Give some examples of everyday vibrating objects. Which exhibit SHM, at least o, oi ;)g1sib5-vlbosapproximately i -1gv5;o,ol )obsbsi?

Is the acceleration of a simple harmonic osb4/5qhss(11 yvl q uy 5pm+gg 3oqfe8ucillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine.bb94lhp4 tp xwvw uc+:j2 j0k is approximately simple 4t: j k94jhvcp0plbxbu.2ww +harmonic.

Real springs have mass. Will the true period and frequency be l(-5zimp v lco2arger or smaller than given by the equations for a mass oscillating on the end of an5- impo2vc(z l idealized massless spring? Explain.

How could you double the maximumba+s;j qcu*n;na9oh3y45 arg speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical springl-8asjo8/)y mshu60 +z y)oaivjj 1cq scale, and then is released. Describe the scale reading as a function of tim8vao/l)+8u qsi soaz1mjjj )6yhy-0c e.

If a pendulum clock is accaxvh5z0 0go 2l :q (h5eq8rb;tpd x:kturate at sea level, will it gain or lose time when taken to higp80er:5xh x:;bqz0q(2dat5tl o vk hgh altitude? Why?

A tire swing hanging from a branch reaches nearly to the gxo6zb0e0o z( d* dlyo1kyv.u 4 w6io7nround (Fig. 11–48). How could you estimate the hez 7x oey .(o*1koo4 0yz6d0dunlvbiw6ight of the branch using only a stopwatch?

Why can you make water slosh bawts/jfm 5 ) 8ekm6umjho2:9 jdck and forth in a pan only if you shake the pan at a certain frequku8: m )ejshwt5f d92omj6 /mjency?

Give several everyday examd1/6z*oic h nx6qjdk+ples of resonance.

Is a rattle in a car ever a reson:xvdnc h z66f :i)dz4xfuj 5*uance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of :lfx g m7g28wtq9 d1sx pxy:7dits source? Why orqfd8::dp9l7y71 g2xmsgxt xw why not?

Explain the difference between the speed of a transverse wave traveling8zweyl 7m7a7p down a cord and the speed of a tiny piece of the cord. 77yzlwap78 me

Why do the strings used for the lowest-frequency notes on a piaj;jark1k/3otna)015cd rppz d 0w8gono normally have wire a0r1p3t 1 gooar5k njckz0d /8;pj )wdwrapped around them?

What kind of waves do you think will travew5 7g +k+s: j grqct 2g39p80qnczsnqel down a horizontal metal rod if you strike its eng73gq8rcc25+qswqgs kez :nt0j np9 +d (a) vertically from above and (b) horizontally parallel to its length?

Since the density of ai,*p .n6fhv b * shtijvg(f.vakc yk:/1r decreases with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound wave,cf(k g:*fbn iavhh.1vvyt .k/*js 6 ps in air to vary with temperature?

Give two reasons why circular water jmmdn 9(21wop osa8ma 0;5hewwaves decrease in amplitude as they travel away from the soum ;a9a1onehw mo 5(wp 082djmsrce.

Two linear waves have the same amplitude and speed, and otheul*s* on,zpve 2yt7,v rwise are identical, except one has half the wavelength of the other. Which trans,t7o *vy,z levu2*npsmits more energy? By what factor?

When a sinusoidal wa errew)d)bp/ e t94sv.ve crosses the boundary between two sections of cord as in Fig. r9brsedt))4w.e p e/v 11–33, the frequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places,;vrmwjfr(1jcovcf*7 bo/s m)5y f:v you could touch it with a knife blade without disturbing the motion?/c( )y,f vom:;jof7wvrj m1rs5* vfcb

When a standing wave exists on a string, the vibrations of incident and refle sj c/dukj+:gi:9h 8zfz,;mhscted waves canc/9;hm,g j+chsdzus: :k fzi8jel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmittedz-q*z tyug c;9 from one place to another, how might we determine whether the energy was being carried by particles (materiat ;z-*qyuc9zg l bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total dista p4t y f7t1ucm*)y-kaw 9k-enwnce it trav1m--u * 9 )p4tyfecyawktwk7 nels in one period?    m

  An elastic cord is 65 cm longmo7mk)gi/ 9 p9 m59ogg ebj+wpe e479jcsi+fd when a weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs fromfk ++9 eie jeg5om7oms 9bcj9ip7/w gp49gd)m it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-8supv5rd l1*f kg car compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bu8dfsv5 u*pr1lmp, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretche+ n:tmh5w- ivx kk*w-qs 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring sww- km*t- qh+kx5 :nvitiffness 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 frequencyeo7x0 )jxps8 xo.q6 ld of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs foqop)8 d7sxx6l0 e x.jrom it?    Hz

Construct a Table indicating the position x of t(-8lj(ur bz-v zz0u: 5 bmfgws:.ebsm he mass in Fig. 11–2 at times t = 0,ts5--f(bbvj 0.b(rezmu lzgu: 8w: sz m = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 caugh527pyi4;ipeh j fyl7u:7qlap eu16jc t in a spider’s web. The web vibrates predominately with a frequency ofq 1ih72i6je;e:u54l 7papcfp yu7 l yj 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 H4x.)zj;)dz/jea c dsh8m*th xz. When an additional 680-g mass is added to a d js8z) hcx)4dzm/x.t;je* hm, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 x.* n ztw+kjbm+nk95k times per second with an amplitude of 0.13 m. Determine+ . +5 k*nkznjbw9xtkm
(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 SHO23 yw0vs*hyj, fxus 8c half the maximum valu2 xsuy c0,wsf3v*yhj8 e?$\approx$    A

A mass attached to the entkv3 pcbn k x83aawznxq )7;4, .f;egod of a spring is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical l qgv s*:wp91i2 iwc6gspring 0.315 m. If the spring is stretched an additionwcw6isigg:2q9l v*1 pal 0.130 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 spring stidac;n434 ysiq; qxre7d2y h(5ikhzt, ffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its ed;r5 qi k3n2 iah ety4c7, ;hqyxd(z4squilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a toy popgun 0.200 4 tvt+t be)4 dea:6pmez2pdl7m to “load” a 0.180-kg ball. With what speed will the ba4 lde e)v d:+eat6t2zpbmt74 pll leave the gun?    m/s

  A mass sitting on a hori:o.obpgf z9 m/9w/kypzontal, 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 spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a:.m/ywbgfzo9ko pp /9 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 )j8z +.urcov4 e)nyrtx = 0.45cos6.4t where x is in meters and t is in seconds. Deo)un+v tjz)8r yr.ce4 termine
(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 equiqbp9 33 6q;ghk4z /rpqrymjq2librium is the energy of a SHO half KE and half PE pqqqj3;y/ mgrh r2b4pq k396z? ±    A

  If one vibration has 7.0 times the energy of a second, but thei wzx5 zlgfp24gzf5l2)wwd6.qr frequencies and masses are the same, what is the ratio of their amplitudes? w )l d565 lz4fx.2p2wzgqzfwg   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring o,7mqfam jf4q sm ;pa(22rfev* nce every 0.6 v2j2mm apf sq,qrmf7fa;e(* 45 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 iden8 +e c,ehf*b zmvskh/l(.u7z btical parallel vertical springs, each with spring stiffness constant k (Fig. 17vk.*/l eu +( sh8 bzefh,zmbc1–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t wh(tyia zaxb2; ogi-b2* ere x is in meters and t i;a*-(ab tgo2 yxibi2z s in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and B. For each, s u5,-km6 w-nm z1tkzxwhat 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 (kh7(d.htp 9 dorpjyz/2l f; kw9 = 124 N/m) is struck p79ryhwdz9ftjp l /o2k (dh;. by a hammer, which gives the mass an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 38dpz3 w0bg+v w05 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass pass+pwgdz 3w0 vb8es 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 smyskcort, .( c4// grhtiffness 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 qva0/2 etq n(uorygwm*v5s tig.8k,+ a 0.600-kg block attached to a fixed horizontal spring whose spring stiffness co05tmuega s 8,t/ivyk qv 2oqn(gr+.*wnstant 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 re ngx0e 3n7ois8r(a 8ozb2z9 ohaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Cal7ns3z20oz(r a8obogh98e x inculate 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 ib 2mjpovrbl2w;i k.lq: (t rvwhk:.94 n exactly 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 one swing pkln :bic /79vrer second? (That is,b7 c lvkrin:/9 one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a pert.w bcg2mjp .y(xr9*d iod of 0.80 s on Earth. What is its period on Mars, where the acceleragxj 9drmcb* .2( py.wttion of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm j11. sigwk9tk long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulum bob has a mass of a.:qf q+yrtxk:upzp* m+f/y4 365 grams, and i4yrfu x*m : kp:qqf/+p .a+ytzt 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 length1qzwi49 c g)q kfh3+ig of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pendulum? shortened byk)1z+iqfc 9wggi4h q3    mm.

Derive a formula for the maximum speed .dzm2j5nxc ;l$v_{max}$ 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 oym- i2l b18ixaf 2.5 Hz. At it is released from rest startia -ymii21 8xlbng 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 anchore)zhvp+; mp.aad boat every 3.0 s. He measures the distance betweap ;hzva+.m)pen two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency -djt4ui-qbu u bv31)cof 262 Hz and travels with a speed of 343 m/ ctu-1jq)4bi3du-v ubs How far apart are the wave crests (compressions)?    m

  (a) AM radio signals have freque:lw dt 2;n1.4-kqgc v7ngqiab., chjp ncies between 550 kHz and 1600 kHz (kilohertz) and travel w-1hp,k gnvqj;ca7w.4:2ib l gq dnt.cith 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 wd7n+tfp r8g7qaves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulwa(p3 gb( 0mjer()nxy us, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, and by w 0rw egn3((pm()byx ajhat factor?   

  A cord of mass 0.65 kg is strx n+m i0k1a9zaetched between two supports 28 m apart. If the tensioni1a09+ mk anzx in the cord is 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a h0-nwrsyd 4sd /x kj:w5ill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse a:d ywd04s-/sr 5jnkxwlong 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 thehn-a.q7 m h1/6fg o7 a*nsv yd62wnmgy surface of the sea. He hears the echo of tn gaawfyngdm2-y6 76hmqv7s no/1*. hhe 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 spee tu 6dl3j ,m t(n+zud df)mx:;-fy5fuqds, and this difference helps in locating the earthquake “e:uud(dxdm6z u,- 3tfjn; qtf+5fl)ym picenter” (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 approximated by a sim l(yeuxr,vg195o6n s xce (yr,k3dg)nusoidal 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 bu, 5gs1m6yr9,c ((d3 xk erolngv)xyeegin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, * vzbfp:5o r xqk (*db,ryw5/vtnj,b ,of an earthquake P wd,jbb(/5, *w:o v,nkvx5rz *ypbtrfqave passing through the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured to befq)*r o:w0tns f)t:w *osn0r q$ 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 travenu/a i /.,f b)zbyv -f)w6 jlrsl*oj(al through the same portion of the Earth, but one is carrying twice tfysa l-i wz)valr/n.b* fj)bjou, 6/(he energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, bu 8l8,pcy;alzl t one transports three times the powery; p8lczl ,l8a 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 to re4fzta+ 1 v*tqt+zrahj) 45xtal vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If tjrt++ a4ztxf) rae1 zth 5v4*qhe ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11e2(o+ vid+ ,onla6v- xay dw1w d9ez-l–52 are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each othe+2oo1en -xw a6zd(ilaw -y+l,dvd e 9vr, 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, yf33 0m; dzhhewhat are the frequencies of the first fou3 0hy m;dhf3zer harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hi9tr.1/; bzlv.hkiu 3v s3dd zz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way;/1 d3u 3d9rhbk.lzv tiiz.vs down 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 a frequency)5 dddxg ji1dp(.s9ol of 280 Hz. Name at least three other frequdxs) idd pl do5jg.1(9encies 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 staij i*ajw)o (.08bmruanding waves is 475 Hz, how r0j. wmi8jui b)*aao(far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 284kqx(blrol d +t0ktyk209 r lc:ds4* b0 Hz and 350 Hz, what is the frequency of the fundamet dxy49: b0(krl bckt+r do0qk4 l*l2sntal?    Hz

  A guitar string is 90 cm long and has a k-f-.pdq7f+y h ejv8emass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamentaj.8hde- +e fkq7pvfy- l and first two overtones?    Hz

  A particular guitar string is supposed to vibfmxc5.v pj8l ryk/la4 w(1xc .rate 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 the three fre.1 w4flk5y(v .rx8jcapxmcl/quencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibr5yskas li4b6( ate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the6is4lba5y( ks string be changed to correct the frequency? decreased by    %

  One end of a horizontal st td+; ,re0x0llujbqs(ring is attached to a small-amplitude mechanical 60-Hz vql l (x0dr+tse,0bju ;ibrator. 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 otm-7 u/ n-ni8tz1yqtmoving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by vary 1t --t8q tonzn7m/uyiing L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the right freqi*s4u7l xd,h x.v n8dduency, the water alternately rises and falls 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 dx7v.*xul nd4d8is ,his the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a bp.-ggxjgny e n9q6p2 2oundary within the Earth between two kinds ofgy2ngp9gjn- .p 2eqx6 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 veloc4glemb k30 h2bity changes from 2.8 m/s to 2.1 m/s If the incident wavebm2b0k 3ghe4l 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 wpe: k c8f7 e8-jvqao8xq qo, ecn;vf;+hen it hits a layer of cold, dense air. If the sonev;f,88cpqq-o :qf vj;+ kae o7 8excund 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 wai(u:i66l 3coti4 lzte ve strikes a boundary between two types of rock at alei( tiz 6ct:u6 34oli 38 $^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m in diameter. According to the4xlc9 h d)8 9abtbia/h user’s manual, the dish has to be pa/ch9 da9x)i4 t blhb8ointed 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 km and velocity 750 km/h travels across the Pacu1 t87, omljdvuas-uosf x7;i bsp8.8ific Ocean. As it approaches Hawaii, people obser,u7s-u8uojmfa 1s;xvb d88ip.t s7olve an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness c 37deljt0 l4qpr n6pey8vh0. ionstant of 550 kN/m Find the maximum comppqe6lt0d.03ir 8ev4n h py7jl ression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which stretches t 14ur8 n l+ll(fo:x3n0/uyw)egxo smthe net 1.1 m. Assume that the net behaves like a simple spring, anoytl)o nxlxn+s34 m1f8r0w:ul eu( g/d
(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 97dbg (b rrso;spring. The mass then falls 33 cm before it stops and b ob7sr9b(d;rg egins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22b7 e wnt;lz(y/ m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of the z yw/b(nl;t7e 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 tq*u4 s3v6mmu p (*mzq, jmejnys8 a*;cm) at just 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). Estimate the speed of waves in the co6mv j8(*4m, q3qnzspa t;mseuu*y* jmffee.    cm/s

  The ripples in a certain groove 10.8aeo 5:ohsa s35 o7jk)s cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequenso 5jhs5 eo so)3a7:akcy of the sound emitted?    Hz

  A 2.00-kg mass vibrates .*(cj t4vpthk,y yul04 ftjg3 according to the equation x=0.650cos7.40t where x is in meters j.40*ylhc3y4tj( ktg,ptfu v 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 i me:n g1,l ae3s 9jlre-vev*v:7 d,tobs its frequency if it acceleb9 me ,td grv - slv3jl:a:1*ov7eee,nrates at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft flo7sr5x4/eooby 5n.s krats on a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deepe755o. /rexn4kryso bsr 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 instrument are tuned to play at 392 Hz (G) a :hcv tjy.(,cvnd 440 Hz (Ach yvjv(.t,c :).
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stretched :ul5te /o.s srtwo-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 sectio:/s .le rstu5ons. (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 each pron12hp,zc l+2r0 nqx2;jzf wxdug moves z1,hq 2x+urf2xcdzlw0j 2;np1.8 mm to 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 simplhes)go 13jy,z e harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in s)z31ehoj, gy order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a ringby*80zdi7df l epc0l6jj 3dj:e0y1g c that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a sigcd :cy8jy0l006bl 3e jzd7f e 1d*pjtring with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s s-j.p;5blo493sqonv opqz 2j — each one-way swing takes 1.000 s.ov. q- oo4 j;q9p3p n25lszbsj
(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 oscillao /e c(lrsj28erye)n1 te 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/yr ne1jsel8oe2 c() r 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 pulse htb907+ a1reddga5vhis generated at one en d9e10t 7a 5drhh+agbvd, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with spring stif(:i exho3z ka;fness constant k. A p3 ;:ekoz(axh ienny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cable isdka 5lm*u (w;n63c w;as(d mlo 22 m long and has a diameter of 6.4 mm. A breeze starts the (6*wc awlolsm ;dd(3;uk a 5nmcar 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 (which also gives 8z.s 6/es n6k0lhb gsvthe dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) ofss.ek6 g0zs6 8bl/hv n jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz