Give some examples of everyday vibrating objects. Which exhibit SHM, ap.5he d7spw af)lsm4 /y 7j*kut least approximfhw)75j spdka* /s.7y p4lemuately?

Is the acceleration of a simple harmonic oscillator ever zero? /whx6)ipwo1ol2ch f)d s2 0i eIf so, where?

Explain why the motion of a piston in an automobile engine is app2.2 j i/ yk s aknc2e1zs*h7fa5l6gtdnroximately simple hard .s6a5j2g ikf2yeshkc71ann/ l*z t2monic.

Real springs have mass. Will the true period and freqro6uc0kyar mau) l7za5b-6q:gep + 3yuency be larger or smaller than given by the equations for a mass oscillating on ther y37 b5qp+ g6zmul-6uca: e)kaoay0r end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscift,ezz76)hkio esg8 c) cw-h9 llator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, jt0x6,c iuu:ms7zhb 7and then is releasexj 60u:itc7s b7z, muhd. Describe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose time when t7b)x o11pyl ;p6s7pk dt(whd dtio v1*aken to hhpod bl1)w* p1dido7kt7yv1st x;( p 6igh altitude? Why?

A tire swing hanging from a branch reacheslaitd;nh* 3 ne3 cs07r nearly to the ground (Fig. 11–48). How could you estimate the height of the branch using only a stopler0 73t 3in; acs*hdnwatch?

Why can you make water slosh back and forth in a pan only if you s98 wz4:hmoodchake the pan at a certd :o9 z8wmho4cain frequency?

Give several everyday examples of kswfag a::) (e3j ylx:tisy920e 7xxlresonance.

Is a rattle in a car eveiv4i n10fw 6lzr a resonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of its sourcea,f.+cut7y( e/na ( j-ibgio5:zxz wx,p 0rsp?0o zy,jxnax5 z+ g.b( /:7ifica,e upwt (s-rp Why or why not?

Explain the difference between the speed of a transverse wave traveling down ab;;2 q vv6hh8cmw*.;.3l aaymudxkx d cord and the speed ofv8mhxa;ldv k;*3.b;26qa d x.m ywch u a tiny piece of the cord.

Why do the strings used for the lowest-wvx18g+ktv7. bvfr rs:r gz:7 frequency notes on a piano normally have wire wrappt vv7:8+ g wbxvr1frrg:7.k zsed around them?

What kind of waves do you think h61l: ndznw g.will travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally d1 6lwn:z.h ngparallel to its length?

Since the density of air decreases with an increase in temperature, but the b4)mastu4f2 g9/omw i nxh3 fhe47asyf8g8m(w ulk modulus B is nearly independent of temperature, how would you expect the speea893)n4 t/2xf sowg hw(4a hmu84yifmmgf s7ed of sound waves in air to vary with temperature?

Give two reasons why circular water waves lap-2y uwto7)d6 nyvq,ed*e.8 *sl12cxsw zr decrease in amplitude as they travel awa2prsl1* n.dqst7 de8z * ,cl yv-2uawy6)owe xy from the source.

Two linear waves have the same amplitudec 6s/d.la3r( aa n gvyg6l6(sk and speed, and otherwise are identical, except one has halac( asnlrv 6a /gk(s3 g6y6dl.f the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two secp/1ll,n3hbf ipk1y.01qnnc -kizl (htions of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocihb,y1 plzp lqkl nc.-(f /h3iin 0kn11ty do change). Explain why.

If a string is vibrating infuawe fnpo3+m w o 2;e7hrd85+ three segments, are there any places you could touch it with a kn7 3 o;duarfwmhe2pfe8+w5no+ife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incidentfkoj-oyx rb dkd6 3wjz*s5t,6 0o /w8h and reflected waves cancel at the nodes. Doeyjok6o*st0h wofx-r w3j d6zkd/8 b,5s this mean that energy was destroyed? Explain.

If we knew that energy was being transmiry ki-yy-nbl88 ao-o 2tted from one place to another, how might we determine whether the energy was bei--o krybniya l8 o-28yng carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with am8 v0ag bc mm+uyp:*h zs+cj:.eplitude 0.18 m, what is the total distance it trgs mch+v0 eu :zmy.cj8b*p+:aavels in one period?    m

  An elastic cord is 65 cm long when a weigap.cv s5s * qeg* rojh8,8sws;ht of 75 N hangs from it but is 85 cm long when.res*p ss,c;8h* oga85wvsjq 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 its 68-kg d7/9e b8yl.: qqcpwsny river gets into the driver’s seat. If the car goes over a bump, what will be the frequsb/ q7. pl 9e8cwq:ynyency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (a) Wc6 qif, kty58khat is the spring st, 6qtfc8kiy5k iffness 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 vibra:v (utmh +5yhv 4etbavg( *uc:tes with a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 vtyugh(c*ev:auv: htm+4 b5(kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11– qx3nn7 auibcxh;;j+ *crg*8 w2 at times t iu jb*3c7ach ngn+q 8;;xw rx*= 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 caqocgu)jve.-/l:s xu;ou ec(,ught in a spider’s web. The web vibrates predominate,/-u) u:qe ugo l;x.c vsc(ejoly with a frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency of s4 uc xs wxlq)//i7e(w0.88 Hz. When an additional 680-g mass i//slw7 4wex)iu cxq(s s added to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end o7b2qi 7jp( h5td.lmgkf a spring vibrates 3.0 times per second with an amplitude of 0.13 mj.ig727hpl bm5qd kt(. 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 ur6nn-:.q9q dw 77kevwse/ zca SHO half the maximum value?9-: en 7kserqz/cnduqv6.7w w $\approx$    A

A mass attached to the end of a spring is stretched a kqt7pkt*x/ (;(xjb f+xxw0awdistance $x_0$ 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 stretche(u-x abm3tp0b:o t x-ds a vertical spring 0.315 m. If the spring is stretched an additional 0.130 m and released,bt o:0(txupax-d-m3 b 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 sth dcc18)d1suuiffness constan1h u1c 8dcud)st k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/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 80.0f gc7u)6p: xch 3ec2ek N to compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what sh 2kceg )xc:ef63c7p upeed will the ball leave the gun?    m/s

  A mass sitting on a horizontao;5/bbv kxc z*8tl-6jwh ;jill, 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 6hl- jv85cl; k*i;xzjtb wb/othe 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 the equation x = 0but a+s6aw-ib.cx p3fb( k9d7.45cos6.4t where x is in mep 3ak+ (a7ubdbws6b ic-x 9ft.ters and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibro+ae vtg.8)xbh0 j (h;uzg cq:ium is the energy of a SHO half KE and half PE? ± gxqchog ;h t0j.8: bau)zv+(e   A

  If one vibration has 7.0 times the energy of a second, but their frequen/1x 3qe2sw0y ev3(dh4kqx e qycies and masses are the same,wxq0q kv e hx32(y1yd/s q3e4e what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light ( -r96axlf (p,if kn(f vfdyq i5*v7cwspring once every 0.65 s. 9ly6iwq-5*v( na(7f fi(fpdk fx c,rv
(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 supportedd6l4 xih38ajk by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of v 3dlh 4kxij6a8ibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x is ip/rk.m2 xixa:0kox x/n meters and t is in secokxopxxm : 02k// rai.xnds. 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 tc nvpx-thy 30;wo examples of SHM, labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a hn we:w,74nj wporizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initi: ewnj4,7 pwnwal 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 305 N y*+n:z2x fsk3 ytag:uoj; ,jh/m vibrates with an amplitude of 28.0 cm when 0y*;gjnojy2 x3z+t:hs, kua f :.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connecte4gy gn79niy.ud to two springs, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.6joq i*,9sl6wz00-kg block attached to a fixed horizontal spring whose spring stifszi,ow*lj6 9q fness 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 fromgjkz9y(pq g5t/. ,t3ae whvh) a high bridge. After reaching 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 )eg3/.wq9,k tztp5jy ah g(vhthe 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 ,0bd6 zdul3livibrations in 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 pe 97ik:7 v2hwr * jr8wqt0tnhcar second? (That is, one complete vibratk wt jv7c9a8h:qw2t n0rh7ir *ion takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is itsg,2.(j5b ps2ay kqe ok period on Mars, where the acceleration of gravity is about 0. j (qk,yeo2sa 2p.b5kg37 that on Earth?    s

  What is the period of a simple pendulum 80 u fsida tr rnee)c/3.e;93n0vcm 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 2cjuw -ngrdp : +jac;q2e29 xrbob has a mass of 365 grams, and9wdp2u2ner2:+ ag - cr;qcjxj it is released at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9+ .iqa;berg- f2 o6dlg930 m. If the clock loses half a minute per day,qorie b -a6g;l2fgd.+ how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maxzdlnkt,t7 2:9vw qab9qf 1c:a imum 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 oscic 2ara rw+*w;jllates at a frequency of 2.5 Hz. At it is released from rest starting at an 2j ar*a+;w wcrangle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchored by, g2+z t lrsp0i7+wsqoat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the waves traveling?g +p+si,lyt2zrwq s70    m/s

  A sound wave in air has a frequency of 262 Hz andv ojrily/qchm6). ns;x u.81 a travels with a speed of 343 m/s How far ap8 ijla6h).r1qvx;y/monu c s .art are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilohertza m -x0i9ajuc; m1-lzy) andai;yx-ml-u0cm9j za 1 travel 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 ofd9*4- r5to(drkvvux p: u7ijn vs.x;e longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one issw;,ez,- yja(f e9nl/h lxk,i twice as dense as the other. In which rod will the-h/es,k(l; nyf,z w,jxi9ela speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg ipe9m : vqqekejj (bd8d915tk0s stretched between two supports 28 m apart. If the tension in the cord is 150 N, how le:m95vddpjkb 1k98j(e0qq e tong will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a stedhsq 9ogfvh, b;0(wg.i l6*wuel 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 along the cable. It is observed that it toig(;d q* slh6f vobw9g0w.uh, ok 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the surface of t48:mda.bchxz he sea. He hears the echo of the wave reflected fmxb cza d8.h:4rom 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 spe/lgcd. rv 2(jy4zzuluo l1 9w3eds, and this difference helps in locating the earthquake “epicenter” (whe9wljcv/u.32y gz(ld loz4u 1rre 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 anxu4o;h 4wi ela l+t/ q,d8;gu7gyd7 x sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objeculoy7ue4qt;d7xdx+;i48g l /nw gha, ts begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of sv.a8c5b 3nbs(a) the intensities, and (b) the amplitudes, of an earthquake P wave passing through the Eartvbc 8. s3b5sanh and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an ea 30lu:uue*2fyd re*vf rthquake wave passing through the Earth is measured to be fvy3rd2u e** u0f: ule$ 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 th wmon-+0mm,szrough the same portion of the Earth, but one - msmzwo0,+nmis carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string hav 2mfokzq q(nl/j 0a)l1a/ (dwoe the same frequency, but one transports three times the power of the other. What is the rationq1wf)qdo/k a l(2/zjol0m(a of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to n-/uac/kj j; zp 1gss:move up and down a total 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 maximu kz1s/;cajgpn :/jus-m KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) Sk4q:e10 rdyk)nc emh:3yz b9 pgetch 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. c pg e4kmh bz:qy9)3e:nyrd0 111–36a, 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 are c7 wuqhc4j 4y nyz.xtf:161xn the frequencies of t1c fu:yx.q x7tnj4zyhn64 c1 whe 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 frequencwz.h: tubw*a 0y will it vibrate if it is finger th z:w0au.*wbed one-third of the way 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 of 280 Hz. N,3d 9tlx uimnyb id+1)ame at least three other frequencies a tli d9y31ubm)i +,xdnt 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 standing waveyf sac 2ft45kyx /tjyp8u(l772 aboc( s is 475 Hz, how far apart are two cl a2ftyb7c 42(xk(7ytpf a8j/ysu o5adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, what is4q564yrlkh 9k( vk7gmakwo.hpwqh51 the (4hhy5rkkoqwg6 4 kphv71q95a mlk.w frequency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mas:trqj4 nu q79vvtkj) 5s 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 funtt47rnj vq9qv) j5:ukdamental and first two overtones?    Hz

  A particular guitar string ispzd7 ablcap0.4 b-2o k supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what pod b74 l0b -p2pkz.acaercent should 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 strie;cwvx/fpnqm(u j9. xm,v 2i7ng is supposed 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? qp2v,/j vimxw7x. mc9n;u (ef decreased by    %

  One end of a horizontal string is attached to a small-amplitude mechanicalbldfef3ej+jp;k; w6jvwy -;b, +x6yw 8la ih4 60-Hz vibrator. The string’s mass per unit length is wljb;vfb 3+ae iw,4f8e j l6+w-yh;yj xdp;k6$3.9 \times10^{ -4}$ 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 mo1hadyrnd0 4l1b (hdwga7 h1 v;of.wg1ving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be ach 7 (1v. rbgh1ywdf1nah1w4a hl;0go ddieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the rp ,s:.c/gng2-36t 9*cej5 rlj dxak xy8jeatw ight frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. xj n,lettxjjgca9 ey c2s8rgpd5 *6-3k.a:/ wSuppose 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 13 :, angu,tw6hr8t7obc io qza boundary within the Earth between two kinds of material. If it approaches the boundarhqto3,1r 8inzu,cob67: a twgy 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 2vki9 qlfp 8d/velocity changes from 2.8 m/fk/qpdvil2 9 8s to 2.1 m/s If the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layc6+8 kf x t9:zkif; qikl00acjer of cold, dense air. If the sound wave hits the cold air09i ci6jx+f:za 08ktlk qfc;k 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 earthquakaqhu )bp*h9 0de wave strikes a boundary between two types of rock at a 38 h0pq dub a)*9h$^{\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 diamete5j0wwdf c.x /ar. According to the user’s manual, the dish h.fxd 50ww/ jcaas to be pointed 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 bg-of4f rpj* a9vd8k1travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximatel4* 9 jfakodg -br8fpv1y 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 conb: s 8cc+2lhqtmu9-al stant of 550 kN/m Find the maximum coclh+uqm 9 bal28:tsc-mpression 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 stvuyx7hy 8k. z+retches the net 1.1 m. Assume that the net8h. yuyzv7+xk 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 thzcl ;0bp qkcrr;)e.,c9our ( x1hnv,re end of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequen.zvbkrlc one0q;,( ;)r up r1c ,xrh9ccy of the oscillation?    Hz

  A 950-kg car strikes a huge oylwu8m9/yw- spring at a speed of 22 m/s (Fig. 11–54), compressing the spri-uwyw8l/ym 9o ng 5.0 m. (a) What is the spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just the right pace of/dgs phzp3tn8kpmb2 ** s/1jb about 1 step per second, the coffee sloshes more and more until eventually it starts to sn2 *kh/1zj8d *bs/tpmps 3p gbpill 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 center of a 33-rpm phonograph rg.1 /oi nzjywu;pa(4lecord have a wavelength of 1.70 mm. What will be the frequency of the sou.ap/jnyo w; z(u14i glnd emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t wheh/(jmw+. 9mkd (iovvwre x is in m(j (vwwm/+k hvi 9od.meters 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 is its frequency if f ngp*cj4x 7j1it accelerates at 0.50g (nf pj*17cgx4j a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raft, it ue 5hebnn ferp0n)+w;3.3yul sinks 4.0 cm deeper into the water. When he steps of0n3w.b ) f rhyn3+ue5elpuen;f, 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 3928y hqsz(*dre/m9z oq, Hz (G) and 440 Hz (Arz9*sd8moq, eh yqz/().
(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 - ndorg8;+ :n7pekn xxtraveling down the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the samee:xrpx8d7+gnn ; ok-n 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 eacjrk 6hsh1m:9dh prong moves 1.8 mm to either sd 69 1rsm:jkhhide 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 simpl (+j3:l7c9lc zd zkeoge harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not loskj z cdo (eg7c+:l39zle contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a ring that can slideji1cs6 h(r0jvr*n* e4b emj g/ without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of sucgjmb0**cvejj r en4r h i1s(6/h a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly k* gt 67qi5yxe:ss.tas4k *n 8gdt(cxvoo, g 72.000 s — each one-way swing takes k7a5 .d* 8qggsx7s6(io,n*tv:ykesc x t4got1.000 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 oscillat-bafyduw ty/c7iv ,6uy h8-.je in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one isi7- 6jb.,/dfyhtvu8w-a yuyc 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 underqg8fiw 9gs) yx,xwr3;3c3 a rz a tension of 255 N. A pulse is generated at one end, a yr333)ggx,sz w;qai9 rwx 8fcnd 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:9 c dz-chhh)m suspended from a ceiling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the bld-zhhcmh c):9 ock. 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 cabot-ecfof8- ew /eg ,n(le is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refege-n c,o/t-e(ofwf8er to Table 9–1.]    s

  A block of jello rests on a plate as show gh9.iq /:qajgxkr)cl** bh)nn 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 xan.b)gr/h*icg k: hqq)9jl*begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz