opoint, 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 Fig.x3h+s1j7 4osz;vhtrk7r l up5 11–52 are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap;uj 73vrhz7p4 krs5+ 1shlto x. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at 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 fundamental frequency, what ar 3b) lmb4psq(we the frequencies of the first four h( )43bwl msbqparmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates atiggxk2;03nbh 294 Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down 3; 0in2gbkx ghfrom the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a fre :lsze r sy-v1j1nn 5)wle3lv4quency of 280 Hz. Name at least three otheelny wvs1s )znj:1e5-l r43l vr frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s I(l-qshwxxn :ew x9*:jf the frequency of standing waves is:*jx sw:lw(h nxxeq9- 475 Hz, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280rv x -wb,5-o6z b*mxp-e6pty c Hz and 350 Hz, what is the frequencywprxx6e*- zotv,--myp b5c 6b of the fundamental?    Hz

  A guitar string is 90 cm long an)b 5 g6yjnl;qbd has a mass of 3.6 g. 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 fundamental and;jqb6g 5)yn bl first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is measured*xdqkx(d/e h5i ox(z(msi c9; )lpx0t to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequencies ar(ic0xsez(m ;l)(5kopqt 9dxx i /dx h*e,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string igup- :2rj4t gms supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what pgg4:r j-mp2utercent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mechanical 6y,kl1v ukb2tr63cn)c 0-Hz vibrator. The23c rltbuv,y6cn1k)k 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 the string may be adjusti p;g rk)z7u7a 7lv b6,ftyiz6ed by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm ai6 tl ,yaui);gvk 6f77zrb7 zpnd 1.5 m?   

  When you slosh the wat;/suswv vi*5 bw-.dqidi28 leer back and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to producessu wbviqid.8- d5*ie l 2;v/w such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s striymhk eq dj3u 5i+01 /s)5hbcezkes a boundary within the Earth be 5h)kde1+ei0zhu/q sc 5bm3 yjtween two kinds of material. If it approaches the boundary at an incident 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 underwater “shelf” where the velocity changefalsl05v -b .t69f miqs from 2.8 m/s to 2.1 m/s If thi aq0ftv.5b-9l mls f6e incident 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 air when it tmke6k: eicd9qs+fs6f ciex(1 i (q ,2hits a layer of cold, dense air. If the sound wave hits the cold air interface at an angle of 2 q6 keec+temx(ii(qs: ,1i6dfcs 9k f25$^{\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 4-urkkgb)u 5 ba boundary between two types of rock at a 384)b-bku gu rk5 $^{\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. According to the usernv3q p4v +s */up*juap s,(/s7bljlrz’s manual, the dish has to be pointed ivppn4su*+sbazpjs l r7j* ,uqlv3(//n 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 acro( ytjhaiog+s:8/1,v s nxna1 ass the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to runa :xygo +vj,/( 81asshai1ntn 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 consou* 6-x)ft,ck i9 c+t5xbujdk tant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use con 6ccxf)kktio u ,u+d* 5-bjx9tservation of energy.]    m

  A 65-kg person jumps from a window to a firehov- 7)-3 k xi-vapa l7ph/nqc net 18 m below, which stretches the net 1.1 m. Assume that the nethx7h-p onvaci- /q3kla -)v7p 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 placed on the end of a freely hangr,;f tr1ftg:ows9vm .ing spring. The mass then fgwm o9rsv;1:f,t tfr. alls 33 cm before it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Firzl;hinmwd;h)t q c:+q1xio l3 4gh3,:qqb +rg. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffnend 3gor,qtlh: 3 r:ci);qihwx4;+ mqh1+qblzss constant of the spring?    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 (diameters:rr7i 8i, fg b3d9izf12 qpei 8 cm) at just the right pace of about 1 steprzif9:bdgii s1 7er3i qpf,2 8 per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm f a4p x75r lk2kjsr0on-rom the center of a 33-rpm phonograph record 4ko7p -ksan 5l02xrjr have a wavelength of 1.70 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 wa-g 4 :31bre)np m5mn3gbiaqk here x is in meters and t in seconds. a3am:b3r)ng 1bi- n4ke pq5mgDetermine
(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 oscillates with okvoy/sj.b* j* m o-- .voyr4 /vsiy+tfrequency f. What is its frequency if it accelerates at 0.50g (a) upward, ts.rjj./* ko om -vv +4yysib-*ov/yo    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 7x:n5-bs ogtks9x9* tc 5-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibnt9 -ogk5 t*xxss:9 bcrates for a while.
(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 tuned to play at 392 Hz 5juaaf3d; 9 dg(G) and 440 Hz (A3;ga5 j9dfd ua).
(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 F3k3)khqr / gqjig. 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 wavelength greater in the heavier se q3hj/q )3krkgction of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip ofjrz-q 2jdex81 9tqyj 7 each prong moves 1.8 mm 1yqjqjt -d ex2rzj798to either side of center. Calculate
(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 frequency 1.5 cycx0j;rby/ cs: d;rcik,les per second. What is the maximum amplitude with 0c; bykdsxir r;j,/:cwhich the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a ring that* 5nc1rq9h bg1,j 2ovzn5n xqz can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations gx9znq1jn 1 rc5*2bv nho,z5qof such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swing tay.pc p: q ma fao7n-pp*u;-wb0kes 1.000 sma yw*nap0b ppc;-u:p7-.f qo .
(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 oscillate in the vertical direch)o483ov47yaadhu e(oc7bw n tion or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillativ 8yo 3c4oh(h)d a4a7u wobne7ons 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 stretchedy(o-8i// xaefn u9y4ny )y xvt under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the oppost-9fy4y/)/x xe8nia y ynv(o uite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a sppd x )*ya46scq4o zka/ring with spring stiffness constant k. A penny of mass m is placed on t*4yzd xs/a ko4q6pa )cop 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 crane d.xmp g udf7sep6-h:)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? [Hint: Refp):h gd.6 s7uemdp fx-er to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which a.hlzu;2t 3zh*jl6 udalso 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, estimate the frequency of this vibration, given that the shear modulus (Sectz zhd.a;juhult2 *6l 3ion 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz