Give some examples of everyday vibrating objects. Which exhibit SHM, at lo1: ce mztv5rc,-u67 mlzm de5east approximateeo ,zc7-lz1c e565mr:mmdvtuly?

Is the acceleration of lt8q k2n/rrjuvgm75axl/6 )(ps p2bk a simple harmonic oscillator ever zero? If so, where?

Explain why the motion of a pis** )k2ceou5rx jz ks1l:z1xnq ton in an automobile engine is approximately simple h)1rzs1x unkxqz kco*l2 j:5*earmonic.

Real springs have masg-rgan. m c23g. 5torls. Will the true period and frequency be larger or smaller than given by the equations for a mass oscillating3.tgg2.mo - lrr5acng on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple hudzyaca0c: 1/ armonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook,r/ wrz3d2ujs jh3 b7l of a vertical spring scale, and then is released. Describe the scale readrb/,3wr zj2 uj7 3lhsding as a function of time.

If a pendulum clock is accurate at sea level, will it gain or p bo7krifmq k;:yj.4v3p . c9klose time when taken .: kkvpmyc.f3rqj7 obpi4;k9 to high altitude? Why?

A tire swing hanging from a branch reaches neas0w-y 0pmph x(t*sheozvd))3 rly to the ground (Fig. 11–48). How could you estimate the y)md*z vo( etpx -whs0sp3h) 0height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shakehq4.t dyz (-qv the pan at a certa-hv4zqyd( tq.in frequency?

Give several everyday examples of res7)p i,f 5lbeofonance.

Is a rattle in a car ever a resonance phenomen x+ v82vaqkb5mtt +:xton? Explain.

Is the frequency of a simple periodic wave equal to the frequency vxv -bz qg,j60of its source? Why or why n6qb vgj -x,zv0ot?

Explain the difference between the speed of a transverlgj l(mm;,szwj* 9 ,pgse wave traveling down a cord and the speed of a tiny piece ofmp9l j(zls;j ,*mw,gg the cord.

Why do the strings used for t.m7 )kei qkfp4he lowest-frequency notes on a piano normally have wire wrapped7mpe) .kqif4 k around them?

What kind of waves do you think will travel down a fs7k,(j +cr s(04rmvv w501qy1q tvbrr8sgu ahorizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parayvrtgc0 s q47 , bmq(0v(r8asrj+ 1urws v1f5kllel to its length?

Since the density of air decreases with an increase in temperatusxpj0 es8h0k ;4v cw4mre, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with4wcepmh4;0 v8 k0ssjx temperature?

Give two reasons why cd d( hn2g-f4kphs-ro8ircular water waves decrease in amplitude as they travel away from the sourcedrp(8nhg o-4hfkd 2-s.

Two linear waves have the6 rwsqglkve/1 ror *:. same amplitude and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmivwogr/ l q*s61:r e.krts more energy? By what factor?

When a sinusoidal wave /;lt 6meq/tf .-zocqu crosses the boundary between two sections of cord as in Fig. 11–33, the frequency does not chang u;/tqc6-fz/olmqe t .e (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places (np9)d q lr1yayou could touch it with a knife blade withry(qpd )a n9l1out disturbing the motion?

When a standing wave exists on a string, the vibrations of incident an o;)zmvunqqpdf5,b2q* .i zt(d reflected waves cancel at the nodes. Does this mean tha m zp.qo;tbz),f5 u2*ndvq(qit energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to another, how migh fdv) :)/q xmgme.ti8(-z l4x 9dwpe 4bio*pjpt we determine whether the energy was being carried by:e i/dfz p.vx*tx-gq )ppi4jd8 9lw4)bmm oe( particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what qab odf/ i 9y.4ft.q+xis the total distance it traq/4xiq9dtyf.b+ . f aovels in one period?    m

  An elastic cord is 65 cm long when a weuc**x c+71y,mns9bmn km myk.ight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs c9 mmuk*+1ynm, c*byxn. ms7k 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 :,qq*i s9vrngwhen its 68-kg driver gets into the driver’s seat. If the car goes over a * 9v:i,gqsqrnbump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretch:m j45jl9 n5mo6vn uhtes 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffness constantmuvm 4ljo:tn559j nh 6 $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mass of 0.60 kg ish/+1r,wh0hk trv3e 2 wedmyp0 hung from it. What is its frequency if o 1hk2 dvyh/ ,rrteem+w0hwp03nly 0.38 kg hangs from it?    Hz

Construct a Table indicating the posg+u8jx voce(k- w9h uu h8v7c5ition x of the mass in Fig. 11–2 at times t = 0 oecwck-57uh9u8vjgh+x v 8u(,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 predominj0 q0(a7k0hk v, p2edtjjss(nately with a frequency of 4.0td2v(,hs k jp njsa0e7(kqj00 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 vibr1oi59)-3 2pb r*/wv feqs0fq*vslt a* yinurgates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the valuql0tnfq*g yoi *-/v3bu19 arwrfes2i sp )v5 *e of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 time .uk+pi :owtlc h4rmo+ .*,yocs per second with an amplitude of 0.13 oy+p,o lo*rc4m.h.c:u+w kt i 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 equilibrium is the speed of a SHO half the mkvgr3c43u)i- b f e0wjaximum valu f3cj0u3 rbivgkw) e4-e?$\approx$    A

A mass attached to the end of a spring is sdt b7e;j/q( pkju/m t3tretched 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 spring 0.315 m.k):f0t/rjmdlzx8; 9 qqi3 xnq If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium position agaifzk j/ : l3qqmi;x)tx0qdn98r n?    s

  An object with mass 3.0 kg is attached to a springr 4(ijigyetz.d4yzju2u 8 c2 + with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is movin yge4+2c ii 84(dzjur z.uytj2g 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 sprpvh18 ,ktqa 7 tol79zfing of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will ta8h17zk, 7 opv9 qtftlhe ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one end g9 ughd 5wm: *9dfijz4of a :fiw hguddm g9z*945jspring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum 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 th,(dn:1t rxqbjz*rb s) ln:n, re equation x = 0.45cos6.4t where x is in meters and t is in seconds. Determisj,1*)tnq(nb rln:rz r:xd b, ne
(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 issflty , r1dq./ the energy of a SHO half KE and half PElrsy t,fd/. q1? ±    A

  If one vibration has 7.0 times the energy of a secdqc; l(jb+(xi,ee9-a jw xh5rond, but their frequencies and masses are the same, what is the ratio of taj+q-e(5cedl(bw jxrxh ;i9,heir amplitudes?   

  A 2.00-kg pumpkin oscillates u(3sv l7mi fp krxildb.lo1) +e95wu,from a vertically hanging light spring once every 0.65 so)(fimvl3bs,r .9u+e d 5kxwul7ip l 1.
(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 bypb+p9fte/uojsle, y+ 9 t ki;/ two identical parallel vertical springs, each with spring stiffness con,/l+j;+ttep/ 9i sp9eoykb ufstant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38s7,ugqpzodtsyv w;sq65 a 8o7y (9l in/in6.5t where x is in meters and t is in seco6zyy;s 5g7 t(89,dqswuno/oalipqv 7nds. 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+ff*vw xxz7wv 82x mv8 SHM, labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal spring (k = 1 9orttq5setf 0(b 0t+r24 N/m) is struck by a hammer, which gives the mass an initial speed of oter0q+rb(s95 tt 0tf2.96m/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 consl)-ggkna(b; - oyk zzc((1 kyztant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass agoky(k-byz()l (cg n1 z-z;kpasses 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 sprin,.gg/umx/r4gxln -cyg 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 attached to a fin v1/ x hunfbz0zt/47o12mczk xed horizontal spring whose spring stiffness co12uofm bhn 4kt znc70/ v/1zzxnstant 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 reachiv2u4q9g sdqae+8l2 dmng 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. Calculate the sp de2mv2s a+984ugdqqlring 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 v 5zxp,jl3b0 nexactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendul ;85pq1b4kn7dc qib 6 apuym:xum be if it is to make exactly one swing per second? (That is, one complete vibration takes exactly 2.0 k 8cn;xi6a 7udqqb4p:1p b 5mys.)    m

  A pendulum has a period of 0.80 s on Earth. What is its peyy:))zcj ) bl(al1bceriod on Mars, where the acceleration of gravity is about )z1yeccy) j:al blb ()0.37 that on Earth?    s

  What is the period of a simple pendu;le; d)k43n wttg:x grlum 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 ztq; 4x;bx9ukpendulum bob has a mass of 365 grams, and it is released at an4kbxuq;z x;t9 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 hasykj 4j::lwan( a length of 0.9930 m. If the clock loses half a minwyk:(j an:l4jute per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the p:t qqb904q/ 3bukuuwt,dkl9 maximum speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.p, e*wab*r knr*rs32awev+0 2p n*nup) tm+ zu5 Hz. At it is released from rest starting at an aarn*wptv+a* pe n2)krunu32m,wes0zrb *+ p* ngle 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 wjw 6fz gs+j) g45mspyf85swu-ave crests pass the bow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. Hogupw s-j46y +swf zmsj)85gf5w fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and trav)tcy84xx3ip u xi 8q4jels with a speed of 343 m/s How far apart are i q8it 8)xxyu4x43jcpthe wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz .o7y)cfj j)f havmn-z+ea vc d45v:i5 and 1600 kHz (kilohertz) and travel n-aa)m)j czfc475 5h.f vdovy+je: vi 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 longitudi(4ai 6 iiaf4 36q.0 gidlqhdlvnal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as densw* y) fzf/yv.se as the other. In which rod will the speed of longitudinal waves be gre sz.)/fyyvfw*ater, and by what factor?   

  A cord of mass 0.65 kg is tyq2max1pv6g i+-/7q:xpo wl h8g im, stretched between two supports 28 m apart. If the tension in,ql1/p8yq tvi+:mxa-m7ig h6 o2pw xg 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 thev ( rdyy6q1rm4 top 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 bumps into the terminal and sendsvr14y( ydmqr 6 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 vz 7l,e+uw/ nghis ship just 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 e ,vn+/gwu l7zocean at this point?    m

  P and S waves from an earthquwk-5vlhcq+lxshda i/-+ t/s )ake travel at different speeds, and this difference helps in locating the earthquake “epice tw)ai5d +sk/-+hh/lcsx-q lvnter” (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 4p+m9dmr5 .aq+ dxyrp :bv.zf sinusoidal transver.mfrq5zpddy 9+.m :a xr4v+bpse 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? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (wtcm3sw7q)6 fojph5o *+ d9zfb) the amplitudes, of an earthquake P wave passing through the Earth3h*js7f mfzdc w6 9+w)otpoq 5 and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an e8z u(;ac13 89aca:kb c3yemvyjz gfa* arthquake wave passing through the Earth is measured to be *;913fevcacj y z cgma z(8a:8abu k3y$ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency travel through the same po +vzb q67j zrqko+6bt5j1 vhquca9r: -rtion of the Eart jvq b6jh6kqtuz -b71r5 +:+ ozrvca9qh, but one is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, b/tqq1m58p1 t+vrzwn xut one transports three times the power of the other. What is the ratio of the amplitudes of the two w pwr/xzt+1n1qv8 mt5qaves?   

  A bug on the surface of a pond is observed to move up and down a total verticalu0 bcw 0grbmq6.4ep e8 dim4u br.epw08bqcg 0e6 stance 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 change?   

The two pulses shown in Fig. 11–52 are moving ts6. iy;s; adz qg gbd7)3a7ljyoward each other. (a) Sketch the shape of the string a7sybiy.)a63zq7la g ;dj g ds;t 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 this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, what nqr fjp:,rxgc*.(k4;b ao 3snare the frequencies :(gb; ofj c rsxkqa,.43pr n*nof the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequexk /*5qou* wljncy will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds xk*5*oj /q wulof the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequen, 4+e yb1 8ptvei*cvsxcy of 280 Hz. Name at least three 8v ee+ytipc41vb s,*xother 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 92m/s If th)0: bip,aet uw0:foj fe frequency of standing waves is 475 Hz, how far apart are two adjacent nodesp0:jt ofu0:aw f)bi,e?   m

  If two successive overtones of a vibrating string arebzs6me .7829kfxxh sq 280 Hz and 350 Hz, what is the frequency of the 7sxshm fbx69.kz q 82efundamental?    Hz

  A guitar string is 90 cm long an es-g8rb 3coa6i)qsip,ksafud7 6s6+d has a mass 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 frequencir scik86-36 b qoa7ssfg,pe+ 6 id)saues of the fundamental and first two overtones?    Hz

  A particular guitar string is suppynfn 265e g 6b3aan)z5y-u(d wiczn :nosed to vibrate 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 thre:66funnyzna(5ni dz)53-cb2 gyaen w e frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supp6h9 1l s*7nttiesdv74 y; rcluosed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to cil4 y e7r6s79h v*un1lct; dstorrect the frequency? decreased by    %

  One end of a horizonta3k b/orp95 nwtl string is attached to a small-amplitude mechanical 60-Hz vibratk 5/rpwtnob93or. 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 e a i p0;j5a+,q 7-c hyw/jhzr2)zcknlstring may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by v rhnz7k+;2 ywic,/a5 j zech0-j)pq alarying L between 10 cm and 1.5 m?   

  When you slosh the water ba,fs9u*sx lrt 4ck and forth in a tub at just the right frequency, the water alternately rises and falls at each end,9 4 txsu,f*rls remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary within the zcz7km. 0z7f* (baus nEarth between two kinds of mater*m0(z7nf zk z. sbcu7aial. 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 underwate1ryj,odmm74 jr “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crestsr4o j1dm 7jy,m make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer o 0)ano6uq8c lsf cold, dense air. If the sound wave hits the cold air interfacen ulao 8q60)sc at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary between d (x(*npgo2rztwo types of rock at agpxdn*ro(2 (z 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. Ab 1y2 pr5nolehv*g:;g ccording to the user’s manual, the dish has to be pointed in the direction of the satellite, but 1yeron v5pgg *h2:b;l 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 Pacific i.sxu ;i) yj66uh9 7op 2aqbsvOcean. 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 knowl6x;ah. bsiq v 796oiy2usup) jedge 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 constant of t(.3lrrq 3 +xi4u0c3pyk qogp550 kN/m Find the maximum compressionrpx3q +(0 p3it4k3lgu y c.roq 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 belo9+ml8lmt e bk5,ut-n qcn9p2kw, which stretches the net 1.1 m. Assume that the net behaves like a simple spring,t9n2k eu lt q5b,lmc+89mn-kp 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 h7qh gls+m u6*vanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of the oscillat7+mv lh6qgu s*ion?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 mm2,qesff(sw( /s (Fig. 11–54), compressing the spring 5.0 ((fesf2,ms q wm. (a) What is the spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just txk2)hpltqhn5*b tn* lt 6. 3zshe right pace of about 1 step per second, the coffee sloshes more and more until eh 2t3lkz.)nb 5tp lt *n*qs6xhventually 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 thqkp ruvct3mrc6,i1/hd . ; x,te center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be thekvrhdt,.;ccix1pr3,t m/ 6q u frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.6j.b k,q )j)2p)hck yqq50cos7.40t where x is in meters and t. bqq y)ch)q2j,k)kjp in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. What is its frequency if it 3/z qnqx0nxg6bqb3gk( awjo9 q(a51raccelerates at 0.50g (a) b1gx6wq( r(okqb 0a n/9qqg a3x3 n5zjupward,    f
(b) downward?    f

  A 220-kg wooden raft floats 7zt2pqgm ,:sd on a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibra zqp, s:gt7md2tes 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 arx8mv1ki v6lu- ws 0f4ze tuned to play at 392 Hz (G) and 440 Hz (A).6kz81v lx4vw0 umifs-
(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 trave./l)uj1lqg6 1 05f j ejxgopwzling 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 jju16l5 jxq0 gpg fwzl/e o)1.heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates a .1we*lji-y ndsjr 3v-t a frequency of 264 Hz, and the tip of each prong moves 1.8 mm to either side of center. Calcur.3jw iy*ve-jnls1d-late
(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 ofzz flfzr,plr+0 bozh 9q8t bm00d72,o frequency 1.5 cycles per second. What is the maximum amplitude with which the end of tfz l omodz9qh0rbtl p,b+ 0z 87,z2rf0he board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached hlxi4wk:o;0 z to a ring that can slide without friction 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. 4khlz0 x;io :w

  A “seconds” pendulum has a period of exactly 2.000 s — each one-wz4w0x +etyd( yay swing takes 10ewzt+(4xyd y.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 oscillatexhgss - 78o+ov in the vertical direction or can swing as a pendulum of small amplitude, but not both at o78shsgo-+ vxthe 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 tts5 y pqyh(4 ;7vilr+co5 ijp:ension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is+yit :p 75qvlr cp(5;o4yjsh i generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by ayphir p;xj6 t,7,p1nc spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations th;n prt, pyicph,1x6 j7at 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 pgn.4 m1 -xyeathe junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end gm.pnye a-14x of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plat8uef udvb 8.0we as shown in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analo88e fuud0.bvwgy 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