Give some examples of everyday vibrating objects. Which eh+qo1t bjjeup 2y22jt11t rc ,xhibit SHM, at least approximatel buoph+y 1jrt, tjct22jeq121 y?

Is the acceleration of a simple harmonic oscillator eveu9zwi.g p(vu1 r zero? If so, where?

Explain why the motion of a i,w4p2xgkr.l -ue d1vpiston in an automobile engine is approximately simple harmoni i1ew p.kv,xl2d-4ru gc.

Real springs have mass. Will the tru fugsshx:8d 8(e period and frequency be larger or smaller t: dsxs8g(huf8han 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 simp,lq 4dfevr 4.cle harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the h5aoc x8z .5,pv4iru osook of a vertical spring scale, and then is rr4coo5u sxi8pz5 .,vaeleased. Describe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will iq426zk3e n+ml p0y(1lrw efszt(rxx) t gain or lose time when taken to highy1+4elfxr)0r z(x6 mpktn e(l 23s wqz altitude? Why?

A tire swing hanging fr:ij 0kfn7s8mp q2 /f.tu ri4urom a branch reaches nearly to the ground (Fig. 11–48). How could you estimate the heijrfsqpi2/8. t4nuu frk7:0m ight of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan onlyn da 3n:oxmmsx e6*m;8 if you shake the pan at a;8nx: *e6m nsmd 3moax certain frequency?

Give several everyday examp *e8-q;nwqgw0 q q(tbtles of resonance.

Is a rattle in a car ever a resonance phenomehj-dgv2k:rbl m1j f:2 non? Explain.

Is the frequency of a simple periodic wave equal to the frequenfjp:6u0f+:6p d/onr aattk 7acy of its source? Why or why :t/u:tp+aj 7op 0a 6rd 6anfkfnot?

Explain the difference between the speed of a transverse wave traveling doz2tok01x 7di6 (r9br+bvhl mywn a cord and the speed of a t 6hm xlr9b1z( +ovk27ir0dtby iny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano nojfw /d+oqbxbzsajt)l4 s;j (/. sb (jm0nc, /nrmally have wire wrapped around t)bl /(x(ojbn.wc/j, f/4nmjq z 0j d+sabsst; hem?

What kind of waves do yoq u)xb8 m5s: /yyt/vhg ks0,vnu think will travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parallel to its len8/0tb),m/kv gq5nvxsys: y h ugth?

Since the density of air decreases with an -xfg 1ahqb*:yd/r:o( be:e t dincrease in temperature, but the bulk modulubb eho:*y:tq-f :d(dxra eg/1s B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplim,(o cb5ff x*,0e loqgtude as they travel away from the c,x0 l(oq,5*bf mfeog source.

Two linear waves have the same amplitude a) kag6eqizdydq0 kz-g 8139us nd speed, and otherwise are identical, except one has half tk6 zkiz1y9da3)gdu8qgs 0 e-qhe wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sectionfjx lx4k5t2oxg71n i7s of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Explain x fx4i5ojnxt2g17kl7why.

If a string is vibrating in three segments, are there any places yo. +up -kx2 6mvx0gs/xz:l rofpu could touch it with a knife blade without disturbing the motionx r6 -.sfkl:u02oz vxp+gxmp/?

When a standing wave exists on a string, the vibrauu8ugyvkp2clw ;98b xn 0q m)7tions of incident and reflected waves canc2ykm7bq 8uu)vu8lc xw;gn p09el at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy wn ui/./+nlok9lvt4(sy4 4ccm0 gzblk x(-pqxas being transmitted from one place to another, how might we determine whether the energy4i9( cvl/ln gtbxq 0z-pcnol /+ms(x4u.kk 4y was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total distanch895 mre kl+v :,7bcfm ubtjm9e it t:cuvb8t7 +,9r9 hlkbjfm mem5ravels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but is 85 axn3; mm9yxug- c3 6po4hdo/eh*w yb+cm long when a weight of 180 N hangs from it. What is the “spring” coxgcxa6m*y d/ o3h43myeph9buw -o+n;nstant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kgqt j njp02v5.d py7p:si.z ;cf driver gets into the driver’s seat. If the car goes over a bump, what will becjv:q;y. 7. ipnp2p s0d5zjft the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a ;d slv)qpr j-02.7-kg fish hangs from it. (a) What is the spring stiffness consta j rq-0p;dsv)lnt $\approx$    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 when a mass ofmd.xx1 d3ah qq0ko-le8()h ot 0.60 kg is hung from .qtlh q1dxokd)eam (h0 -x 83oit. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating 5 f60) pic bbz*b5faclthe position x of the mass in Fig. 11–2 at times t = 0,t = b ica65lf) p*fbzb5 c0$\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 spide/xd7-e8 ift bvr’s web. The web vibrates predomina- fbvt78ix ed/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 0.8;mh/71gnp i2sxuy4 fb8 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. Wh72gbyi nx 1fhm4u/;sp at is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second wmgve/8)vf:eaflh: ) with an amplitude of 0.13 m. Determilv/ew m:f :)hfeg)va 8ne
(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 maximum vaane ono+b sx9/,c+qsx cc,//rlx/oceraos+ /c,x9n/bq,+ scn ue?$\approx$    A

A mass attached to the end of a spring is stretched a dista i7dvbpfs0l5( nce $x_0$ 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. If +hnfb0rklf+g 6hl 0g 2the spring is stretched an additional h+2 00nfbllg+h rk6fg0.130 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with sp3i p;r+/r76* tynft rwebsh yj,hp2 m,ring 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 moving with a speed ofh/rrh7 wtfp, b+nymtie,p63 r;2y* sj 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 towow;qq(wz kms 9);7ck compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave the gun?(ww)qso mkz w 7kcq9;;    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one end ,+twpn /wfsn .of a spring; the other end is fixed to a wall. 3.0 J of work is rw wf,+.ps/tnnequired to compress the spring by 0.12 m. If the mass is released 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*auggrh im9z h3.i7 g+ to the equation x = 0.45cos6.4t where x is in meters and t is in seconds i3.h z9 aggm*urihg+7. 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 aoyn9:rm i3w9u5hjm. equilibrium is the energy of a SHO half KE and half PE? ±m5u inj.9mr3y haw:9 o    A

  If one vibration has 7.0 times the energy of a second, but their f:ke8 m n-nmm;a ej6oxeozg664 requencies and masses are the same, what is the ratiakomoxmej8m ge ;4nen66-6 z:o of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically han 2dz3lnqxh( 1 gviz;7vging light spring once every 0.65 sl3 gh(7 v12z;nq zvdxi.
(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 sukjx39v* dnzlg: e /m5wukl5o 4pported by two identical parallel vertical springs, each with sprinzm4 k*:5vxl 9kgj5nldu/weo3 g stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equati;f +uqfa(vlc 4+dso;llfbj 7 5on x = 0.38sin6.5t where x is in meters and t is in secljaq;u;d 7(l4 o5+ cv f+sblffonds. 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 each, what is hqz,.of6 v nzw yi0*7z
(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 r8gy c.. nu)sosfz;otit; r+8rest on the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Detu +of;g) 8to.nst.yc ;r iz8rsermine
(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 sgz3 n ddhkdib 60 u42:qbm1q3gpring stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it.b3gq 3 dm 4:gdzi bd0knq216uh 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, with spring stifrn;6ni98p (c,qhu*fbx s np7s fness 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 aizt.9)i9mr nx wzgf5 : fixed horizontal spring whose spring stiffn: 9r9zzxfn5mitwg. )iess 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 reacu;-itfap)*y l4b+al ahing his lowest point, he oscillates up and down, hitting a low point eight mora-iut* l ;f)ba a4lyp+e 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 ex6hbo/x+ps bh.actly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exlq dgp9(+mj1 o n:d7nt;+nzv factly one swing per second? (That is,pf97o q( jm:ndn+ +lvt1gzd ;n one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its pemrq. lq73hm5e riod on Mars, where the accqrmme.5 7 l3hqeleration of gravity is about 0.37 that on Earth?    s

  What is the period oyed2e8k5 3usa4 ikp 1vfvtr .)f a 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 pext.ja zl(c7ya;6s((i gpuna0 ndulum bob has a mass of 365 grams, and it is released at an angle of 12.0 . 07((a p(izgcja6asutn ;yxl$^{\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 clocrkkuf0q(xs b)2*nhx 1 k’s pendulum has a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pnkf )hux2*0rqsx1b (kendulum? shortened by    mm.

