Give some examples of everyday vibrating59 eh* yyfxo8f objects. Which exhibit SHM, at least approxif xeoyf859 h*ymately?

Is the acceleration of a simpmmd wxd ,9;jto-oj6bw q6ot9-le harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston edf oa1e6+:p-u7vbraka3e ; ac . czm/in an automobile engine is approximately simple harcf+ee 7e1azm-;oapv 6./b : acra3dukmonic.

Real springs have mass. Will j(5v w9u(1 lt 7vtoxahthe true period and frequency be larger or smaller than given by the equations for h(5uxto (j lvt791vwaa mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscimx*1sn tr:0 hsllator (SHO)?

A 5.0-kg trout is attached to th-klp4fkx iwt.vq 6lp/;sn y 5/e hook of a vertical spring scale, and then is released. Describe the scale re4.ypsllt k nxp/ q-6wk5/ vf;iading as a function of time.

If a pendulum clock is accurate at sea levexm 5sq ij bsbn5;r(4e:) bjs9kl, will it gain or lose time when taken to high altitude?k)r5esbsb9:5(s4j ;b x qn mji Why?

A tire swing hanging from a branch reaches nes4 l o ss.r a1m, )4rt4pn,ze6uahs7mfarly to the ground (Fig. 11–48). How could you estimate the height of the rl.46 ,fssshe1 s4rz)nmuaaom t7p,4 branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake the pi r h/ev-+3hqnzm*kr( an at r3 /km* h(+-evzqhinra certain frequency?

Give several everyday examples of resonl- 5y:vqd-dlc+yxc2zance.

Is a rattle in a car ever a resonance phenomenon? Exn , 3pvxvds)y3d9zx4h,o3f7cx (hrvhplain.

Is the frequency of a simpbdalit nz3;5ry 5nw51le periodic wave equal to the frequency of its source? Why or why not?btzwy nr55 ai;1d3nl5

Explain the difference between the speed of a transverse wave trp,g4fhar95ebk y/ 4ufm ,myh* aveling down a cor4hf,myhf9 ag4u5emy* k/p ,brd and the speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a3tq mpzimh 3; 8 4j9tweb0kdm; piano normally have wire 4wibq3eptkz t;9m8 0j dmh3m; wrapped around them?

What kind of waves do you think will travenf fd,l0ni.o 9l down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parallel to its ,noi.n 9 lf0dflength?

Since the density of air decreases *qd yzcqolp 971k76howith an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves 16o9 c dyq7*lpkz7hqoin air to vary with temperature?

Give two reasons why circular water waves decrease in y9/8xu :z44p ob ttgatlhp(6lamplitude as they travel ala/ zth( 689b4p:uyttlxgp4oway from the source.

Two linear waves have the same ug9de4 .k2js.l fas:vamplitude and speed, and otherwise are identical, except one has half the wavelength of the other. Whic2.a.ss v9u4 klg:je fdh transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary betw4: e6 rqju;r.aom1ymkeen two sections of cord as in Fig. 11–33, the frequency does r6 :y k1um.m;ojq4raenot change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places you could towqgpvxn ys0 hpl)98 u6 +x9qe1uch it gyl hvx+)01p9p sun9eq6 q 8xwwith a knife blade without disturbing the motion?

When a standing wave exists on a st5d /c14p4 ,tdqthcv drring, the vibrations of incident and reflected waves cancel at the nodes. Does d,d 5hq44/pc1rd ttv cthis mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to anothermq3a q21d;01:/ueb s ewnqmvl , how might we determine whether the energy was being carried by particles (materialqe2db3/w;naq vm u 1:1leqs0m bodies) or by waves?

  If a particle undergoes SHM with amplizwo+a h yd0 step.h0: tlkb9*qpv-2a -tude 0.18 m, what is the total distance it trav0 2wzb.9olpt es t-0a+d*yavh hpk:q-els in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but is 85 cmu2qa7r:. w 39ylbnov4mbbee - long when a weight of 180 N hangs from it. Whatyb.4e739-leq vb2rwu : an omb is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when c5mfl0b4p uspjuq8vn 4adn46 :c 2br;its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequency of vibratildqbncfv; 5 m2 rsnp6b:4uu4 p0c j4a8ons?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (a) Wham(jsd ;h*6y 6;gzstzat is the spring stiffness ;*ag 6mzsdjsz6hty( ;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 h6ih :(fk6ualc /frd. 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency irklh. ic6h(d 6:/f afuf only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at tim9impy-g ctt 58s 8kip0es t = 0,t08ykip tsic8 59 -mptg = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 0.2j(bkdq,u lcyvssfc5l,.(wdw.t69, r6jo2 dx5 g is caught in a spider’s web. The web vibrates predomi6f,(lrk jd6qdwy w2cc. tjssudl,o 9v .b,5 x(nately with a frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency of 0.88 Hz./ )7 )bvaoifqcfv*e;o 6umcy6c (kf5j When an additional 680-g mass is addm7*c)6j v6v5 cf;ofcbu ak eo/(fiqy)ed to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the endd4z-tksc2)e) g ck4sj of a spring vibrates 3.0 times per second with an amplkgj4) ts) z2sec-dck 4itude of 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 equilkvtqefoc8:y he/ *(gf q1a rv6h-3 cy6ibrium is the speed of a SHO half the maximum value?h:a1-khq f e6*8 te/f(cyvv3o 6yg qcr$\approx$    A

A mass attached to the end of a spring is ec7n+p/9k0 ztlyzeg d sll653 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 stretch )jkj.lyvfo +v5h*ip0 es a vertical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reacjkhyi*0j+ 5) lop.vvfh the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffness constant1-/sl dv5a hzngyz4 /t k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/d/ly-svta1n 4 hzz5g/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 popgumoez f 8jd i-5fqbi:/dgo3 w/ y9c7p/sn 0.200 m to “load” a 0.180-kg ball. 3/smf8/po dy/ igqcw-fbe5:ozjid 7 9With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizonpb:fcg-v.h. f tal, frictionless surface 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 .gh f:vbc .f-pspring 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 to the equation x = 0.45cos6.4t where c jrlp:-4w3crx is in mc wlp3r4rcj-:eters and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of a SHO half KE and half br*u8 j 7 x.9wxcu*pplPE? ru8.wb*p9xcu p x*lj7 ±    A

  If one vibration has 7.0 times the energy of a second, but their frequ : 2k7pu.leyjzencies and masses are the same, what is the ratioje lyu:7pk2z . of their amplitudes?   

  A 2.00-kg pumpkin oscillates from ;*:**h bi .aedojbjlra vertically hanging light spring once every 0b :.jad ;lo**rb*ejih .65 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 vertical springs, eac ,yusjs*o w19:rwio( ph with spring stiffsrs 1,u:(op9jyw o *iwness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates accg:kpe p*,jqtyz3hr;0y 8vx: j 4g/hheording to the equation x = 0.38sin6.5t where x is in meters and t is in seco3;xzj08h py t4jkv: ep gqh*g/eyh,:rnds. 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, nqz2vt -a8.qnlabeled 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 ai qs4c9/7fsj(x 32dziivi oj1 horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Determine q231j( 4xj 7ii9d/fiszv c osi
(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 305 N/m vibrates with an a y *gde1dqv p06h9cxy,mplitude of 2 1gyp6de*09x,chvqd y 8.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring stv av5 tn8o,-wsiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed horizontal sprim bj00kv q/wa395we s/4bqs sang whose sprin 0 4j0mewavs5sbqa 3/9kbw s/qg 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 7b i9,)*jtae it4yk3b3tapfj s1 c0ti from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. t1pb atj,0e3safi)9itki jcy7 t34 *b 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 si89sedyh28 h7hq-lf ,ycc fcqsl5w k0jt3 ;/ exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simplr+g p;yk 0j5xo7su t:cb/ 7exne pendulum be if it is to make exactly one swing per second? (That is, one complete vibration takes exactly 2.0 0n/gex5; oc trkj:7 +b7yxusps.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on +g+m; cnzm2l5 teaae:Mars, where the acceleration of gravity is about 0.37 tha+ :tena ;c2azel5mmg+t on Earth?    s

  What is the period of a simple pendul:y5/x7b +ho jq- czg a0 88yugliav,eeum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulum bob has a mass ov kwpt382r9 dtf 365 grams, and it is release9d 38tptkrv w2d 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 clockjeg1u o* p j6 v:yabko ze2v(eyhm97() loses half a minute per day, how should you adjust the length of the pendul v6jkaeuv)y1 (hy(gom2b oe* 9:ej7pzum? shortened by    mm.

Derive a formula for the maximum spi:cxh1fmo aa9at .e543s f* sleed $v_{max}$ 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 it is releasc4e5cr3 fw2i f2p+gutotp :wcj.5t5ced from rest starting at an wo f 5crijt+ cugtw5 5pe.2:3cpfct24angle 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 hym h.;t8 osblq3hgq2k q1+ h,his anchored boat every 3.0 s. He measures t.yqb 1golqhhsqh; km t3+2,h8he distance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed of 343 jhk15i9dp.5yox-2 zzjy7j (j / qddbqm/s How fayhjo dkjyq(i51dz75 /zdbqj-2x 9pj.r apart are the wave crests (compressions)?    m

  (a) AM radio signals have frs1-8+8xprtvconf sj jc3(,mkij + je.equencies between 550 kHz and 1600 kHz (kilohertz) and travel with a spee8(sk f .i3j-,mpsnxrcjj1e8j+co +vtd 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 wavespyhua. vb1 ;4m in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, c) u5vlxyi)pl: hu4(u but one is twice as dense as the oth( yhuc) :45puiul)xvl er. In which rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supdgsaa i.6:p e3ports 28 m apart. If the tension in the cord is 150 N, aa ie dsg6:.3phow long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected6 xoiz9+8;t4 wcz tpu k1*5v idiea9rp to the top of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comppk uw t* 6ei1io9xvdz;4895a rzt ic+es 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 8dd2szo ij7-/fkkqnxevd; o c *; u3t(of his ship just below the surface of the sea. He hearnxd- 8 vokut;iec/z3djs ( kof;*2 7qds the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and dbz;: 3 w3daf0: j+aux-sku lathis difference helps in locating the earthquake “epicenter” (wh+ 30 bu3xazua:fwa k- ds;dj:lere 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 b ;7q u86u9d tr,8dehhqkve, pqe 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? [Hinthtpve q kd8u; que8h,7q,69d r: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the *i a+guvgffbq+x1fxc0m+m0( amplitudes, of an earthquake P wave passing throufxf+gu i01 g0fax(m m +*vqcb+gh the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake 32t5 ucop2czt-dkda fd a6pw s8/l-v:wave passing through the Earth is measured to be kd acl w8td-2oudsp5 3/2f 6ztp:a -vc$ 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 frequenqemgqw fh y;hac+/7 gu8c 36)icy travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of thqhawm;fg) q8cc/uh3i+y7 e6 ge two waves?   

  Two waves traveling along a stretched string have the saodk g8a3mf a-3me frequency, but one transports thr3a3d-ao fkgm 8ee times 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 down a tota.uitg695sqirgs a :5ql vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decregt69sqg5. ri sua :5qiase to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each otheyr7s2 rb i,x(qr. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later.( isy72r ,brqx (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,+ wsc1i p3urb2 what are the siu3pbc+ r 2w1frequencies 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 r-g4* mhj)lsifi7uf4. 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 vibrates as a standing wave.l )mgji*7hi44fu f-rs)    Hz

  A particular string resonates in four lo9hw,h:j eckcumx .dlwr3d778ops at a frequency of 280 Hz. Name at least thre hhdduk3l7wcw8 . :9r e,cm7jxe 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/(ui erh4zi+qhl *o; jlub60c 92m/s If the frequency of standing waves is 475 Hz, how far apart are two adjacent node( rbc;uh lzi0ohue q*+li64j/s?   m

  If two successive overtonej 3knong 4p -wnsm w,0tnrz)8:s of a vibrating string are 280 Hz and 350 Hz, what is the frequency of the fundament,p 4szw3mn nwnj8 )0-grno:tkal?    Hz

  A guitar string is 90 cm long and has a mass of 3dm0w/*ofv)-5zv y deo.6 g. The distance from the bridge to the support post is L = 62cm and the string is undeywed)5 omov0*-vd /f zr 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*hw(+. v vzt7eolgr 1v:(mmch at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So(*vlm+w1vot. hm 7zerc v(: hg the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it is measuv2tqf+swd)n 7fgii ,m0ph55ored to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency? fiin5o,tqg2wf m7p+0v5d )hs decreased by    %

  One end of a horizontal string is attached to a small-amplituxe+aonlogdis ,n b-9w.jz7* 7de mechanical 60-Hz vibrator. The string’s mass per unit length isn+gb7lo i-d jaz*o7 wnxe,.9s $3.9 \times10^{ -4}$ 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 t0 q zpubusw5+0he pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing w 50u+0wpu qzbsave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the wat2)xvhji2b5q+ k yadacg.ht+;er back and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wavbvk;2 . h)dtjaxa++qy5chgi 2e 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 witdnh+1 ngt *cd9hin the Earth between two kinds of material. If it approaches the boundary at anhd 1gdt+*nc 9n 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 undefxh67 otbvs) 8o 6a6qrrwater “shelf” where the velocity changes from 2.8 m/sh )tvqr6x8aso7b 66 fo 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 nf;0ryo( *cqk u:b qz6when it hits a layer of cold, dense air. If the sound wave hits the cold ;c0fzqbu*o yr 6:(qknair 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 earthquak jty1w(s ipl,6:t-fl qe wave strikes a boundary between two types of rock at a :1 wy(lt 6ptf,jlsi-q38 $^{\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 diaqvl)i6 8j*f .ga,t .; cixr)fh4fr enhmeter. According to the user’s manual, the dish has to be pointedjhq rvxa.) ;c, lnffih6i t 8).g4*rfe in the direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 k v1s,i3n0 wkzp*c :dbzoc2tv, m 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 bv3 n,,02:ocvt zczk*pds1w iabsence 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 a6j.9s h+vrm5iy 7myoj spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with massm5 j6sm+h 9yrov.7jyi 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a : (q .phu3yr 3da vtx/:tp5dtnwindow to a fire net 18 m below, which stretches the na/(ynu v.tt3r:dp:d q3 xh5 tpet 1.1 m. 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 hanglhehlf(; vp7;ing spring. The mass then falls 33 l(plh7 v;efh;cm before it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–52kb5tt /9rcvgeq gn3j+8gp r6 4), compressing the spring 5.qev/32 9r k g6r5ct+n8jbt ggp0 m. (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 jw1 zeao5uznl-h w28p/ust the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estima/ewaw2ouhn 5zp-8 1zl te the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the8 ((yx+i b) :wkab)chkchn+f f center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the soundwh k+)c)nh(cfi kbf(ay:b+8x emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.: iku*au3 ze6e(llc5b650cos7.40t where x is in meters and t in seconds. Determin5a elk6uu3 :*ielb(cz e
(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 freqr5ylp 8i fby4;uency f. What is its frequency if it accelerates at 0.50g (yf 5iybr;4l8 pa) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. /s- dodus( r1kWhen a 75-kg man stands on the raft, it si o(rk-1s/ud sdnks 4.0 cm deeper into 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 iaa /p)v e*7fu+mos7cz75swsc nstrument are tuned to play at 392 Hz (G) and 440 Hz (A)5 +z)77wcse /vuao*sa spc7f m.
(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 trdqm / jpv:o8)laveling 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 sectionsp:mj lo)/vdq8 . (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 they ty +qxu5+oa: tip of each prong moves 1.8 mm to either side of center. Caxqyyu 5+at +:olculate
(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 frequ;9ewcd/gq+9nvl (rgn ency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order th/lv9+ ngd;(9w rqcgenat a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a4+zc7by127uld (is () anfrmjh1 pj kf ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of 17d z fhfy7bkl2u (a(pi4cjj)+s 1mrnsuch a string with one end fixed and the other free.

  A “seconds” pendulum has a period of v(msjd gzt09; exactly 2.000 s — each one-way swing takes 1.000zt9g;0svdm j ( 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 jf0 se33 )givhvertical direction or can swing as a pendulum of smvg ie03s3j )fhall amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched under a tension of 255 N. A pulseonghzs3bhe2 p6- hp .x7ha4*o:cad* d is generated at one end, and 20.0 ms later a second pulse is generated a-ap:h7ags oen 6 *4zhd.p h*cxo2d3bht 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 stiffnjt;kkh6 2q/r 2 1 kb/gwe5ynlgess constant k. A penny of mass m is placed on tk/16we;g5jtk qr2 lhgkb2n y/op of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The stdf(drb v(;g9f h (pdjqa0tysp9- ) +qfeel crane cable is 22 m long and has a diamet()hb q9aft09yvqfgr( d +s-d p(;jfpder of 6.4 mm. A breeze starts the car bouncing at the end of 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 a m vhi: ii9haqytca97c+js8036ni y; (which also gives the dimensions of the blcai90hmti i 9js 8nhyc 3yvq:; 76iaa+ock). 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