Give some examples of everyday vibr/( ntjjjv ot(jw0u 25vating objects. Which exhibit SHM, at least approx o2j/jvutj(5(vnj tw0imately?

Is the acceleration o**8) ndnpne 6y,zzdak6wj( ygf a simple harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobilp 7a,oys;q yz8 hyfc+1cu3 id7e engine is approximately simple yu1aid oqzcs, 77f3+yph8cy; harmonic.

Real springs have mass. W.:d cf l/qckft,-:re- cwxw(till the true period and frequency be larger or smaller than given by the equations for a mass oscillacxe/c-f w.td f(rk-c ::twql,ting on the end of an idealized massless spring? Explain.

How could you double the maximum sd1r2 ob8oumm4in1 h8uiqw2 i(peed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hoo gvag k. -(.izsi*tm2lk of a vertical spring scale, and then is released. Describe the scale reading as-ai m vk(ig*2 lgz..st a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose gtm bb b1,4t(ctime when taken tot (bc m,b4t1bg high altitude? Why?

A tire swing hanging q l vjb; (6d378 cj9*e:shda6lbbqc htfrom a branch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the bra 6j ; c3b(qh9 sd*a:bhvqe76lcdtjl8b nch using only a stopwatch?

Why can you make water slosd ji.p )b1n7t3o*mlgl h back and forth in a pan only if you shake the pan atmg37lil*j.t) pb 1odn a certain frequency?

Give several everyday ex/q*tzsnzw 5)x amples of resonance.

Is a rattle in a car ever a resmmt(g8)/( t soe 2y+mei0sg jtonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to tqvr 9qo4w 6kk2iv7tm9he frequency of its source? Why or why n9k m27 kro9ivv4qqtw6ot?

Explain the difference between the3.fsq 1uvlnd39v u8b f/ ck5fz speed of a transverse wave traveling down a cord and the speed of aq3 buk v5lcu9.1ff/f dnz83sv tiny piece of the cord.

Why do the strings used fkrq .etd,/k7 wor the lowest-frequency notes on a piano normally have wire wrad.qktk 7e,r /wpped around them?

What kind of waves do you think will travel down a horizontal metal rod if yexzl+: 5nknqe9i8 w/mou strike its end (a) vertically from above and (b) horizontally parallele/ie8 :zx+nw9k5mq ln to its length?

Since the density of air decreases with an increase ing ,m6 ljhs.n5;t hpov9 temperature, but the bulk modulus B is nearly independent of temperature, how would you expect th vs5 hlh9mjt6,gpo;.ne speed of sound waves in air to vary with temperature?

Give two reasons why circular watery,hz..9 yjt zn waves decrease in amplitude as they travel away fyjz.t, y9.zhn rom the source.

Two linear waves have the same amplitimfg8.r8g 2uk ude and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits more energy? By what factogf g.kmui8r82 r?

When a sinusoidal wave crosses the boundary between two section- s ezan+.x.(huaa-5des(hkjs of cord as in Fig. 11–33, the frequency does not change (although the-d .hee(k un.a-5jsx+haa zs ( wavelength and velocity do change). Explain why.

If a string is vibratingwrxs( ixs*aapk + ,)pk+/xv7h in three segments, are there any places you could touch p aa )xs pxwks7r(vi/x++k,h* it with a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incident and reflw1lq ,6 n6dpyzr u,*saected waves cancel at the nodes. Does this mean that energy was destroyed?u6szdp61, ,a ylw* nqr Explain.

If we knew that energy was being transmitted from one place to another, how 3yp3)ea t6epe might 6e33 )ta eeyppwe determine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, w(b1 jb0cr5que; g1qzthat is the total distance it travels q( bjz 51u ct;b0g1rqein one period?    m

  An elastic cord is 65 cm long when a weigo,z i:g2( v;62bnnyq vh xkdrmo3g :7cht of 75 N hangs from it but is 85 cm long ov;mvc 63(x7g 2d2i:ghknbyz:n oqr ,when a weight of 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 when its9;zf m il8jav+;(gxobc sk /m5 68-kg driver gets into the driver’s seat. If t/gj ;5; 9o vzma(kf+sl cxim8bhe car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 nvqc)ip a/9 0mcm when a 2.7-kg fish hangs from it. (a) What is the spring stiffness constanv0p/ nqa 9)mcit $\approx$    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 H(7wjplhb1 m5rr1-x7h wf vq e0z when a mass of 0.60 kg is hung from it. What is its frequency if only wx1 1rwf7(7pv0-qj mh lhr 5be0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of el(:4. ,j xoyagv 3xnbthe mass in Fig. 11–2 at times t x njxl(v:.3,g4ao eyb= 0,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web. The web vibrates predomil8hts( z;3 hqcnately with a frequency zth; 3 q8chs(lof 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 hp8,73gwi orrl q66lsa frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the value of m? ql36 ir7phg6lw o8rs,   kg

  A 0.60-kg mass at the end of a sprinj-1+. 2 a4nuis5bysdtfo d;djg vibrates 3.0 times per second with an amplitud .u14d i52yjjtsb+d;afs d- noe 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 displacement0ql /,si3rdlf )fb+pq from equilibrium is the speed of a SHO half the maximum valf l+)s / lrq3qpi0fb,due?$\approx$    A

A mass attached to the end of a spring is stretched a dist d6)la+ibr,p g *zx9yeance $x_0$ 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 ver/ 10k xmzknxu(tical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium posk0mx(1x /zk nuition again?    s

  An object with mass 3.0 kg is attached tj x*)kh zkv0)+chnm0ko a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium pk*)hnm0jvx )c0zkhk +osition, 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 m t(nd0dkz;q hegk8/qs*o “load” a e kdq/ngzdk;0q(h8*s0.180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attach/hhex1w8xk- l ed 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, h h8w/-ekx1lxthe 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 x i*oxu veg.t 5y.s in meters and t is in seconds. Detxv .gyo5eut. *ermine
(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 halfvna a*3hs sz-- PE? h-v3a*s -aszn±    A

  If one vibration has 7.0 times the energy of a second, but their freqce .vv: l(lk2quencies and masses are tv2qe.cl kl v:(he same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring once every 0.v-sef /+zv.avqig(z ..gvfv iae/-. zsv(zq+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, each8v +iohyx s;uq :kl76s with spring stiffness constant k (Fig. 11–49;khv qss6 8+xiluo:7y). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5brl*: tgk84;vci - wnxpdh)l3t where x is in meters and t is in seconds. Detekcnt)4l3vih db -;8lg:p*wrx rmine
(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 e:+msnxp 2 7hx wyoyggxp91o(5ach, 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 en cs, fxuorh;)im0f-a 4d of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Determaffm-0h ; c,or) sx4uiine
(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 stq 4kq 2qcxj3 3mh,tr;fiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. 42h k,m3qqq3c;xt fjrThe 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 sprinl7-dal-abuq y3b l7wwbdd: wb..z52bgs, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attache6d8r a h*zgho(d to a fixed horizontal spring whosar8 h*(o6g dhze spring stiffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from asjmq;5o7:ixw+vfwb*m x*a n; high bridge. After reaching his lowest point, he oscillates u;m;*swxqmof*i+ b xjw:7 nv5ap 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 exactly 60 s. What is its(ll c* 91rmdcd5it xo.
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly iop*)*2dev 4rpksib * one swing per second? (That is, one i o i ppkevs*2*r*bd)4complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s: eqmeaq8rtfy 0+2t 8u on Earth. What is its period on Mars, where the acce+et8ur2 8yt:qem 0qa fleration of gravity is about 0.37 that on Earth?    s

  What is the period of a simpl0wwyf mc:yr 8dq8b;s4e pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulum bob has a /*w zqbv)p:l+pl g0;tz-vmm emass of 365 grams, and it is released at an angle of b0evp)tl-vl/m+gmz ;p z:q* w 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 td97obgq0i5 tdhe clock loses half a minute per day, how should you adjust the length of the pen9d qit5 07bdgodulum? shortened by    mm.

Derive a formula for the maximu85:m; gw y/ bqxemhyskn3q+p ,bud/4mm 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 Hz3)h okxr2yj wjbv9mbs8o0qsf o,*7u1 -qqpx.. At it is released from reu 1 y8 b9opj k*jq2r. 0-hfvqws b)7o3sox,qmxst starting 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 anchorcdvgqp e 1q. )wp 2d9in1v;(uwed boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the waves travnpv ) w .d;9ecqdqvw(g21uip1 eling?    m/s

  A sound wave in air has a frequencycj9mu 8s p7fs+h df+2/e:lld y of 262 Hz and travels with a speed of 343 m/s How far apart are the wavl sdd e 2/9+f+8y7clu:fp jshme crests (compressions)?    m

  (a) AM radio signals have frequencies betb roa rrw),eh+() i efce3qp)48 u8qswween 550 kHz and 1600 kHz (kilohertz) and trahw)eqwq ar fb8o, p)4 8re)i+r3c(uesvel 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 longitudu8(h y -khgq*final waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the sf h hzg;t55)v;yq 2opzame elastic modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, and5y t )zh2;f;zq pg5hov by what factor?   

  A cord of mass 0.65 kg is stretched between tw* li*nj /atlq6o supports 28 m apart. If the tension inq6 l a/*nli*tj 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 toph6zuk7/bu o+ r of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it buh kz6/ouur+b 7mps 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 2kp 9mtinkj-n* yd.u.cd8+jqjust below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this point? k.2 -pd n.8kic +nju*td9 myqj   m

  P and S waves from an earthquake travel at di+76ly3m nvo/ cv knugz5y agey ./75asfferent speeds, and this difference helps in locating the earthquake “epicenter” (where the disyv z3.vgn s loa5/6 7ye5/+ynug7 cakmturbance 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 sinusoi:b dwaqtz /r6m2bk x-:dal transverse wave. Assuming akw:/b62 qbad zmr :-xt 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? [Hint: Set the acceleration a>g]    m

  What is the ratio of (khtc x *63u+8 bas7xfja) the intensities, and (b) the amplitudes, of an earthquake P wave passing thrs683fcbh*xk+7 u jx atough 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 Ea8hm .4pretxzxu3i. b7 rth is measured to be thm.8ib x4.ur3xp e 7z$ 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 fs rf p4uzi- f:/m6*rucrequency travel through the same portion of the Earth, but one 6pr -mf: fc/4uzirs*u is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have th ga; 2q0q /xg2c. jfeg+zh4huhe same frequency, but one transports three times the power of the other. What is the ratio of the amplitudes of the t4x+ agehuq;f g z hc2.0qjg2h/wo waves?   

  A bug on the surface of a pond is observed to move up and down a totap f7v.(ic 0hjkg4*7jz2 gxtm ol vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE cha 4(*ojg2hvic x0kf7jgtzp7 .mnge?   

The two pulses shown in Fig. 11–52 are moving toward e: q0;f0t*d oqb wrelu x008 :dxvxoe-mach 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 energy at this0x;dwvt: 0-m8 deqqr0 xu* bofe: ol0x moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, what axv98ge)b q1a b4ks t,x3u0qebkk9j w 2cke d48re the frequencies of the first fouqk91 tksd8e)qubk2 x3,g4 bbvxee98 4awckj0 r harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency will it oi/su7i:5oso vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of thei7ui5o:sos o/ string vibrates as a standing wave.)    Hz

  A particular string resonates in four loopj(4;hc;( 3q4m04t apm/qdzqlpldhwj s at a frequency of 280 Hz. Name at least three other frequencies at which it wp4p0hml4wq; zm4q (jlatdh jd/;3q( cill 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 fr9: x:gbtq.nlhl (+p n:qtcv3 qequency of standing waves is 475 Hz, how far apart are two adjacentg::(nt lhxqqb 9. qc nlvp3+:t nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, what ie5hovy+hs gqnps,ku /al),h;5x dhf7-e ap14 s the frequency of the fugeh5h s45, y;hfxpqdusp ane),ka/v+ -l ho71ndamental?    Hz

  A guitar string is 90 c10lp ce kwlol1ir0 *5bm long and has a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string ilp0kr011 bl ic loe5w*s under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar strinb k:3nbiu- cqt yr21 .5gxab3og is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent shou-t x nar:3 ob3uc5kib.2gy1 qbld the tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to viwry ka9s21j w(-jnt 1rbrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correcj-1rw(yr nwk 19 2jstat the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplituda4 p-u9 pzg3sihie 0z(e mechanical 60-Hz vibrator. The string’s mass per unit lengthh(ez 9is3 puazpg-i04 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 mov9 mmzj.tfsv m*1v-p j4ing the pulley. If the hanging mass zvsm4mjm-pv1t*j.f9 m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at +ui3 sp- m ih;cmu3b0jjust the right frequency, the water alternately rises and falls at each end, remaining relativb+-ih3 js0c mp;um 3uiely calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s s 4ib no*usffei;m7*s2 p8o 2fstrikes a boundary within the Earth betweso pnf;sif*bi8 7m2 4*use o2fen two kinds 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 und sj0h1 pq evek6xb(d u.(/;qucerwater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests make 0cs(e6uxvdhbq(/q;p. u k 1jea 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is travex-22ra prr /- pa4*lwflodqk0ling in warm air when it hits a layer of cold, dense air. If the sourx*f rl op-wrl42a0aq/kpd- 2nd wave hits the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes lgh cz(gv-ozd8d zadt+/: )k8 a boundary between two types of rock at a 3 g+z(td8 d/k :zc zdg)-h8lavo8 $^{\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 aboo wb q(f6;hig:ut 0.5 m in diameter. According to the user’s manual, the dish has to be pointed in the direct; h(goqfi6 bw:ion 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*dzqmdf)78d2q* x 7 h w+ahun27zijot km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishesdu*i zw77n zd7hdt h+ajq8 of22 *qxm) and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 550 kN/m,z:e6jn2 mxh-ms4 ks/0 quxjt Find the maximum compression of the bumper if the e j/s-60sm4txknj,um z q2:xhcar, 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 sdhrk*c +rqa- oyq.g + 4tn05xa window to a fire net 18 m below, which stretches the net 1.1 m. Assume th .qcna rs4t h*5ydgr-xqo 0++kat 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 hanging spring. The mass 6buj7p/ht12f bz- gku then falls 33 cm before it stops and begins to rise. What is the frequency of the oscillati ug2ujpfkbt16bz7 /h-on?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), comr siejf .39kt-mj8z0dpressing the spring 5.0 m. (a) What is the spring stiffness constant o9mtrji f0 8ds.3jkze -f 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)) 1d/+ mvymncl at just the right pace of about 1 step per second, the coffee sloshes more and more until event+ncd/)1 ymlm vually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the ce/ny(qc65.k fv ab8ji+m vj-umnter of a 33-rpm phonograph record have.f5nmjv jy8i6-kb uv/c( +qam a wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x is in pf ,q7hdd5omjk:w98o meters anpm75 89jko d,w dq:hfod 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 ostxstl hyuen)**7wg( hs -dy x9dbt3)0 cillates with frequency f. What is its frequency if it accel 7t9e)gssw u)dl-d0n xth b(*3t yhy*xerates at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raft,(*d c f1c0svqi it sinks 4.0 cm deeper into the i0 f*svcqc1( dwater. 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 instzinl *zcmz hwt-c7 ,bq.z8g6 7rument are tuned to play at 392 Hz (G) and 440 Hz (A). i6-gnhctm.7, b*w qzz8czz7 l
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stretched two-paryb *bf8+ka kg9t 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 thb g8+9kyk*b afe two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of each prong mov oi u)( cmjemh;,83mpces 1.8 mm to either side of;3jum mph8e )c,cio( m center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of freqf/4*2av pw raiuency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact *arf a 2/wp4ivwith the board during the oscillation?

A string can have a “free” end ia*arrrnkggay:p7 ;e )qm0a)mcu y (+3f that end is attached to a ring that can slide without frictiry)reyauc; )q *3mrapg k m (7ag:0an+on on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — eac. j1*bw/b;gl5j gx0qvs r,3) mscskg uh one-way swing takes 1.l;v5b. kwqb sg*jsu1/gxgrc )0js m3, 000 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 vertical direction d;wg5dz6gc7z)w tn1c * 5e v fpphc*o8or can swing as a pendulum of small amplitude, but not both at the 6;hopg5 *z*w 5 ecz)g fd n8tcv7pwd1csame 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 stretcg fkekz c+rqf/s315 ehdc2w+4hed under a tension of 255 N. A pulse iswq4k3 gh/ffcs2 +e5 r de+kzc1 generated at one end, 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 iseibhe9dz 294t suspended from a ceiling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximu bdize9h429te m 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 is 22usz+oze n/:(ow -4erpx/y1 jz m long and has a diameter of 6.4 mm. A breeze starts the car bouncing atnpz yz4jx ro(oz1se+e- /u/:w 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 als*7 -r a:lf qftfj8qgxp.f o):so 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 fa8tf-)lsfx*gpff.:: r7jq qorequency 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