Give some examples of everyday vibrating objects. Which exhibit SHM, at lea7 z)kovrm10h pst appro7z0)1vk phr moximately?

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Explain why the motions ii j*5kmd* 3:*bccet,qwv6h of a piston in an automobile engine is approximately simple veih5* c,cbjqtsw:m*i kd*6 3harmonic.

Real springs have mass. Will the true period and frequenmnx9e; m+ixz ; y*)i*fujb bm2cy be larger or smaller than given by the n *x;fmbj+ ;2 xzmi)*uyiebm9equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillatorh+ nyzppss3c 3/.4 c,h bit-ts (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring sc8rw 7hc/cnc 9pale, and then is released. Describe the 97 prcch /cwn8scale reading as a function of time.

If a pendulum clock inwq ufhu)9h;f h*: zo:s accurate at sea level, will it gain or lose time when take fn)o:w ;9hhuh q:fzu*n to high altitude? Why?

A tire swing hanging from a branch reachnh 16o inpqukfj:+8h q:kj:n w-fg0jqy )j9z8es nearly to the ground (Fig. 11–48). How could you estimate the height of the branch using only az u9nhn8jifw:: o 1kj8fp q-kjhy) :g0 qq+jn6 stopwatch?

Why can you make water slosh back and forth inv )qjr8gif ,7y a pan only if you shake the pan at a certvjfg7 ,) iy8qrain frequency?

Give several everydayvs*fgez k6zr o 1ut)1;uu34uq5 h)b mq examples of resonance.

Is a rattle in a car ever a resonance phen 4 pv ,fahsmcs-pyohfg:yn 1 b08e.*1ep)s8iaomenon? Explain.

Is the frequency of a simple periodic wave equal to the freq53/mmhts8q5 8g( h8u;yrg csd oo 7iiluency of its source? W u lr53hsh(7/i;sgtmimgocq o8 d858yhy or why not?

Explain the difference between the speed of a transverssmq, invl)+ b35ppch6 e wave traveling down a cord and s6pp+,im hvn lb35)cqthe speed of a tiny piece of the cord.

Why do the strings used for th*se - 9fikvc.ue lowest-frequency notes on a piano normally have wire wrapped around thciu9 - vkfs.e*em?

What kind of waves do you think will travel down a horizontal metal v6/ b)ogbtxf-rod if you strike its end (a) vertically from above and (b) hoftog)b6x b/-v rizontally parallel to its length?

Since the density of air decreases with an increase in t 3y5 ,a -ghgbu+lzb0ojcqp8t; emperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to va 5b,a hy8lc og ;+tgq3zbp0uj-ry with temperature?

Give two reasons why circular water waves decryk6re. i5 v,,0eklk1 n) rmdasease in amplitude as they travel away from the sourcnmvl0k6 rs1yd5e r,k e )k,a.ie.

Two linear waves have the same amplitude and speed, and otherwise are id)g1 (hl q)bcxgg es.g:ag djg3+q0yj9entical, except one has half the wavelength of the other. Which9yg1gqxsa:+b) (jggj d0.h q lc)e g3g transmits more energy? By what factor?

When a sinusoidal wave croc5(jzj;qx7ba a 0ok- psses the boundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength azb7qo0 jxaj c5a p(-k;nd velocity do change). Explain why.

If a string is vibrating in thrz--j2u zd6 4aac3fezo ee segments, are there any places you could touch it with a knife blade without diz efaz c--2a4djo3u6z sturbing the motion?

When a standing wave exists on a string, the vibrations of incidentt-)zcdd)iw2rwj, r a 5 and reflected waves cancel at the nodes. Doejca),r wr-t)2 didz w5s this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place t,ctegw yr104 * 6vook e*k5zaoo another, how might we determine whether the energy was being caetk kwo 6vo ga*ecoy,*0r415 zrried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the tot-wa:xxue( 1i kal distance it travels (ik:x-uawx1 e in one period?    m

  An elastic cord is 65 cm long when ow*q,b g 3p l3hri,r6ta weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this elastic cordtq36gp ,3hl,bworr i* ?    N/m

  The springs of a 1500-kg car compress 5.065a i jja 5e6fj+e/c7zmyfjv- mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, whac7m6/6ya5iz - jf aje e+jv5fjt will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale skryc +qdqc0h5)o 7p(u tretches 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spq(kqdh7uy c+rp0c)o5 ring stiffness 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 a frequency of 3.0 Hz w 8gavzr:y 7hdv o4-+wohen a mass of 0.60 kg is hung from it. What is its frequency if only y 7zvadw4og+8vr:-ho 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass ingr,vvza zg.-(vy cd102pv wz( Fig. 11–2 at times t (g.w za2z1v,(zcd0-r vvvyp g= 0,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 0.25 g is caught in a spider’s web. The web vibrates 5pls- . 5vhencpredominately with a frequency of 4 psevlnc.h 5-5.0 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 vib+uln0wkzrw1 5rates with a frequency of 0.88 Hz. When an additi 50+nwrzlwu1konal 680-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 the end of a spring vibrates 3.0 times per second with al/4hh q:4vvlu n amplitude of4/:l4uvlq vhh 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 from equilibrium is the speed of a SHO half the macm1u4btw-cf 7dv 72k hximum valdh7w u kbf-2m7tc1c4vue?$\approx$    A

A mass attached to the e81:4my atj.p mmg6 dgo-pp7oqn 6dr:d nd 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 a15p9;;mxe+ b5oyt5mqgrzou k vertical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does okegozrmby59 t x1 +5;5pm;qu it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 ke+q)k wr z65w 7j uzygj4()amhg is attached to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is movinghz7 6wmk+4zj5qu )ry aj ew)g( 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 to compress the spring of a toy pf2n-v )*r 65jtqgj atpekn.g -opgun 0.200 m to “load” a 0.180-kg ball. With what pn6)t5k- afj.*gejvg-nr2t qspeed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surfacp/; d*fcylp1 k4m 9 vh*8l*ql.q deeywe is attached 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 releaseqlywfd.y*qp **m;/dk cv he9l8e p4l1 d from rest with the 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 equation x = 0.45cos6.4t where xs u6p fhmxd u9iih+0,* is in meters and t i* , s6+udfxh im0pu9his 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 ener ;pjpa+qt 2n.w +m :onzs07f rn1rzyj-gy of a SHO half KE and half PE? ±; 2nyp j prt+f+anz7ojn s.zmr: -w01q    A

  If one vibration has 7.0 ti2p /nju 6fnjm-mes the energy of a second, but their frequencies and masses are the same, what is the ratio of nf6m2ujp-/n j their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertical)p1u-x,,ca , nbhqhhyly hanging light spring once every 0. bchay ,1,)q -huhp,xn65 s.
(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 sup+olhsrg3;lk6.h4n -5xkzm dlported by two identical parallel vertical springs, each with spring stiffness cond;.4glsh5 o6kl+ knlrxz-mh 3stant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x is )e-wf1z),m e 0 dbcmosin meterdm)mzs,co0 b f1e-ew )s and t is in 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 A and B. For eabu 2eldksj9k42- -ngo ch, 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 horizontal sprj y3xheq/c:l4 ing (k = 124 N/m) is struck by a hammer, which gives the mass xqeyhjc/:3l4an 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 stiffne riysoe h2- ok2,fb5k4ss constant 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) with positive k2o5bi 4 yro,kh-s 2efvelocity 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 spri(4 i sman86 y7a1e/cu,ncimsh2ss rv)ngs, 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+mbswabw (o z ge9lh+;v- 5tc7 attached to a fixed horizontal spring whose spring veto +ab7hwc+5l;ms9 -wzb(g 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 bridge. After reaching his mxcb( )h/8l 3pv xfg8jlowest point, he 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 (/8g)b8flpmj h x3vxc 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 exactly 60 s. )radd (+ qos cb(9*vzuWhat is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it+4qcfz,2w0 n8hambtc/ - jt1 pd) efgp is to make exactly one swing per second? (Tha2p)fg+maj cqze1 0tf/8 ,w d4tnb-h pct is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on 3)/jmflhfz o5Earth. What is its period on Mars, where the acceleration omlz)f jo/h5 f3f gravity is about 0.37 that on Earth?    s

  What is the period of aoeed b15 6mde9 simple 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 masfi 2u: saft j-(p(-ydos of 365 grams, and it is released at an angle of 12.0 ui:sdj-opfaf t-y2( ($^{\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 h wi(bm9.gp i4clock loses half a minute per day, how should you adjust the length of the pendulum? shorteip g9hwib( .4mned by    mm.

Derive a formula for term*bj6 )xx* phe maximum 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. m(no1 cohs.x ptz(3 /nAt it is released from rest starting at a3cs o /(o1mx(pnnhtz.n angle 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 his anchored boatpwp 5:/v:tiwr,nf9x m every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the waves tw59xtn, p f :ivp/wrm:raveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed of 343 m/ jmhir,/nxskifnx( 7 6j-/xy 4s How far apa j ji,x r/-hxm nys4i67xn(k/frt are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies v-hclxqhg/cm z5iq +x k68r/,between 550 kHz and 1600 kHz (kilohertz) and travel hcq8m /zxcq5-il/kx +,g v rh6with 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 longitdqow6eqrf c;.)e: .g4bc.ht cudinal 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 t2 euom8o/f 4cxwice as dense as the other. In which ufcmx oe8o 4/2rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two suppzq c n4nj,) w*92eedrnorts 28 m apart. If the tension in the cord n,zweq r*ne 9d4jc2)nis 150 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 hill by a s l3u0jmg5 (vtr2k rljh53 tj*cteel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It it5j3 (tlv0j gcjmu52rk 3lr*h s 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 bevrcj ohq*8.4qy p.do 8j2 k1ullow the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the 8kr4o*d2jq1pv oc lj.qh.u8y ocean at this point?    m

  P and S waves from an earthq674y fm d h*.4zoisixruake travel at different speeds, and this difference helps in locating the do.fz4 x y4i6 sm*hr7iearthquake “epicenter” (where the disturbance 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 surfac eav /rxn-ecj yh,j 1r4s-7 ,ve9-nryze wave can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hin7sj- ye 9 ,xrvn hryja1-4,/ecz- vrnet: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, gy d a5u4.p0 z9g.gx5ds)rwg aand (b) the amplitudes, of an earthquake P wave passing through the Earthg9gdga zrw.x50 d5 yagu4p)s. and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured :5jn c+av0w lgto be :j+ gna0c l5wv$ 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 of the same frequency travel through the sameacrbi2iq/a**ac 4c,f portion of the Earth, but one i */ab2ci4cifc a,*arq s carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, c.yzkp(6 r wng0dgk (8but one transports three times the power of the other. What is the wrg( 806 (.zkgdk pycnratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down a total vertical qy 7qtfhlg xr:6+r1apl5e: g)distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease q6l qgt1fp)ghyxl7ar5 r::+e to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11)*8mr )ni.;tnqyw u it (bwppq* me8:j–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 fe *w )i.itbp;u m pwy*n:t8)( jmqqen8rw 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 a( b/z /mhbuu*/tm7evi0kb t4are the frequencies of the first(tb/ai */7mtb0vbekzm /hu 4u four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrated,p)fdbq xz7f(y 0l0y j ud5de5 -e-mes at 294 Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vq0 f0, bzldfjepx5 -(yuem y)5d7dd -eibrates as a standing wave.)    Hz

  A particular string resonates in four loopsgwlxg +:*m3qu , lky/j5( ssgz at a frequency of 280 Hz. Name at leauj lgk *,:5syqw+l (szxm3/ggst three other 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 If the frequency of standing wavp ,d(2*dxdwa pes is 475 Hz, how far apart *p,dx(d ap2dw are two adjacent nodes?   m

  If two successive overtones of a vibrating strin-u.jcc(,b yroi1v0 iog are 280 Hz and 350 Hz, what is the frequency of the fundamen0ci1iv o.j y ob(r,-cutal?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The di,t7aut( ez0so06j qx astance from the brixzao(utte6s ja ,q700dge 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 first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is m fzob k.qb141geasured to vibrate at 205 Hz. By what percent should the tension in theg1zq f4bb .1ko string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it isi zgm8ly 1*f9t5 m /soxks+,or measured to vibrro8 /zm9s+s l,f5gix*k ytmo 1ate at 205 Hz. By what percent 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 60-Hzspq3 5;yg h*oo vibrator. The string’s mass per unit pgh*q;s35o y olength 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 adjusted by g9 h -6a-22mlpyej ldfmoving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achie hp-ajl 2dg9-6m 2lfyeved 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 frequency, thth0iv ijcho9t95x.2q e water alternately rises and falls at each end, remaining relatively cali.o0ihc 2x jq99 vtt5hm at the center. Suppose the frequency to produce 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 strikes a boundary within the Earth mqao(6y+ih h+between two kinds of material. +( om6hyiqa+h 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 approachqvodm snb*i r9w1 )n8 26d+oo56oescf an underwater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the id+cwosi5 mo896 of sv r6b2)onq1de*nncident 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 hits ,pa0fjssa:(e a layer of cold, dense air. If the sound wave hits the cold air interface ,sfaj :a0(p seat 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 be86 y , pbj.qilbt.bxu0tween two types of rock at a tibl.6.y xb q8puj 0b,38 $^{\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. Accord1g fws/d0hpj1 ing to the user’s manual, the dish has to be pointed in the direction of the satellite, but an error of about s 1gfhdj0/1pw 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 Paci42 vau(asicm4 9qft9tjq:fe 8, vi trgr8).fsfic Ocean. 29q, m ivfs 8ajvfu:4tt.9)cgiaef8trsr4( qAs it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much 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 550 kN(g6i38q bu yuv/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed3 uuqi y68bgv( of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumpsh zf+-zp/.4t hcw+fhz from a window to a fire net 18 m below, which stretches the net 1.1 m.+wfhfzz- t/4z+ch hp. Assume that the net 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 hakop50cqaq++czlccq0n hf7 * ju2br 66 nging spring. The mass then falls 33 cm before it stops and begi2 c0 u*0q67c6cclrz+knpf qq+5jbaohns to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed ovwck b e)4tfz ;7uj8(fv/6q pmf 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of the spring? um6 f8vwkc 4)jt; pqze7vfb(/    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 cid6pc -2kfmb t-u bgb18wwxr153op(fm) at just the right pace of about 1 step per seibu6tf(- pp d31g2r b 1ox8 fbwmw5-ckcond, 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 from the center of a 33-rpm w p5 3e6vvxv 6g gtisr)bwi3(b*v*v 8zphonograph record have rpw3*vesibvw v6 )8g (xvzib6t v3g*5a wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation3 ; co8f8y:0vk*x7rh himrvnx3ir k 1v x=0.650cos7.40t where x is in meters and t in second1f 8xnxrv 08ohr : ;h3mky7 rc3kii*vvs. 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 oscillates wbb4afx0f)hpiv q)qr i: y1a/1ith frequency f. What is its frequency if it accelerates at 0.50g (a) upward,f0 b1p)v 1q i/riqfa :x4y)ahb    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on tx/2w/8s ,x( xajn y-sb0uqavuhe raft, it sinks 4.0 cm deeper into the wan/-ux0s8sjb a( /2xqua y,vwx ter. When he steps off, the raft vibrates 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 inrpg0rx +xv:( lstrument are tuned to play at 392 Hz (G) and 440 Hz (Ap vrxlx rg0+:().
(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 of9ebj9b(v lzi7s v;2she:.y du Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy 2;vzueb7e j9ss y( dvb.hi9:lsection 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 section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip bsx fioy:n)yz *e;/7xof each prong moves 1.8 mm to either side of center. Cal)bo 7yi* yn;z/: xfxseculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with j-l m6(a ujn-4t3nylzsimple harmonic motion of frequency 1.5 cycles per second. What is the maximum ampj l(-ytz-nm aju6n34 llitude with which 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 xg+ydn ili,(. if that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57ng.d,iylx + i(). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of p :q4ptg4v noe hy1r*c:y0f,v exactly 2.000 s — each one-way swing takes 1.0*v0:yf1c n ,44:evtphqyorp g00 s.
(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 vertic4b+j5/lgo *tfgcgb7:nch k )gal direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer/)5t4ccg gb: gk7jb*ofn+l hg, 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 st ,ry.*y3a z foyap5q;xretched under a tension of 255 N. A pulse is generated at one end, anyry 3p;f aoz,*qa.y5 xd 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 ssq01dt:sybj1 pring stiffness constant k. A penny 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?syj:s11d t0bq (Assume $m \ll M$)

  A crane has hoisted a 1200-kg df 3.nrg +6pa t,ogmk)car at the junkyard. The steel crane 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? [r,dtp)og+a k 6m3f.gnHint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (w. 9u nx4xb;c1exg n)xghich also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begn n4;1bex)cxx .xg9guins to vibrate. In analogy to a mass vibrating on a spring, estimate 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