Give some examples of everyday vibrat, a8hkjrj4 xk.ing objects. Which exhibit SHM, at least approximatel4j. r8xkkh ,ajy?

Is the acceleration of a simple harmonic oscillator ever zers*)bc 2phxv4fog*rnp9ra4x )o? If so, where?

Explain why the motion of a piston in an automobilea6g2a1niea3o (gldh7 p5k;( c s5xrdb engine is approximately simple harm(5 1r3a5d g x6 2sca p;(nkbaoigd7ehlonic.

Real springs have mass. Will the true period and frequency be largerrlc 0 s,bh1ig( or smaller than given by the equations for a mass oscillating on the eng0 l ,csihb1r(d of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillator (SHO)? 2 bfk2b7s6fdo

A 5.0-kg trout is attached to the hook of a vertical t gqdh2f; 6vrh ;gj0ji4kf5*fspring scale, and then is released. Describe the scale reading ash; ;0v djffkg*hi q625f4r tjg a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose time when tab ;.4h j2u b0 304pph.wgqgsef5kuc spken to hje4;k 0gpus3 qb us g0phh2 fw5.4bpc.igh altitude? Why?

A tire swing hanging from a branch reaches nearly vzq6kllug f-, gwzgo --8a.khg0a3o) to the ground (Fig. 11–48). How could you estimate the height of the branchw-6 kz k.g,ug gq ozl3-a 0v-)f8hglao using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake the pan a/:vpibay e v o3/2b.tdt a certain frdyi 2tpoa :.v/ /bvbe3equency?

Give several everyday examples of reso6 s 4m7h2 .yuwm(dywutnance.

Is a rattle in a car cm9k9 k4 0p+xvcm5eoz ever a resonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency orm mz 1v+ glx 8,h;ac5yr6xtmh)a -ul/f its source? W+avlmh51 rlth6;/x8uc-r m, z)xa gmyhy or why not?

Explain the difference between the spe,mgvg2k7,(wjd2zv9; kn z efd ed of a transverse wave traveling down a cord and the speed of a tiny piece ,knzzf d(gev kj,2vdwg m9;72 of the cord.

Why do the strings used wbfk ntn :s2jb 6jiml(1qj;6)for the lowest-frequency notes on a piano normally have wire wraps jlb6(ij)k t;nfjm n61:wb 2qped around them?

What kind of waves do you think will trl38cl mb, 8mm1(eopdbavel down a horizontal metal rod if you strike its en,cpobb m edl3ml (88m1d (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperaturd4f ofzy) rx7pr)a, ire7 mk**e, but the bulk modulus B is nearly independent of temperature,*m7fpr ,eiy)xf4orr)d azk *7 how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decr-sk 2wm5u 0bz e42ssouease in amplitude as they travel away f2essum- kz0 254 ubwsorom the source.

Two linear waves have the same amplitude and + rxh2 8ekc fd,n)(x2vyjlzm8speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits more energy? By what factlr kzjcnmf8dx+)y8 , 2e (hv2xor?

When a sinusoidal wavq- y9ps8/i e+fzeqaf;f(smh;e crosses the boundary between two sections of cord as in Fig. 11–33, the frequency does notfa9f(-h/;+q zeeisp sy8; fmq change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segmem 9eicuk/ l 9xjxu5//ints, are there any places you could touch it witk i 5/lx/ce/umi9x9ujh a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of inc4: zdjj*ysj l-p/wo83k w 7ktoident and reflected waves canclwyz/*k d3tpoj:o s-jk47w8 j el at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was beva//nrv7loxfhak 9 1 ;ing transmitted from one place to another, how might we determine whether the energy was being carried by particles (material bodies) or by waves? n laxo1;a9/hv/rk 7vf

  If a particle undergoes SHM with amplitude 0.1x ps /w293voaq54mno4 tra1am8 m, what is the total distance itvt5 oaxwqa234nos m19 rp/m4 a travels in one period?    m

  An elastic cord is 654hxujsb f, mp2)i27u g cm long when a weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is theu ,7u2)4xfmjgh p2sib “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg c/ 3 6mnqlijdd.ar compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes ovm id/jqldn6. 3er a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fismxv trd l8-l mb63 upv46n:3wnh hangs from it. (a) What itmuml 3643:8pwx-6lvrvn bdn s the spring stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a m -,q e1zbpk,lkass of 0.60 kg is hung from it. What is its frequency if only 0.3kq1ep bl,z k,-8 kg hangs from it?    Hz

Construct a Table indicating the positioh,/ gy a )hzdck.:tgw.n x of the mass in Fig. 11–2 at times t .ygc,hhkg. wad)tz/ := 0,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s w 1ld8 pbuekuas(1+iv2eb. The web vibrates predominately with a frequency 2edu(pli8s b +k1va1uof 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency of 0.88 Hz. When an zkz(qxz1 zn.,x, tf0padditional 680-g mass is added to m, the frequency is 0.60 Hz.kxzz 0(p qnz, ,xzf1t. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibratessq1xj.(x*gf)exr)h6 ic aue 5 3.0 times per second with an ampl hsf. iu*5 qx)1recjaex)6 (xgitude of 0.13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibriu m v,:kq a:k9 qi.axjfot1ckbpy)x4d68x:i +o m is the speed of a SHO half the maximum valcfky+ix.m xko6vip9:1)ak xq:bd8,oq:j4 t aue?$\approx$    A

A mass attached to the end of a sprin0-x r/y1 x:aarrfd m+ng 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 spri q.2k +93c ketmy4revwng 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium position agk+m94 q.ce vyrwe2k 3tain?    s

  An object with mass 3.0 kg is attached to a spring with kz6i4rspl:t*vt 0- aqrd1c7aspring 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 moving wi-k7a aqzr ci6srdpl4t:1 *0tv th 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 c3b,7 *owou g,s mvixx.icsxig/ t*1 ;gompress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With whag/og uti7xcw,3,* xv og;s i1ib*xm. st speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one end of s3x7rl15 g)n ogt +lqxa spring; the other end is fixed to a wall. 3.0 J of w)+ 5n tg1 x7xqrg3llsoork 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 the equation x = 0.45cos6,-p:jk rs . t1n 2blt es62uzzl1y1nos.4t where x is in meters and t is in se1lyns ,kjo t6z e.bns t2-2s1:rzpu1lconds. 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 equilibrium is the energy of a Sp z p0ln: mv1ek jb0fw+d40zh(HO half KE and half PE?p wk b (1nf4pv0+mzz hd0:jle0 ±    A

  If one vibration has 7. lrx6c),5o m 0dp7cqzh0 times the energy of a second, but their frequencies and masses are the same, what is the ratio of the5 pc0,r 6hcodmq7z)xlir amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hangixym*l 9q3n:ll q.gilb g.( o6kng light spring once every 0.65 s.k.q3l:ly nog9ql(mbx6g.li *
(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 suz43 dcx)/)6ptnp8ip5;a oypumu q x q(pported by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of v pynu5 cpp da(tq)xq/u 836i4o px)m;zibration?

  A 300-g mass vibrates acaxeg:vy5:3r x cording to the equation x = 0.38sin6.5t where x is in meters and t is in sec5:xgy3:avxre onds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and B. For ea 93q1,sy r+t1aov n1g0cybffach, 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 = 124 N/m) is strbl5;yrm43;9v6 fufc4wx2w0i i r ak diuck by a hammer, which gives the mass anfi4va miw ;firw23l;6ydb4rxk 09cu5 initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305 N/m vibra7 azze1bd;xi;i,,iqxc q7)psp0k 1 f ates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass pass, af7 i;k)qi ebx0zx7c iq1;pd zp1a,ses 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.cm7qvsoz*cy)lf : d6 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 0.600-kg block attached to a4cmnump)trll c0* 2; x fixed horizontal spring whose spring stif) c*;p r2tucl0nmmx4lfness 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 bridge. After gxdpk wy7 vu n.;*k9a/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 beka*vxwkpd7/yn;.u9 g low the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 60 s. Whagfs2u ;vdt*o+ t is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swing pww*du uc hq7z.x0,-a mer second? (That is, one complete vibrath.ux ,wqmua0w7-z *c dion takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on v u g*bhjb)m.3c6qd3 xhgyzb;we:1y )Mars, where the accey3weg u xmbb) yjg6b:d z)1.vh*q3;hcleration of gravity is about 0.37 that on Earth?    s

  What is the period of a simpl +e cit3,(po -c hxc*4rrtdta)e pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760-.u.. +nqxdc2+mbcd5 7nc5 pjdrg lin m, the pendulum bob has a mass of 365 grams, and it is c 2c.+pi7bng5 cq+5umdld dx-. n.rnj 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 0.9930 m. If the clock lol,oj -lz g -we qe:85wml7afx o;d03clndr7o.ses half a minute per day, how should you adjust the length of the pendulum? d-go-7rewx7 z.mqlc,olf0 3 o8lnw:5el ;jadshortened by    mm.

Derive a formula for the maximum s thlx*c2k y-7speed $v_{max}$ 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 fr0q 04sycx46 sv uyvov;equency of 2.5 Hz. At it is released from re4vxy6yu 4qvss 00v co;st starting at an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass thej5q6o hntc65w bow of his anchored boat every 3.0 s. He measu qn6t6h5jo 5cwres 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 sr l qln*)14* vhgoo/jfrequency of 262 Hz and travels with a speed of 343 m/s How far apart are the wave crests (compressions)? rs4v*1jgn*qo o )hl/l    m

  (a) AM radio signals jkf*s6p ,5vcrxd; 53hma7mkok 5 i6tfhave frequencies between 550 kHz and 1600 kHz (kilohertz) and travel with a s kt;5fk7*5kif6vxmsmr5d3 ,a hpc6 ojpeed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal ma 8y7qt,o/hjj/ht .b waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, butgzc6zy jvq 9 x6m28m/k one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, and by whagczzqvk6x9 m62 mj8/y t factor?   

  A cord of mass 0.65 kg is stretched between two supportd2txyl(o8wg5 rhl + v5i2n ej1s 28 m apart. If the tension in the cord is 150 N, how long will it take a 5x 2l(vy8 12hgnt5iowrjel+dpulse to travel from one support to the other?    s

  A ski gondola is conneca5wa 4gt 9dsd/ted to the 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 termig waas94tdd /5nal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his +6t5lwhib v9fship just below the surface of the sea. He hears the echo of the wave reflected from the oceai5btfvl wh9+6n 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 speeds4ynm .x7g 0a, j0sr 5bjvlxy1y, and this difference helps in locating the earthquake “epicenterlr g v4mn50xby1x7j 0j.ysa,y ” (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 sinusoidal0d6zqvyjhuc 7jw9l r.t-o 8z. transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the accelljh9.o8d07t .rzyu -w6z v jqceration a>g]    m

  What is the ratio of (a) the intensities, and (b) tq,jra/(/ :qwjg,n czrhe amplitudes, of an earthquake P wave passing through the Earth and detected atc /rqn( wjz :g,rj,a/q two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave ;+ls:t-d qd/ph az0 podcz1p(passing through the Earth is measured to be /tp o+0pd chq(als- dp:; dz1z$ 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 portionj 5fm)if,tkwt-13*txxn 8a z.xrg5 e j of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of - 5jjxtai3f twx,ze.r *1xng5kmf8)t the two waves?   

  Two waves traveling along a stretched string have the sam,yn*engxf0d bemj,r la r 4/lw4,-)nne frequency, but one transports three times the power of the other. What is the ratio of the amplitudes of tj4-l,d e fbgm nynn ,xrnl/0r*w)4,e ahe two waves?   

  A bug on the surface of a pond is observed to move up and down a total vertical d:)xerpd6xiz86 ec (r dis6 e6xrec) px(:d rzdi8tance 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 movi f t-;hv.li k)/.ox29jxmrmp ing 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 mo)j xpto9rxv; -/ k.mih.fi ml2ment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at (3h 3zyhqzpk 78gqy: k440 Hz as its fundamental frequency, what are the frequencies of the first f( k:8h q g37zhykpqy3zour harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unf5.2l7m mlta)0uetq2h 6 cpke oingered. At what frequency will it vibrate if it is finghu)5cq7o k6em llt22 .0mpte aered 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 ouqldcc60bm1st2w6 u lt5llr*q6n 9 8df 280 Hz. Name at least three other frequencies at which isq16lnw89 trul5utcmq*0 c dl2b 66dlt 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 staaz h.:jv) g.rsnding waves is 475 Hz, how far apart are two as .rav .):jhzgdjacent nodes?   m

  If two successive overtones ofm:v7eqec76b f 4 bu8aub+,p cbh zikh6gg1t)8 a vibrating string are 280 Hz and 350 Hz, what is the frequency of the fundame6ufac i g): pt 1vg,h7e8 8ebcz7m6+ buk4qbhbntal?    Hz

  A guitar string is 90 cm szrn 26/5xmjj( jo *wolong and 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 tensioo*2 ( jmswrj6nxj /5zon of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 3td4 2qbrw *(uxuit4n fcb2g+Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequ24ft g4u(+w c2 *bqti3 xrbdnuencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it is meab7mn; ya +oh)6gi2xhasured to vibrate at 205 Hz. By what percent should the tension in the string be changedx i7y2a+b;6hoam g)hn to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-d ; (d4ee1oa7ucmwz 2kamplitude mechanical 60-Hz vibrator. The strinakz1edw4 7du2(oe c;m g’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 oaw ;n ()pof3:k: n uccht1/uuadjusted 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 varying L between 10 fp nn(:h;ck/ouwu:o u3ta1 )ccm and 1.5 m?   

  When you slosh the water wxr(;(ubm8 otback and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relaxubmtw( o( r8;tively 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 m qt1-z7fcjj i.,k.flcb- ,meat k.0 km/s strikes a boundary within the Earth between two kinds of material. If it approaches the boundak7fecl mb .icjtq-- zf.,m,j1ry 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 velocihx b21am02((6w m rwkeyzh cj5ty changes from 2.8 m/s to 2.1 m/s If the incident (w61w5cxyrm k a0ezb2j hhm2 (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 otyf5 l kykb9s +ep)hcy(z/)(hits a layer of cold, dense air. If the sound wave hit )c)yos(h p lfbyk5t/ek9y (+zs the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikesy(jr yg)mt9yxca5-)mq 1rl,+1o xv 0lz jw,nb a boundary between two types of rock at a 38 jwygbmx)yl,(oqy)rta zn xc+51-j r01v 9 m,l $^{\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 diametejwrxyx)ux*bg v:8s: 5. as fy4r. According to the user’s manual, the dish has to be poins5* gyxyu x )jfxwvr4a.b8::sted 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 750yk0ug bh b,wr,;uy6 esn2t; *n km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In by,0g s*ue6ntunhrw;b,; 2k ythe 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 bup nj2qebcr gk*x42yg-y qiba/ ;.8w2xmper has a spring stiffness constant of 550 kN/m Find thg exacyix24wk p- 2;qj*gn8rqbby/.2e maximum compression 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, whiceh )kxg2f; zs0 kb9+ad/db9cwh stretches the net 1.1 m. Assume that the net behaves like a simple spbbx/d s9)khg kcwa fze2+90d;ring, 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 sprin mo*h;h(alomrr 834fy g. The mass then falls 33 cm before it stops and begins to rise. Whatlrf hmy 3o(a ;r4m8oh* is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11lqc;2md8)9 lkoaq4 ng–54), compressing the spring 5.0 m. (a) What is the sprin 9ad;8c qmglk2qo4l)ng 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 jk* nf5r1jto(pjhy,u .ust the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill ovk o5y(h1nj ptufj,.*rer 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 3ydymx t38pw ;wo 3p:b:3-rpm phonograph record have a wavep3bowmp8ydx:;w t: 3ylength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x is in51 h+gv+s-/vp qh bm sjss/6tm meters and t in secon bpssg/ vv6+ shm/h-j1 t5q+msds. 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 wi+ )cawf7e 78 m v u7zb)8i.eov 0nlddanr+loy9th frequency f. What is its frequency if it accelerates at viearo))z n 8bf978uen7l.w7lc m yoad ++ d0v0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. W jx1h66hg0qx hl-.um(c xhxb 5hen a 75-kg man stands on the raft, it sixb 6hlxq.5cm 6hgh1( u0 xj-hxnks 4.0 cm deeper into the water. When he steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical inst0a5v+ xqtdzb4 rument are tuned to play at 392 Hz (G) and 440 Hz (A). bv4+d50zatx q
(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 strajgjd c lgzru)8n5418 etched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of ua4z8lndrg85j c) 1gjthe 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 same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, a8rkh: 9dj9h3pu .vj0ktbd 8c ind the tip of each prong moves 1.8 mm to either side o:r3hd 98c .k0 tkdvj9 ubjp8hif 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 simpleenmpe ft qf)/,ki-bv s,n s15zhw8p53 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 lose contact with the board d),mf1i5wb5s/e-spn3 ntqzh ,f v 8 pekuring the oscillation?

A string can have a “free” end if that end is attached to a ring tha; ak ev4cksx68t can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with onea ek;c4vksx68 end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.8 pv y48;k o:*- hrbsnoaaa7ws000 s — each one-way swing takes 1.sbahv;nw8a8 kya-7r: soo4 *p 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 springehl0:jke / uo gfy7*5e can oscillate in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations:5e7 0ghu jky *efl/eo 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 st4 biaee3b8dxou*ha215.l zi w retched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms d4bze1w8x ub2la3ho iiea5 *. 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 sprinn w1 (2au -xax i;qasbwz1ii59g stiffness coni bxnsqaz ix;waa 19w-2 (5i1ustant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel pz*if l+-t04a ndh1 bqcrane cable is 22 m long and has a diameter of 6.h1fqtd+nz p - 4ila*0b4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shotlpnphw -7w5h3yj8 0;vfz u+gwn in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, an vt0 ;+3uhfj758pgly h- wpzwnd then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz