Give some examples of everyday vibrating objecly l z20.qsi64q dwau)b3ywg,ts. Which exhibit SHM, at least ap2 uw.64zw ldi )0gylqya3sqb,proximately?

Is the acceleration of a simple hare;r7/vc(gvxt jq )q6 nmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an ag:/ cvyfber// utomobile engine is approximately simplve//r yfg/:cbe harmonic.

Real springs have mass. Will the true period afobihav 69 nx-5e*y0dnd frequency be larger or smaller than given by the equations for a mass oscillating on the odhia60vb-*eyn x 9f5end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple hau2onw q *-en+armonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook;oor3 g)c ms ya).qhe2 of a vertical spring scale, and then is relc) ro m)ag.e;qo3syh 2eased. Describe the scale reading as a function of time.

If a pendulum clock is accu:ue7n-uks 5kz rate at sea level, will it gain or lose time when taken to high altitude?k5-su z: eu7kn Why?

A tire swing hanging fr(aot feo1hmj5k xc8nz/g 5+.kom a branch reaches nearly to the ground (Fig. 11–48). How could you estimate the jtz gx ko (co+8/5a.m5 hfn1keheight of the branch using only a stopwatch?

Why can you make water slosh back and forth in a uvde:h 81)n jepan only if you shake the pan at a certajed 1u ev)h:n8in frequency?

Give several everyday exampd, y)tjfarnigd 63:o -les of resonance.

Is a rattle in a car ever a resonance phenomenon? Explaif rn;g9 yp0x,a8 *tkwkn.

Is the frequency of a sibi/z.k-h.xh v p*slq(mple periodic wave equal to the frequency of its source? Why or h* /q(lvh. i .zspxbk-why not?

Explain the difference between the speed of a tranz wnw,f+dej9.d wkg ;2sverse wave traveling down a cord and the speed of a tiny piece of the c9+.;g fzwdw2,jndk eword.

Why do the strings used for the lowest-frequencyc,kgi r: qppi(i:,vf2u *ar,b notes on a piano normally have wire wrapped around t,ik, *rgb(qp i,ucv2 r:f:iap hem?

What kind of waves do you think will travel down a horizontal metal rod if y/ ra1wcbbe 7h8ou strike its end (a) vertically from above and (b) horizontally para hb1w/cb8 ear7llel to its length?

Since the density of air decreases with an incr* )m 7kylji8ggease in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temper 8jigy 7kl*)mgature?

Give two reasons why circular 3whw; en.lhemj xz8+. water waves decrease in amplitude as they travel away from te8emhx.nw+jw l; . zh3he source.

Two linear waves have the same amplitude and speed, and otherwise aazf*h9f ( sy 1zati27+r ov9aqre identical, except onea19sf(f+a9o*rtzh yaqi7v2 z has half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary bef 1rd:d yzq z+8n8l8o.n4e ,9eb fmljatween two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). r+1lona, j 8 8zf .9eq:8n4mydlz ebfdExplain why.

If a string is vibrating in three segments, an/n0qu / zu 9:(vfb-iciri6gt3ns9sy re there any places you could touch it wi3 nvut/yn(9rscu:qg-fi0z96sin b/i th a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incident and reflec:z6jih2p*wmq jh1j0-h gvt;xted waves cancel at the nodes. Does this mean that energy was j ht-p1x6qmv;ghj i2 w:* 0hjzdestroyed? Explain.

If we knew that energy was being transmitted from one place to 4s enba1mji ;y-m(t6h(- w eqpanother, how might we determine whether the energy was beinge-hjw1pq4b;esam-y(i (m n6t carried by particles (material bodies) or by waves?

  If a particle undergoes SH 7cdnciq *r1-aM with amplitude 0.18 m, what is the total distance it travels 7qidc* -n1a rcin one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs f7m k1k s:99/gfsi ohefrom it but is 85 cm long when a weight 9/17f feg9k: smi kshoof 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 wqmkb 7tgv7bgi 38b-7d hen its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be bq7tg b 3-km8d7bvg7 ithe frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it.gt6p w,c9qcd 1 (a) What is the c,pdw 1q96gt cspring 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 whex5wzolq )/a1z-oq 5 g)0qwu qhn a mass of 0.60 kg is hung from it. What is5qwwl -gqauo 0 h5q)q1z )/oxz its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the masc xz uj tlfm/:3em-0ntq9x*o4s in Fig. 11–2 at times t = 0,tfux* 9 m4ex-c/3:ttj0oznq lm = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 spid xy;1e,cpblm,g/a f;g er’s web. The web vibrates predominately with a frequency of 4.0 Hc,f ;pxl,e/1yam;bgg z.
(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 ii/ozjenh/ r h ,x:gnd45n(in s5kt,, vibrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What ir5/ xnzh hn/:,d eg (i5ojni, t,ks4ins the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second with an amjhp- +ck+ ;ukjk:tnpi5*9qkvfr /c7 splitude of 0.1+kcv;kf* u :i- + np /k7c5hqrtjk9spj3 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 *pz2a,r7e p upequilibrium is the speed of a SHO half the maximum value,p *7 azpre2pu?$\approx$    A

A mass attached to the end of aa+rmo+ p j8xcp3r//f b 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 springsruf g90*hhb8 xxv*2v 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibriu v x*gb0xs89huv *frh2m position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffness consta.nha 0 * 3/,ifjcde/qxzj2ddfnt 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 0fdj f2xa3enq/,jzh dd/c.0i*.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 c+ hoyj1pc2/jyompress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will thej1 opyy2h+/cj ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless sb7 if*zl 3b7(xa2ybbc urface 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 released from rest with the spring compressed, the mass experiences a maximum accele*acx 7b7yz f23bbi( lbration 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 = 0.4,6hi uyr f 6i:4*jyr* 8gax:/efyd bts rcx))v5cos6.4t where x is in meters and t is is4ytg)8 a)ud:rff erxvh ri6x:** bi/cy 6jy,n 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 3qr)x-a-/uec y vx-vl half KE and half PE?v-/3x lqar)-yxeuvc- ±    A

  If one vibration has 7.0 times the energy of a seconf2rd 8cx y0c5.1 mdht:dk;ie)nh8arkd, but their frequencies and masses are the same, what is the ratio of their amplitude r hd0e: ;m2.)8d15tdx fiynakk rcch8s?   

  A 2.00-kg pumpkin osg;pui0.aw1l)hp5 uk ocillates from a vertically hanging light spring once every 0.65k. g;p o05p huia)uw1l 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 supported by two identical parallel vertsdgq*aire ow +;m2 -g)ical springs, each with spring stiffness constant k (Fig. 11–49). What will beds-g)w 2;igqm* +aero the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x is ied9b4-wsw:o qn meters and t 4 qsbwow de:9-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 tw(hb9m-eg /pzt uk+h2p jq q25jo examples of 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 on the end of a horizontal spring (k =ey/cm9w31w 05pod+kz yl n6jl 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.9lm cpw0l dj6n53/z+19 wyok ey6m/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 constant wrm ;dij4y1)zuz,8cj bj* cf. 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) z1j4mbiy*j;d8c u wj)fr z,.cwith 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 e/m5yd,3j r ieto two springs, 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 strikesh hwvvm9 q +u( nse22dq.n3x+d a 0.600-kg block attached to a fixed horizontal spring whose spring stiffness constan 2mv(n vwnxq2+d.q39ds +huhet 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 higra6pi1;,eej z2w,hdj a) u1dm0-bav/uhvx : fh bridge. After reaching his lowest point, he oscil hx0,u16ebdwjv;v af2rmh-azj/1aipud ,e ):lates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in ex pgc.p5xqp o) ch:y45kactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly oo*clln t8 9o*fne swing per second? (That is, one complete vibration tak of ol98c**tnles exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is it1/( vo.wyuubh3f6xw*x bhh m ,s period on Mars, where the ac*mh1,h6bv uy.(xwwhf3 bou x/celeration of gravity is about 0.37 that on Earth?    s

  What is the period of 6hwj; (rnhxpg 8kp0e rl34p(pa 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 0.76ko)dho lw+5c):gjo o40 m, the pendulum bob has a mass of 365 gramsoo:j54+)g dohkclo)w, and it is released 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 losesxo 6fvfs4r q29pjcq( bm(b;z * half a minute per day, how should youzfvq(2sm4;9r6(foc *x j pbbq adjust the length of the pendulum? shortened by    mm.

Derive a formula for thtrz9)i p kima8m v(otcf(*x(-e 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. At i, a5urak) xth7 yiavfzh+0qh d 4;xz(. q,xir8t is released from rest sta.xa kiy0iu 48 xthrr)vaxqa,qd5+; fhz(, z7hrting at an 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 bsdlnw4x uexsn /y98,38h.coyoat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the wau/ 9,.8n 3 sdxxlw4yc8snohye ves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travelus n.tw0vvc 4/s with a speed of 343 m/s How far apart are the wave crestss 0.vv wtnc4u/ (compressions)?    m

  (a) AM radio signals have frequencx3d2rs:ka(h v ies between 550 kHz and 1600 kHz (kilohertz) and t(ras 23kxd:hv ravel 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 waa1j pg-edo-v, ves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as dense as the ixqesnv+j6p0x82 -6m zh mz/cdbxh / /other. In whmxi8n zhc0ebj/6s-dz/x v2phq 6m x/+ich rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 ndr4j( 303ajgk fadox *3rh w0m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one support to the other?4 ngw3d of0 j33r 0akjah(r*dx    s

  A ski gondola is connected to the top of a hill by a steel cable of length 620 m w dsq +l.3k*ru x+-m;gk-klt *td*wba and diameter 1.5 cm. As the gondola comes to the end of its run, itarglst b* +*.du +3;kkw lxwqk-dm*-t 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 just below the surface of the sege:cly 3liw(3r/( b zoa. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is3(zye g lo wi/3cl(br: the ocean at this point?    m

  P and S waves from an earthquake travel at different,co1lqr pm6sm9x,x 6w speeds, and this difference helps in locating the eart1xx w6smq9,l mo6rp,chquake “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 surface wave can be appr6+rny9mh .8p iexbl i9oximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually incluiexybl9nhpim.+ 8r 69 de 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 ajjr, j t, .gwk dwowtv4 f74a13l;g/gnmplitudes, of an earthquake P wave passing through/7 tw jj 3,j4,lv1w;ntgag rf 4.wgodk the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake w,6t yj;bc-cl, pquws 0ave passing through the Earth is measured to be 6 y;blcpqjswu, 0-,ct $ 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 portion ofp o pyz-mdq ) ;spb+6h28pn/k v4e6bvk the Ear- pk/kz8 qopnhyeb2 pmdvp;)v +6 s64bth, but one is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretchedoc*(znxq)kj 6ru9 o8s string have the same frequency, but one transports three orsc x)(6z q*jn9 8uoktimes the power of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and do;e-.l r36)u dgdnz kfswn a total vertical distance of 6.0 cm, from the lowest to the highest point, a;gnde)r u - f3zk.d6sls 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. 11–52 are moyn.7nej5sms g ihq,.y;5 o p7yuhx s3.ving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the enegyj 3y e5,5.oqnu;ss77ni.shhy p.xmrgy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, what are 4u/arh a7x -vstheushv- xaa7r4 / frequencies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibra9xryt *0kl .y a56ufa6p 5zoqdtes at 294 Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way do 9ukrztlfo p.6a*x6ayyq50 5dwn from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at adfi*yu(n- 1;fngn: sa frequency of 280 Hz. Name at least three other frequencie;n(sdn: gf 1ifua y-n*s 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 qh v(; aad96gq sezg) o224ksqstanding waves is 475 Hz,sz(dq)ok ah2qv24g;a 9gs6 eq how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz a i-f*ypfbg0 /nnd 350 Hz, what is the f- fb0ngyf/ i*prequency of the fundamental?    Hz

  A guitar string is 90 cm * v5dfn4 4 *dvzzia-mtlong and has a mass of 3.6 g. The distance from the bridge vm z*afni-vdz44* 5dtto 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 -sl,h f;ye2emcmpa-+ it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequenciem,lhe2s fcp+--;amy es are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it is mea5gzdjh8 5he3 ynd/uv,sured to vibrate at 205 Hz. By w v3dej,huzh 8g5 d5/nyhat percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attache2z a-jgotx 4ld n4f/*kd to a small-amplitude mechanical 60-Hz vibkl*oftz ndg-4a/ 4x j2rator. 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 str 91i5l ucmhl/king may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achilhi1k9/cl mu 5eved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the b4vq 4oz c/zd*5gt+s mright frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequenszq /bg*v+co5mz 4td4 cy 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 boundaryeisltde/vx org*u y*0/g.1 : m within the Earth between two kin0 *gxoies/u *d1 vy gle:/rmt.ds 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 changes frxl)v 4 uq q30cww.3putj4 e6eyom 2.8 m/s to 2.1 m/s If the incident wave crests makwquyq)e. ju v46twpxl330 4cee 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 a layer of cold, dwl :kj7z i rfs5+afd5-ense air. If the sound wave hits the cold air interface at an angle of 2fj l5ia7d: r5wkf +zs-5$^{\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 boundan: g 3)e+m 8+i kwqhpu;knrpj*ben;a 7ry between two types of rock at a rp3;;wnujk )k e7 q+ni bp:8e*namg+h38 $^{\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. Accordings )eriwpx 09q21t msd5 to the user’s manual, the dish has to be pointed in the direction of the sates25s9)rwmqipt1exd 0 llite, 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 across0j9q/(5 j *u2nr mwq)i4cb:z kz( sgim y/xcjq 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, some of them attracted to the shorem2 qq in(jj /)cwsqu:m49rc0* yj ibg (/z5kxz to see stranded fishes and boats.)    min

  An energy-absorbing car bumj(-gr:ix g /otper has a spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collidrigj- :/(tg xoes with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 ;3sna y:w9m h54muqi fl wu5z6m below, which stretches the net 1.1 m. Assume that the net behaves like a simple spring,lh:zmf6msu5wwn4 qy3;9 ai u5 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 hanging spring. The mass then:oqgvoq :nr+z60 xahwj1s1 8p fallhg o8r1 +1anqzsw:vxpjq6: 0 os 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 m2kbd k2 ug9a2nk3hcg//s (Fig. 11–54), compressing the spring 5.0 m. 3n2kh k29ck2ug/ ad bg(a) What is the spring 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 the2erx(4ca t wkb7-1qmp 0go x*c right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves xk4pat0 bc w1qxo (-gm7c2er* in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-rpm phoni zz-7 /deyc4(:rjeqp-xu 2qx ograph record havup7q4ex yx /(cq-2:zrjzi -dee a wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates accou 1nopqo0j fxlf5-x (ak7.6k trding to the equation x=0.650cos7.40t where x is in meters and t in k6l u1xpf.-0o(q 57ft ajnoxkseconds. 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 frequency if it accelh5q ye6ktov p(/ hkd61erates at 0e/5hq o1h 6(dtk6pykv .50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg manyrzels6rro4d, wt pln6n6*15su9 10bwhdx t 2 stands on the raft, it sinks 4.0 cm deeper i wu e*z,y 4p612n1dsl0rrtw6 5t r6xbh9lnd sonto the water. 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 instrument are tune.keaer8 o+zzkhzb3 5/ aba)tl4lre- 3d to play at 392 Hz (G) and 440 Hz (rh+84 letb/k- zrzee.az5a)a3 o kb3lA).
(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 wavefciw;2 a;z tsn 0mm5(xcf(b/l traveling down the 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 ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength 0m nxs;2(w;mcaczfb i l/ft( 5greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 2643 upx2o30dvrsmfbf q. 3tk59n Hz, and the tip of each prong moves 1.8 mm to eitherrm t.2nuo b5930dfq3vpx s 3fk 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 oscillaterg c5qex*n4q x:5r sr*s with simple harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placsxqn4:r*x 55 qre*cgred 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 c1 a f 8b ua(vo399gu1uqnejok8an slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end9j8 1(g uv9nua ouba81e3oqkf fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one oi mq05l8hz3kcd.(wppe4/ j h-way swing takes 1.000ch5l/ m0.i pqho4w 3d8ez(pj k 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 s ckf1.7 xp6copg(kic* pring can oscillate in the vertical direction or can swing as a pendulum of small amplitude, but nok.k6*c cg (1pci pofx7t both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched under a tension od ta1+cxk qz*9si4c/xf 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the / k+1a*c9zcxisdtx 4qopposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with springi-g2cmpngrdhl470 +n 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 onn2cil p0h4g-7dm+ rgn top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at ths8rb ylbvxj7:*(+ l+v ,rhgv ne 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? [H bb+7nrlrshjx:8y v( ,vgvl+* int: Refer to Table 9–1.]    s

  A block of jello rests on a plate 574iak- ,o fp;l5 .tk zgwd m.rvkg(rsas shown in Fig. 11–58 (which also 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 thi5a;m- ,(zl.4w .drg7vstokigfrk5pk s 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