Give some examples of everyday vibrating objects. Wh xco-xs5n7.os he8q8t ich exhibit SHM, at least approxne5-h8qt 8o .7xxssoc imately?

Is the acceleration of a m,*dbbo61 ijj*pcr1a m8b bns;j) kmlxm3 x(0 simple harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approximately simpy hnksv0( pm)3le harmonic.yhp n3 (0vkm)s

Real springs have mass. Will the true period and frequency be larger or smallern7ww gouu k1q .kx--7b than given by the equations for a mass oscillating on the--uk77 nu1. wxgbowk q end of an idealized massless spring? Explain.

How could you double theqide9, 5ghf/t cx4- /iny .kzg maximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and then 1ursge+ gvn2 s*a9 h*nznd.l+lkw .6kis released. Describe the scav nzk .9*dr2g.gl +k6 s+1*esnwhulnale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose time when ta*fvcw: qn)g2-xpexu am:+yf; ken to high alti2p g yf)vw *c-um:nax;x +:fqetude? Why?

A tire swing hanging from a bra1 a :lvt-kq*5b4p 0xbj+/ hilotwiba )nch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch usin w1 bvaaptl0 b/i*)xl4o q+ki-h5t: jbg only a stopwatch?

Why can you make water slosh back and forth in a pan only if you sha 5kw g jse0d(9*f++fnwia0pqq ke the pan at*wei dsff5w kpj9(a n+q+0qg0 a certain frequency?

Give several everydayw-za.q59 c voa q:k2k6 /qvxuy examples of resonance.

Is a rattle in a car ever a resonance pillo 5*hs ot:9henomenon? Explain.

Is the frequency of z (2(pmc0xxqb-djz2kk 1fasp.d2lk7a simple periodic wave equal to the frequency of its source? Whyd 0xpl2.(7z(zax2kq1d2f cbk -p mksj or why not?

Explain the difference between the speed of a transverse wav3hbsy e4df ,sr.zkc7 q2aol+a2 jsl)(e traveling down a cord and tza r e 3,sk)d+qjlo7cas.ly h42(f2sbhe speed of a tiny piece of the cord.

Why do the strings used ju3e+rd784zuo.f4xabh6 i x xmfu/2c for the lowest-frequency notes on a piano normally have wire wrapped aroundr+hmc84beu2 zd.uix6 4o7f ajux /fx3 them?

What kind of waves do you think will travel down a horizontal metal rod j: vmt)br1j)f2 x*dhpif you strike its end (a) vertically from above and (b) hor )*j tmb:f)rpj x12dhvizontally parallel to its length?

Since the density of air decreases with an incre3s. e *xd+ph4qysa+ mgase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect tg4+h*sa e +p. qydsmx3he speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as6n7x 7m;at sqbj111abep7v ru they travel awaa t;q ae 7xmp6bu11b7jn1rs7v y from the source.

Two linear waves have)hi x7 (q;(sp fj:szbh+;zdcy the same amplitude and speed, and otherwise are identical, except one has half the wavelength of the other. Which trxzsi); zdp(s : +qy;h7fjb(chansmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sectinm*3tvc, gli8 kh0+l ions of cord as in Fig. 11–33, the frequency does not change (although the wavelength and veloc 03cihkg*ll8tmnv ,i +ity do change). Explain why.

If a string is vibrating in three segments, are thputc9o3 8nnnea 9,h(rhxs 80o ere any places you could touch xrnt, 9hoo0 9upec 8nns (ha38it with a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incide ,rtayjl t dx57aob5eehk/:c:oj 2 +:pnt and reflected waves cancel at the nodes. Does this mean that energy was destroyed:5o +ajxc t57l ehy:bat:jpd ,ke/2or ? Explain.

If we knew that energy was being transmp m w,byiw46 )2nkl/nbitted from one place to another, how might we deilbm,)k 4w/np yn2wb6termine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, w ;d/gtmpfq04md aqh 8:hat is the total distance ittm0f8g/:qdq;phd4m a travels in one period?    m

  An elastic cord is 65 cm long when a weight of mrf qk7 ru6p fy(8tn+(75 N hangs from it but is 85 cm long when a weight of 180 N hangs from itp6+uyrmk ( 7 ftq(frn8. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm wj tg(so ; 5w*v(rsmq7phen its 68-kg driver gets into the driver’s seat. If the car got(sm go57jp*qwsrv ;(es over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from onr*c v39qm*ah.br9p /ry +jeit. (a) What is the spring stiffness constant c3.qab + rep9rj**vo n9m rhy/$\approx$    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 0g4+e tx *qn4ghlkg4 v4.60 kg is hung from it. What is its freq n+ql44v4 4gx gkgt*ehuency if only 0.38 kg hangs from it?    Hz

Construct a Table in( ej-bk0:x c q*(gey 2uahix1edicating the position x of the mass in Fig. 11–2 at times t = 0,t yke 2e*c- x1x0b hag: iqjeu((= $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 0.2lh 0/wyz2 5fogsiu8 j)5 g is caught in a spider’s web. The web vibrates predominately wiy if5s0wo8g2/ zu)jh lth 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 vibraw7cdq- f1gg-k 4ed,,,y6wne/g dynlp tes with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency isydkl7-1cnew,qw ,6d ny4d-gg/f gpe, 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vikwit.0 vqo nwvm:6 h9,brates 3.0 times per second with an amplitude ofom6t.k h:, i9q vvnw0w 0.13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement fdu6: nrr,6xvo rom equilibrium is the speed of a SHO half the maximum value:xovu 6rr,n6d?$\approx$    A

A mass attached to the end of a spri8i2o sk5dglp7fu pm78h d1(fung is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. In tpaynz7883u d) na82zxw +gwi0uc9tf the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilib+ny08u u83ci9t2 at gdn waw87nzzx)prium position again?    s

  An object with mass 3.0 kg is attached to s0 lpsqasf7x el w/6.5g h4x1ldvl2i6 a spring with spring stiffness constant k = 280 N/m and is executing simple hgp4q6h/alwlsx1.lfv0e6ixs sd 7 5 l2armonic 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 80.0 N to compressc-i jqkzbnzm*c+ l(-* 3w1h od the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed wilwk*lzo3chj+cm(- z i-bq1n* dl the ball leave the gun?    m/s

  A mass sitting on a horizontalz 4*g iigfl c;mlwle0.)9y ;xd, 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 thel4;.gi9wf; y)m0giz ld e*lc x 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 = 0.45cos6.4t where x i) ,50npqy4/rokzwgn;41uc uabz) fe os in meters and t is in seconds. Detc;5pf,zy4) 1g w0b4u) zno k equoran/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 equilp vvde+aw4; cjmy.87h 0fu 1vlibrium is the energy of a SHO half KE and half PE? eypa v18 7 f4;0uclvjh+vm.wd±    A

  If one vibration has 7.0 tifwc.i 9kb p/cz *c4(10gzm , alhk9(fgurop-hmes the energy of a second, but their frequencies and masses are the same, what is the ratio of thp(0o ,9f* m w9cbkck-.r1/p(ch4ifuzzghgla eir amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring onceyzh pz3e w .7:rfts ln-+df+h),sbyv4 every 0.65 3vtzs ) h bd,lnwsf.4f-:z7 +y rpye+hs.
(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 supporteecb(nbi+ (rs 1d by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be thnrics(1 eb+ b(e frequency of vibration?

  A 300-g mass vibrateiibj-vvr;w 5g,zg0 xv 4-hp 0kj-j 7gts according to the equation x = 0.38sin6.5t where x is in meters and t is in seconds. De; r,vx0j0b5j i-gk gjw-7h t-4ivpvzgtermine
(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 a o,/xwmt8;c)cn 5mlk dnd 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+7l nr.eg a-x6ip 4f guv-s7-vq 9azjz end of a horizontal spring (k = 124 N/m) is struck by a hamme6 a nvi.7exl uf j9pa g7v-r4zgz-q-+sr, which gives the mass an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiff n* kkl3gxa43k,oh o5)uz1 hxlness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass pas 5*3,ago l1lz k3h nxuohx)4kkses through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring stiffness constantswin ,fo/g2 33vdwo6zi 8*bhi h $k_1$ 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 advig;olx , aih3c,jwru ,c :wg3.1uq5 0.600-kg block attached to a fixed horizontal spring whose spring stiffness cgv3id.,5iqw gu 3r1x, c;w:l,auojh 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 a high br5 cswtpa g3*a/idge. 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 the bridge. Calculate the spring stiffness constant and 3/ wpacsat5g*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 6x* 8m orrrvn.50 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 snj2e,k 6vhvpp99ib. pwing per second? (That is, one complete vibration takes n2e,.pkvihjpv 96b9 p exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, wh 5ye jn6t5o1ct nv8/hhere the accelejn 5e5tn1yth/vch 68o ration of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm long 5gxl;6l v th:9b5detmir, p(mas y6n /
(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 pez;sz.oi(l.lze r 1ja+auls 39ndulum bob has a mass of 365 grams, and it is relealzslzri93a e+s.jz lo1.(u ; ased 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 lengthpn x5 lni4/qp61btdxo8)n ii: of 0.9930 m. If the clock loses half an/i6n)t41xpxnpi 5ibq: d o8l minute per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum speez5*b;erphgr 1)jkh0xw8.+sn gi z9 hnk( yj t6d $v_{max}$ 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 frequsles2gzvjn9d,fmt:6. o 3 ry 0ency of 2.5 Hz. At it is released from rest sta3df2 tervz0sng6m yj 9ls.:,orting 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 u,d/lct 0p ox8of his anchored boat every 3.0 s. He md/tl pcu0x,8 oeasures the distance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed of 343 m/a3+ ,jjgcaz 1tlhu0 s6 ,+thjjzaa0u3 csl16gs How far apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz andsug f+8e y+9t6au8hrn 1600 kHz (kilohertz) and travel with a speed of9sfg88 eynh6a utr+u+ $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal 7o :yzzo;h,h s-ddr1o 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 twii ns9-tkj0yh: ce as dense as the other. In which rod will thek -t0h9ynsij: speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m 3l)2l t au:4-uggnn gpet u, bi4:xrh6apart. If the tension in the cord is 150 N, how long wilb,nh g2l guit3:6ntp-44xu ) rge alu:l it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to 1tk6 t 5 fc 44wxn5ud7/vflqby0lw6sethe 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 sends a wave pulse along the cable. It is observed that it took 16 s for the pull5b /l u ky6qe74wf 5t6nscvx f4d0t1wse 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 hv *q ey14t/i5 do)1+ (,z vnzpsj.nogqcz1hbh is 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 ocean a1 o+in4ht51d *,onz yh(e/vj.)zp1 gzscqqv bt this point?    m

  P and S waves from an earthquake tra ;3 zqoh3dw9hx)usj v9vel at different speeds, and this difference helps in locat)vs; hujqhw9x39d3zo ing the earthquake “epicenter” (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 a3w+- 1gshqb pt sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplit1 hqp+3swtb-gude 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 (b) the amplitudes, of3dj,a ;xv)ae g(.zfmj an earthquake P wave passing through the Earth and detectfzxg,de)vjaj (3 m. a;ed at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is mea:3ms. xx4fp w9r,yo;/m eomsvmtc 6j7sured to be 7yr3cm wp6mm ;so: jot4xs9 v,x/f.me$ 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 tg7+ oi7l wih7ehrough the same portion of the Earth, but one is carrying twice t7ie 77 ig+ohlwhe energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string ha::q 9 +2inhphvsgb0 nys4t63g gn1ind ve the same frequency, but one transports three timg1qn hpsgi9b4inyhg 6n+:s nt: 0v d32es the power of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed tvgnv()7rds v h5. l)dfo 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 fads lh(df.g vn5 )v7)rvctor does the bug’s maximum KE change?   

The two pulses shown92wj5ivic, * qolj+vy in Fig. 11–52 are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happeno5j9*vlj+v c,2q i yiwed to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundag t,9dk;vxy3zxkp ;4q mental frequency, what are the frequencies of the first four harmonicg zqt;4,xkxv39kpyd;s?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency will it vif+s o snoarh1zqu5 8 6u dr,lgj fwiss:6*,6b7brate if it is fingered one-third of the way down from the end? (That is, only two-6f6 u*:ri16ou,+sln wdssgq ro57ahj bz8f s ,thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz. Name at6am,ry3p bzg8mqpj1 u* p iz9ybz651z least three other frequencies at whichur3y yazjb61 g,689 i*mm51zb ppqpzz it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string 1* je4u;+ll0rck+)j 7t0uyt2tnmmuxuymx; dis 92m/s If the frequency of standing waves is 4;xmlnu+2*00ye t ;x ut dj tur)kjclu+m1y47m75 Hz, how far apart are two adjacent nodes?   m

  If two successive overtones of ;* hdmove(0s()hnq taa vibrating string are 280 Hz and 350 Hz, what is the frequency ofahn)*( o;q hm0st evd( the fundamental?    Hz

  A guitar string is 90 cm long a zdv/g5x-y6q 0xxcyk2b-e 2 ans3 p2,zmgyzw7nd 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 frequencies of the yk xmev,5xys6zzzb2y wq-03pc- g2 n 2/7gadxfundamental and first two overtones?    Hz

  A particular guitar string is supposex )lqtz mn.bsi (2h+o)n.ozj8 d to vibrate at 200 Hz, but it is measured to vib2 qzhs i+zb. tnmo)olj8.(x)nrate at 205 Hz. By what percent 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 string .hc*vgn*daj6 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? .ah* nv j6g*cd decreased by    %

  One end of a horizontal string is attached)4cc z8wcl p,k to a small-amplitude mechanical 60-Hz vibrator. T84l czc wcp),khe string’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be ad a+ qbyz(g ke/nzs xdpm u5sks57qo7 05/hd3w*justed by moving the pulley. If the hanging masn /pquw55z/oy sssxqk h3(5d07dzgkb 7m*ea +s 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 bg)d uow1+j7fbb u *hc-ack and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the +w7) *gfhudc -u bj1obfrequency 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 traveli) hbu2nn p.a wd2d5zj3ng at k.0 km/s strikes a boundary within the Earth between two kinds of material. If it approaches the bob)pj23d5uazn2hw n.d undary 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 velocity changes from 2.hl+p xbib350acnue 6a5g 77gp8 m/s h3 x 0p7geuc6bp aa575b+lignto 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 w5zoad/xk, t: qarm air when it hits a layer of cold, dense air. If the sound wave hits the cold air iqx/5ao:zt, d knterface 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 two types of ro -sd;inv- kq2u5*o oumck at a 38 2 o onmvu5ui;k-s* q-d$^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m in diameter. According tok:b,ch+7lonx)l y 9-yi;lbk i the user’s manual, the dish has ch ok9:b)l;yi 7ll+i -bk ny,xto 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 travels 9wueo; j y,0dnacross the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Appnw,9y0doue ;jroximately 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 bump7cn6j;vfq :e .gv 2ezaer has a spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500ee2.j6f q: vvnz agc;7 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,n,hb 8)ielx0l9 qmu. e which stretches the net 1.1 m. Assume that the net behaves lll h8 qub9) ixnmee0,.ike 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 thew)z fkq ,,gg )ui*qb7xn falls 33 cm befokfqbwugx)* qz ,g),7i re it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), compress jh7rd. 2cgm/zing thrzmj/72chd . ge spring 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 juslq qa6b;3 c;qkqm k-ph6ge)*ot the right pace of about 1 step per second, the;ab p- 3*kho66gq cqqqkel; m) coffee sloshes more and more until eventually 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 thm8 589pa2 *f8u wc -kfix zrq6ia.epgie center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sound em8ir- 9x288mkzuiei c *.pqg6a5f fpa witted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7jn uc6j :9,vswxwq5(8 qb y g,jm;s:k4kr jpy;.40t where x is in meters and t in seconds. Determine w,jqps9x4n;m c8jjb:v6 gjsky;rw5: kyu(,q
(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 frequenc. 6ykokbyub7 id 5z.kon*v ;3iy if it accelerates a*65;ydkzi ov3bukyobk n i7..t 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man standsqjsju+0b a;jzz7 +s(qw2mf;k on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for a while.zwqsz;m0q;fbu 7 a2jkj +s j+(
(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 tuneb yy;v jvz:c/ras1 9(gd to play at 392 Hz (G) and 440 Hz (A).v rv:cy (j1gab y9s/z;
(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 two8c rt;w:bvtd *; ked.o-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 sect bwtrc.;e 8t kd*:do;vions. (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 1x-wh) lu4 ejkat a frequency of 264 Hz, and the tip of each prong moves ekwuh jxl4)1-1.8 mm to either side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of frequency wbk78 m+xbef: 1.5 cycles per second. What is th :mekwx 7bf8+be 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 with the board during the oscillation?

A string can have a “free” end if that end ijuo)k1f 2 8faca)yl,z s attached 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 anfacz)a,1jo2y l )8kufd the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swinw:q +u0 7 emcwou-y/ruoz,bs 2g takes 1.:c uzmw+oy-u0r ,e 2w7q/obu s000 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 directionrqmqq gzt6x8:fa. xx b:h17u 6 or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontala:.xum6tqqx 6q b1r:fhxg 7z8 swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched under a tension of 255 N. A pulsefb. )wsx)z1fs is generated at one end, and .s x)bf) zfw1s20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with spd50mhll o2g.nr2eau( ring stiffness constant k. A penny of mass m is placed on top of the h0uam5nor d2(.ll2geblock. 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 au07zx6gttn1 g 1200-kg car at the 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 of the cable. 17t z0g t6nxugWhat is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate asycci to3ssrb2l+ av0nzq2kl,l roews0(5. )/ 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 jelw+3(ql vkribe5,l2. osn0ycszst oa)0r2c/ llo springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz