Give some examples of everyday vibrating objects. Whitsg44fy8z7p;rec+(4 7cx wss 6ck3vi ge*sp a ch exhibit SHM, at least approximft z4g w 4*r +ekys3(c6v8xgpi7sa7spce;cs4ately?

Is the acceleration of a simple harmonic oscillatzs *fq.e q+u; kxd-is*or ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approxaoc5b4 ty yx-b:sja,1imately simple a c:y5 4 bx,-sayobjt1harmonic.

Real springs have mass. Will the true period and frequency be lz0t, sx0p 24oibe /5igfxya.aarger or smaller than given by the equations for5 0o.is4aiaebxt,gf y2p z/ x0 a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscills(+( )*p a pfs56+; ewtnee dqmypyc(sator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and then i bdvxcg4 qipi p8o600 k03dp2 ozdkf.7s released. Describe thc7 gp.oddko02dibqf0p8ik z0p 4v 3x6e scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it3z)(kkts nzm 4 gain or lose time when taken to3kt(snz mzk)4 high altitude? Why?

A tire swing hanging from a z;56oomujlvmy.sm oy ;2c6j i ve47-b branch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of thesb.i- 4j6 25 7my;uvze; clomo6v jymo branch using only a stopwatch?

Why can you make wate6gmjbr4z wcpdodp8 w:0odg; wfn),8 0 2far)or slosh back and forth in a pan only if you shake the pan at a c )rwfond4;mpgg0fr w2c0d,6bp:8 o)w 8az djoertain frequency?

Give several everyday examples odfr0/m2khkg(c b -(laf resonance.

Is a rattle in a car ever a r zj. fg(aw(2fnesonance phenomenon? Explain.

Is the frequency of a svpj(n2prpdkc i 1 bv8bgp:g-i/ax-f4h y 05i)imple periodic wave equal to the frequency of its source? Why or why not?)1jr2ca(p4-ik5x v vndpb0/:pg i8-fhbipgy

Explain the difference between the speed ot ;zzny. youy9*b5iz3 f a transverse wave traveling down a cord and the speed of a tiny piece of the cord..nz*b; uz53yyt9y zio

Why do the strings used for the lowest-frequency notes on a piano noi(8nl- sfxc8 6tsuxj3 rmally have wire w8 c8fxtx63si lu-jsn( rapped around them?

What kind of waves do you think will travel doo6at8s kgz(8p9onisb iw.8lcaw **y/ wn a horizontal metal rod if you strike its end (a) vertically from above alapi.o gi n6zy bt8k/ s8ws*o98c w(a*nd (b) horizontally parallel to its length?

Since the density of aipyzn armf9 m+h9p0v sa y;-0forc,;)q r decreases with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vafnps0q;va0yrc z pyh),-9faro+9 m;mry with temperature?

Give two reasons why circular oarndo 4,43wdg w5x3xwater waves decrease in amplitude as they travel away from t,da4ogdxo3x w4 3w nr5he source.

Two linear waves have the same amplitude and speed, and otherw cg avc4.ogy9w 0u2cm2ise are identical, except one has half the wavelength of the othu4y2a gc0c wmc.o9v2g er. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between twz/fk);h7ir8 jcy m*q ro sections of cord as in Fig. 11–33, the frequency does not change (although trzikhy;c/)rq 7*j f m8he wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places you g i (:iu- ebeh52vxa;ccould touch it with a knife blade without disturbing the motionha:x 2g i(eec;-i v5ub?

When a standing wave exists on a string, the16xgj nyqn)vwrg+i8 0 vibrations of incident and reflected waves cancel at the nodes. Does i1 r ny0nxjw+6v g8)gqthis mean that energy was destroyed? Explain.

If we knew that energy was );cmd8qsi s3 m;0l6lrho 0cqgbeing transmitted from one place to another, how might we determine whether the energy was being carried by partiqhr;cd ci 03ss8lgmo 0q l6;)mcles (material bodies) or by waves?

  If a particle undergoes SHM with a3t l l;z(ugv t+bro0.implitude 0.18 m, what is the total distance it travels in one period;vt0z(i ub3t.lo g lr+?    m

  An elastic cord is 6)yhm+2 q9o9gp*;jcnm pjs x)1jea,wa5 cm long when a weight of 75 N hangs from it but is 85 cm long when a weig12,mpjwaa9m )e) s9o*p y +hncjg ;xjqht 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 driverjct 1gh+a1+ iv gets into the driver’s seat. If the car goes over a bump, what will be the frequency of vibrationvtci 1g ah+j+1s?$\approx$    Hz

  A fisherman’s scale strhby-cs).y mq-d a( jszq 8q*29aswsv1etches 3.6 cm when a 2.7-kg fish hangs from it. (a) What is *a8v(d ssybym2js9. wa-z-)qqcs1h qthe 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 vibrate:nu96.i8li9 y1cgs9ha;ayd2s hr+ ew-y grgds with a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it.e9ssi:9196;yi-d.2ugh8+daw y rglgyn a r hc What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 0nrfsk6rc nt)p2 4c t.wg6 d:z11–2 at times t = 0,wgtn6z 6cptrd0)k.c2rs : n4ft = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 yt s0oh*)zxz+qlzcc:3nm . 1 rin a spider’s web. The web vibrates predominately with a frequencyo3*qznxz c+.s y t:h 1zc)0lrm 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 0.88 Hse3,h upi6z 0, -tiidbz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the value of muisi ,6-zbhpde0 ,3ti?    kg

  A 0.60-kg mass at the end ldp0,nz.3 c j5l *jg5m 9x isug8liep9of a spring vibrates 3.0 times per second with an amplitude 5c ngil * ,zmejpl385x90pijs d 9ugl.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*lh.rtq+/ zzzq(sa1+waxuo8 m is the speed of a SHO half the maximum value?xa( zq so+1r z*wt.+8 zuaql/h$\approx$    A

A mass attached to the ew +q8mfn 5vx8pnd of a spring 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 aav ) th6gl2 bpl/)rpm1 vertical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long dorp /mb 6 h)vllp)ta1g2es it take to reach the (new) equilibrium position again?    s

  An object with mass 3.qt:7t64lrog 2) 8 oandlzyp6s 0 kg is attached to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving withrtqdpot nllo 62agz: 6)ys748 a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a toy popgun 0.q;z3 rz;p5r)gz2.o: gkwk c qo200 m to “load” a 0zokq o gr:3c);kzqp2. ;gr5 zw.180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface ) feum1sj/n5n 1 s+z ige3un:ed,u 4pvis attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from restnjes1 d) :15zsnn+4, euvp/g3imeu fu 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 ej9s- 9uiir(m*v+.rv jqnqn eu w-. f9iquation x = 0.45cos6.4t where x is in meters and t is in seconds. Determine .qvm99qnii. wvn uji-(sr *uef j9-r+
(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 enero ) k 0md xo16p(likwha/r )ihg3a.;zjgy of a SHO half KE and half PEg x10dirwa) hz)ao3m;opl j(.kki /6h? ±    A

  If one vibration has 7.0 times the energy of77a sz04i(npmlpohv 8 a second, but their frequencies and masses are the same, what is the ratio of p(io4n0 v a8m7h7zls ptheir amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring once every 0 91l*tma1 9 ot,pfmtei. m9 1,titolpm1e9ft a*65 s.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identn6vs t 4j vw7*umo9oj)2fq3l2 acdfb5 ical parallel vertical springs, each with spring stiffness constant k (Fig. 11qtn2vv fs uo d3l5fw47*mco9) 6bjaj2–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to.e9sca7l mxl1:bq4 ap the equation x = 0.38sin6.5t where x is in meters and t is in seconds. Deae9pbl 7 sxcq4: lm.a1termine
(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 exam :-x3tilk ztg87srudgl : c-z6ples 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 t7 qvk (ux asss1sh)j14he end of a horizontal spring (k = 124 N/m) is struck by a 1q)(xhs s14 kasjs7vu hammer, 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 sprinkw0t9zbj 6 bvh(.i/p ,3tc0hctdzy+qg stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibri ctz0b,60/h+cp ihqbzdw.t9t j(y3 kvum 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 spri,snj a-c7bol *ngs, 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 a fixed horizonx)pk6ak 2dah3tal spring whose spring stiffness constant is apak3h xd)26k$ 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. Aftern;xb0s 1 h e: h4w()xgjyeu9lp reaching his lowest point, he oscillates up and down, hitting a low poex eyug:j 0(9bp );4n1xlhsw hint eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 60 s. What is (h7x4brj b6j kvkf3jdwj,p 3nk;-p:i its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to pd0*lzh /o. g);8natyt8t primake exactly one swing per second? (That is, one complete vibration takes ezyn ppt8ahlird/ gt to8;) 0.*xactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period *+fwyuv;frficb+u9wqdsw t 2hgf38* */0jzw on Mars, where the acceleration of ggffrwi 8wud0y +f c*ft2+j; w h3w9bs u**/vqzravity is about 0.37 that on Earth?    s

  What is the period o1tnc72ev 1nfyl:9 -gls nnur)v: dvw1f a simple pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulum bob h-r15 aq8jdwh xas a mass of 365 grams, and d-xhj q8rw51ait 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 0.9930 mu 9aq2e0lt 64fx ii1hg. If the clock loses half a minute per day, how should you adjust the length of the pendulum? alexihui 0tf9g6142q shortened by    mm.

Derive a formula for the maximum speed l 2rw1 m q+-v io3h.4vn3rvfnh$v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum osci4v)nm bg3 (l4t lcd8enllates at a frequency of 2.5 Hz. At it is released from rest starting n4 bet4vd3 l(gc ml)n8at 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 thatgh- vtph4kogv.e8cyry 4* b (1 wave crests pass the bow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How vg1.cvhy 4ptebg h(8ko*y 4r-fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed ..sg ou*rg5ecpn74rkof 343 m/s How f por*s7 neu.rgk.4g5car apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 53dcr dc jqc; 14bk54dx50 kHz and 1600 kHz (kilohertz) and trabxj5cqdr4d3k;c4 1 cdvel 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 oun8:vdluqbh uk9 y , 8g18xq6sf longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulzrd x8/uj9rc., m4eql us, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, and equrmz, r8j l94 dc/.xby what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart.nw8 b+q3zn y;t If the tension in the cord is 150 N, how long will it take a pulse to travel from +3qtznyw8b;n one support to the other?    s

  A ski gondola is conn.kzjd9tbc4 sjfwi541 6 klq(xqt3q c*ected 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 terminal and sends a wave pulse c jq9qjw .tksqlik4xt14c5b3f6 zd(*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 shu2g : :2cizdb(a5dgnpip just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s l(zn5g: d2gp:iua bc2d ater. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at di2(qese b rik9)g7 uc/ifferent speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbance took plac)r i(2g 9 ue7qscb/keie).
(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 appr4r 7.r vat(8g6cbdygl oximated by a sinusoidal transverse wave. a(6t r8ylc.g74gvdrb Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the tpl7p ai j()k5amplitudes, of an earthquake P wave passing through the Earth and detected a ikjlap)(5t7 pt two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is mey dc2vy.yii2ul (ms7ci/gm( * asured to be 7m .vcy(yu s22 imlydi i(gc*/$ 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 portion of8tdgvc 39-d le the Earth, but one is carrying twice the energy. What is t3 ge8l-dtvdc9he ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, butktx (dd+.75gir,eae v one transports three times the power of t ad 7x tg(ed+5ir,e.vkhe other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a p6p8b-.pr zsvskin -d /ond is observed to move up and down a total vertical distance of 6.0 cm, from the lowest to the kb-pr-sn piv8d.zs6/ highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) S:u ,ffj* uw9zkketch 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. Whf ufj,9:k*w uzat has happened to the energy at this moment?

  If a violin string vibrates ate.xlbd:2j/d:j 3z )vfx ,cye)ajsw1 s 440 Hz as its fundamental frequency, what are the3b.c/)jf j :12sxvyzds:x d a,e )jewl frequencies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency u4 ulg7)tu 7rigkxv /7will it vibrate if it is fingered one-third of the way down from the end? (That is, only tglv)4/u i7ugr x tu7k7wo-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in *r cro4q*jj i7p;+jxicb 7a0n3(s vyk four loops at a frequency of 280 Hz. Name at least three other frequencryj; arccj*ivx4 b( ijo7k3q 07p*sn+ies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of standing wave7tbwejxu fq)h5/e u7cxi/j4 / s is 475 Hz, how far apart are two adjacent nq /ef/etjxx5 u4i)c/j77uw hb odes?   m

  If two successive overtones of a vibrat5sl,tvwsm ;kt 9n/s3 oing string are 280 Hz and 350 Hz, what is the frequency of the fns5k wmsov,tt 3 l/9;sundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The e m08a.dxh rg(mx (uuhwru0k,j-k7d 7distance 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 fundamental and first two ovemjk -e(d7umu78x xgw(ru.,0hk 0radh rtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but31jua2phot08diu yi 1 it is measured to vibrate at 205 Hz. By what percent should the tension 0uou2hpyi81d t3ai1 j in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar stringjw+4vqb86nv cgbx2f/j;53xs d o g +em is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should b3g4xqdfs;6x8n+cgb5 /mj2wo ve +vjthe tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to ilc1w:j0n7wki k -e 1ia small-amplitude mechanical 60-Hz vibrator. The string’s mass per unit lkjl1: i1iww7i-e c0kn ength 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 oqzl2:/ w c:lsaid;hk8l(nf k7f the string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave :dica/kh k l8wfs n:2l;q(7lz patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the wfvycndsfkn+* 3k mbka)ds:8p )2f/f- ater back 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. S kd-*3n fpm 8/kcfay 2vsn)sd+b)k:ffuppose 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 travep:/jjejm 28kz ling at k.0 km/s strikes a boundary within the Earth between two kinds of material. If it approaches the boundary at an incident angle of 47kj8 p2zm/:jje $^{\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 frompn 29cs6e7hdr6 r3cvd n7ah+c 2.8 m/s to 2.1 m/s If thep7cd 3d+c 6sc6rnr2nh va9eh 7 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 layer of+o5 lnfw 8v5yi4z +mot cold, dense air. If the sound womnl8 yi+45tf+ wzov5ave hits the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary between two types koc -+1ion:vc 6fxlk/ of rock at ankocv:-k fo+ l/i1c 6x 38 $^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m in diameter. According to the user’sp ky;b4xfuigw7*b8 7q manual, the 7qpx7kwf *;4u b yb8igdish has 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 kmibud k2kup7x6 oh-1o3 and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge anu-hkk1x d u o7bop326id 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 c9: ppa ys-q ctx58fg3xonstant of 550 kN/m Find the maximum compression of the bumper if thety p 5-cp98ag fxq3x:s 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, wh34gf dfjdg l0uj :n5i,ich stretches the nf j0g54j, :ig3ddlfunet 1.1 m. Assume that the net behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hangi6r1vb a96lp 2t6f awfwng spring. The mass then falls 33 cm before it stops and beginsbl9a2 wfa 6ft 6w16vpr to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a hu6r s)u9jrco2i ge spring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the sprirs6ju)r 2i9o cng 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 rig7o1jdkwt 4)ey ht pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to sk 4 o71ydt)jewpill 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 wh/fu/))9sz* up iqdlrecord have a wavelength of 1.70 mm. What will uu)*l z/fphsiqd/w )9be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibratehi r- 3m0* wfx;dig0rnipza68s according to the equation x=0.650cos7.40t where x is in meters and t in seconds. Determine rpw nhi-;i0drm3 z x*fg06i8a
(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 freq7 g y,vkjto3i;uency f. What is its frequency if it accelerates at 0.50g (a) upvy3gj7 ,ti;ko ward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. Whe; 9 13avgqhekon a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he vhq9a1e3;k ogsteps 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 instrument are tuned to fsw yv5m1rhv4lr :b1la3) u1;a .xsw vplay at 392 Hz (G) and 440 Hz (A).rv14sw 31ubv:) lyrmv aasflh ;1xw5.
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stretched two-part cord of kmowr x6w. y8: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 i: oy8w.kwxmr 6s 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, ao3(a bo13 mnbhnd the tip of each prong moves 1.8 mm to either side of center. Calcul3(hb 1ao 3bomnate
(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 harmonichbg,lj9o .qaz .sig(5e kvn l:*,yz0k motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can k.(zvakgh* n90jg eib z,l5syl:o,.q vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a ring that canbyute4 hr(.z(l (e: fk2mu7/j3 wu rm yj(i;ts slide without (b.ju4 u m(yyet(h7tr;(kfjs /u3 rwim:el 2zfriction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2 eyuc3ta*23jn .000 s — each one-way swing takes 1.000 c u3n 2*jy3taes.
(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 tq1z lhx t3xf/,he vertical direction or can swing as a pendulum of sm/xh zflt, 13qxall amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched under a tension of 25gm(as5q obb fd/4x- gk(lm6 ncqt75 u85 N. A pulse is generated at one end, 5q( uctgnbxm4sga6 d7k 5f m-/l8(qbo and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from skd6d4z rh 7j3a ceiling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the pesjr4hd 3k7dz6nny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. Then(p2frof ws(cp ;h+)8yclkd1 steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at cdh(sk) fprp;2 ( o+w8ncfl1 ythe end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–v/a6d) 0d h;jqp +nxx1i -daux58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The p1u-a+h x6d;j ix/x qvd0 )dnajello 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