Derive a formula for theqkz-/ hxh-8 jy3v6qwad)y du8 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 oscillatesxcpfj/9p cc ;y : ) yz1+9og6akjc8xbl at a frequency of 2.5 Hz. At it is released from rest starting at an y/6 pxj y+ ;abc1pjczf8)xcg9 c9kl:oangle 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 ancr6 8- o sw1bmk(tvy(iohored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the waves travm 8-i((otyr wbo1 ks6veling?    m/s

  A sound wave in air has a frequency of 262 Hz and traveaaijp:-kk 13jgs 3r(x ls with a speed of 343 m/s How far apart are the wave crest 1jaxrk(p3 - a3ijg:sks (compressions)?    m

  (a) AM radio signals have frequenco*fswb1 jl jc*lr5l5 8x-r 7huies between 550 kHz and 1600 kHz (kilohertz) and tra* llohlbj*jrx7 u5-5s1f8 rwc vel 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 longitudinal waves in dw+d3gsl2a (s: 6un o uz;oaf,
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twic,q g- 0eqkoo;atpi5 (de as dense as the other. In which rod will the speed of longitudin-d;qag 0o5q ot,kipe( al waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between twvdoec0zw y..- o supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pzdv0e- .cw. youlse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of len g:nxoe56mc /miz);4ikqj9cn nm7 vx1gth 620 m and diameter 1.5 cm. As the gondola cx7;n n5m cnv)kzjc/ imqg:e69x1o m4i omes 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 of his ship jusow5 79p6qgqv vt below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly belowp6g79oq5v vw q 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different sy68 s zfjwa*j(peeds, and this difference helps in locating the earthquake “epicenter” (where the disturbance took place).jfwy as8*6z( j
(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 sinrzd(g , /qvpkn3jyov4go n0 1 bhk7,0lusoidal 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 contactd(p 0,g34hvyq lzbnko,0ngj / vkro7 1 with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the iicms aes74+ - d6 du0kt;db;sentensities, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km anddaes detmb-s icu ;0d+4s;67k 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is me71w sysrlg.j* asured to be .g7sryj1ws* l $ 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 same plq ; 5hhz l9f( :2jhnuj(entk.ortion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes ((nlfkqju9je2zh h ht ; :5ln.of the two waves?   

  Two waves traveling alongfln o:hi6ia b ,g0a();x,*yao(mxtlv,xyd(v a stretched string have the same frequency, but one transports three times the power oflyda ,6v0abxoxf (mg, li ; ahnyoxv:) (t,(*i the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is obserfluw j;b2bk74+ w.fcuved to move up and down a total vertical distance 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 ch42+lk w;cbfwbju. uf7ange?   

The two pulses shown in Fig. 11–52 are moving toward each other. uc,iqx fls0kddffr03fyca7+7 0*y/e (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 the moment the pulses pass each other, the string is straight. Wh /iccf70e30x7q+ ylfafu dkf0ys,r*d at has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its frs u lzijz9.x69is j0+undamental frequency, what are the frequ9iz.ujsxl06i9srz +j encies of the first four 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 will it v ;)wteigsu8wxh.* 8unbx g8eic;9tt,ibrate if it is fingered one-third of the way down fromgxusbun t8)e8eit gwx9ch ,t*.w8 i;; 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 frequency of 280 Hz. N2oym0cta 3 o2qame at least three other frequencies at which it will re tqm2 3oyac20osonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string ,*j da)ft3jem zl /29h.rx;n m;qy zqvis 92m/s If the frequency of standing waves is 475 Hz, how far apart are two3h;t2 jvd* r);l.fmajynmz xz q,9 e/q adjacent nodes?   m

  If two successive overtones of a vibrating string arexfkf px wsj4,1zrd60rq*a9; qgap5)s 280 Hz and 350 Hz, what is the frequency of the fundamental? 4jaq,5 s k) wapfrpz9r1x06gq;fdxs*   Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distancc /bwfp 1o6 m8yf7z02ip;sv kce from the bridge to the support post is L = 62cm and the mo7ib fp;6s/8zcf0 y1p w2kvc 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 measured+ *zi musoml3 6d,hi7v to vibrate at 7lud6+*3mhz,soiim v 205 Hz. By what percent should the tension in the 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 vvn;j8 l- hlh9z;v/s biibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to c;zjlb -v;vlh8n9sh i/orrect the frequency? decreased by    %

  One end of a horizontal string is attached t9fa a+si, u. xccid5r. qr;6pko a small-amplitude mechanical 60-Hz ..ci q 56 riruxpa+k sd,f;9cavibrator. 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 the string may be adjusted by moving the pul xos/2f xbj3eh0wba2)ley. If the hanging mass m o xxjb2ha3 e20fbs )w/is fixed at 0.080 kg, 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 acc c.vbh j9n5p6ka 5+w tub at just the right frequency, the water alternately rises and fpkach5w +6cnj.v c9b 5alls at each end, remaining relatively calm 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 o*opft36x/ v vk.0 km/s strikes a boundary within the Earth between two kinds of material. If it approaches the boundary at an ino6o/ xftv p*3vcident 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 chyfcmmh: *e3dx9 5fsgkjm5* -panges from 2.8 m/s xfs5cdm m yh93:efp5m *k* gj-to 2.1 m/s If the 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 hits7wiomyij.q)rpw7 1 1s a layer of cold, dense air. If th.wr7wyq )pioi ms1j 17e sound wave hits 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 rockeg* m.isqe7oi+ql8 p3 at a 38 eqmg*l. iqse 8p73o +i$^{\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 user’s manual,ryx+nuful b 9h4-o 5)hz52dqk the dish has to be poin+fuqo-bd kzlh9)u 2hx 5rn4y5ted 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 rjtyfcd ypmw6 p ;b85+2ars7pxly)31250 km and velocity 750 km/h travels across 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 run to safety? (In the absence of knowledge and warning, people have died during tsunamis, s6w3mbr 7)ytp c5;l1p + jfsaryxd8y 2pome of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring sh25de0zpmfmp2 uz671bvaq2 a tiffness constant 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 2au m7z 22dq5 vbp0p6h 2fza1em.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a wino95-;pa p rgvvc6at+m dow to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a sg m9;p-tacvo6p+ v5ra imple 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 ty8 *ad;r ifxbx,p:og 5he end of a freely hanging spring. The mass then falls 33 cm before it stops and bey;bagr* ,ox5pfx8 d:i gins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at ulb++dzwm c ;8dul.f,+wt4aa a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spr+zl;u4 ,8+acbdfaum wdl .+twing stiffness 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 (diameter 8 cm) at just the rigxj2: lohau/,rho(d .m a ) rjl*vtl/h7ht pace of about 1 step per second, the coffee sloshes more and more until evexua.lmj(hr)2 oll r7/,da hjto/h: v*ntually 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-rpmzvwkz3o vnst *.2t+ ;5kv)ftd)gsf 4d phonograph reczk )vd.5 ); g 42t dnts3*ofwvkst+fvzord 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 whe:ki funizw7( 8ezvto 1 -k:5dore x is in mete8uvt fo:1w-ek(z5ik:i7n d ozrs and t in 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 oscillates with frequency f. What is its fruzna7/s9i8f5av a5 ur/ a7zt fequency if it accelerates at 0.50g (a//au5rt7anzf iasu v578f z9 a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on th;/g6(j3ecp a9f ailzhe raft, it sinks 4.0 cm deeper into the water. When he steps off,zcp /gah;i 6 3(je9lfa 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 musicc,wu gr:)i2py al instrument are tuned to play at 392 Hz (G) and 440 Hz (A). w2u iy)gr pc:,
(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 tusrt4h+hhmo 2s4oc 9 )he stretched two-part cord of Fig. 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 rats rthm)+hh4o 9ocus24 io 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 of eac(kp(f zz -rnnipz-z,9 h prong moves 1.8 mm to pnnzz,f kz-9-pz(ri (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 cbr w)mdov(b3gc)ja ;cl:wh7 wes87q/ycles per second. What is the maximum amplitude wit)m:gjc8rho/ 7sa; b bwdv c )3w7elqw(h 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 “fr0*hrn.aqc :g, bznq+pgv y0r1 ee” end if that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrati *00:gyqbvpgz1,hqn+ r cran.ons of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2uh *0pv v+zlw :9fiurio9 ql)vy8/ )eb.000 s — each one-way swing takes 1.000 sv uzrp:obelqiv yi+ /l09 vu*hwf)98).
(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 c -/uou xw/vnu-an oscillate in the vertical direction 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 oscillations or the period oxounuw/-- u/v f 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 vgwsv*3r :tb(xn,gb2q+l ,su N. A pulse is generated at one end, and 20.0 ms later a xunw*(bl3g , 2vvbg:qstr s+,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 stiffnuj k5ta* bt31tess constant k. A penny of mass m is placejtbt3 akt5*1u d 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 12tk(-1/z 3cqnbwo yr,k00-kg 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-yc,b( 1 r/onqt3kkz w the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (whic(b(2xswytgmw8ukkin v +;+8 jh also gives the dimensions of the block) ygb;usxt +(8wkvkmj82(n i+w. 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 (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz