Give some examples of everyday vibrating obi ux +,ttuo6dikx3s)8 gy9t2ljects. Which exhibit SHM, at least approximat6 t2xd9xt tu ) g,o3lu8siy+kiely?

Is the acceleration of a simple harmonic oscillator ever zero? If sg/sv y cr(/ 3wo+;qy7nbv/ phmo, where?

Explain why the motioni. rnnnmvrky+- )v 1i; of a piston in an automobile engine is approximately simple harmomi;ny kr +rn n1)vv-.inic.

Real springs have mass. Will the true period and frequency b c (56bv kdmjaprudz;);5k9. zp hiq2sq9a,q be larger or smaller than given by the;v., z5ap)zjqau2b6b k;qckh rdp i9sq9( 5md equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximumtx5mr;vv4l m9ltroy6 ,, xs)t speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertic)usq9x * nkii:al spring scale, and then is relenix*i9 kqu) :sased. Describe the scale reading as a function of time.

If a pendulum clock is accurate 9l f1/9amdzojx7bldx c5 :)l 6g1 scsoat sea level, will it gain or lose time when taken to high ala jxo 719/dg6d )f :lzclxlbm15o9scstitude? Why?

A tire swing hangingvm/h)0yg8 st; dor-b b from a branch reaches nearly to the ground (Fig. 11–48). How co0)r/-sgo dbth bv8my;uld you estimate the height of the branch using only a stopwatch?

Why can you make water slosh back an9syf6 zi291hjj0. elt mmse7 ad forth in a pan only if you shake the pan at a ceri6emyh2tmjf9 .esz 71s jal90 tain frequency?

Give several everyday examples of reths9ni 3:c8dcge+ 5mtb c x8z.sonance.

Is a rattle in a car ever a resonance phenomenon? Expl5fol5tfd/pn h+ 68n luwd1 z,pain.

Is the frequency of a simple periodi6wqd lx(d 8eg fqmv0);c wave equal to the frequency of its source? Why or why nlmvx) (q0f6 ;8edgd wqot?

Explain the difference between the spee r k5 2ee)e z6ry)gjarep/0b1qd of a transverse wave traveling down a cord and the speed of a tiny piece of the cord.0g)1p azb/e)erre j26r5 ekqy

Why do the strings used for the lowest-frequency notes on a piano normally hav++4:/e5ui7 g x dlj8uvaymopo(vy cr .e wirlv+uypj :i+g857mrvxc/ u4oea( y.doe wrapped around them?

What kind of waves do you think will traveyc*machj);4q3tc d8 wl down a horizontal metal rod if you strike its end (a) v8 mw);aqcyct j34dch*ertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase nfgqkc7bx;d;l f;1t v)j(b6 pin temperature, but the bulk modulus B is nearly independent of teblvn ;;ptdb)x kj (fcq6fg7;1 mperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as they trav xf87wi+n7/jlubd(m;3wwz lqel away 8wm3;wuzfqd(7i+ lxjl7 w/nb from the source.

Two linear waves have the same amplitude and speed, and otherwise are identicaoc.m t, i4 -taryr4ys8vwk0ka2gj y4)i za72nl, except one has half the wavelength of the other. Wh4v)4 yy47 2- y takkawctimog2jz ,sr0 8.nariich transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sectionem.6rd:dydaxtq t/ /4 td61d ts of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Explt:axem/tddd .t 4dr6 1dqy t/6ain why.

If a string is vibrating in three segments, are there any places you coawd 6d 2ld:xjsn7;qr(uld touch it with a knife blade without distar(;6n dldd7qx2 : wjsurbing the motion?

When a standing wave exists on a string, the vibrations of incidenw 0;l;h(8 di ynv3-* mms o/bgkp)stytt and reflected waves cancel at the nodes. Does this mean tn/*8po lssm d)3;mi;tb t0-w(yhvykg hat energy was destroyed? Explain.

If we knew that energy w tilm5:ow m pzzbi/1:(as being transmitted from one place to another, how might we determine whether the energy was being carried by particbml/:tz z5(:om p wi1iles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is sm pl +smck8(/d8(lvi the total distance it travels in one s8 si(pl(8v k/+lm cdmperiod?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but isdk(;ertu-bn:k(hi q, jb,n,v 85 cm long when a weight of 180 N hangs from it. What kb((rnndv:, ;,j-bket , huiqis the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compr;w(gu7e(f y.h9z/cy n,n umfjess 5.0 mm when its 68-kg driver gets into the drivef 9ju((yw;n.y/nhf, e gc 7muzr’s seat. If the car goes 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 fro r0l(z)m csw0u7t:egdm it. (a) What 7r(du z0tg 0wclsem:)is 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 whe4np; 5qjad .8d isul9rn a mass of 0.60 kg is hung from it. What is its frequency if onlylqnr u5saj iddp.84; 9 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at time,mwfjb0k9 j: bs t = 0,fjkw:m bj9b0 ,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web. Theu .u uc 0stv9,0boeg. ;aqbv6ouw:ji5 web vibrates predominately wibcu;gu0,j s06uvb oq9.ao w ivt.:5 ueth 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 vibrate0r; lqe9s 1ztk(6bbquqe .)yps with a frequency of 0.88 Hz. When an additional 6y(qke ;rq1tlqb9b.6 s0e )z pu80-g mass is added to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 tigzk ;alqm*:1ia (y2wb mes per second with an amplitude ol 1 zya:iw *bkmgqa(2;f 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 equilibrium is the spee8vlwb utt e)rn qx+: :lte);7ed of a SHO half the maximum value?)w; tetlqene+vb7x: )l r8:ut$\approx$    A

A mass attached to the end f e1bmy1s,x6l 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 a vertical spring 0.315 m. If the sl /pe lyig tp/k8b*w7.pring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium position again? /ipwp8* /l l.gt7ykeb   s

  An object with mass 3.0 kg is attached to a spring with spring stifo cku t+k7gyxu87 nmlz-i+4m, fness constant k = 280 N/m and is executing simple harmonic t++8 -ozu 7 7gmnkm 4x,yukclimotion. 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.bnnr)z) .j( ao0 N to compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what spnr )nob(zj. a)eed will the ball leave the gun?    m/s

  A mass sitting on a horyrn(,m16 d0sqvx h1j8(tw :ldn h3iciizontal, frictionless surface is attached to one end of a spring; the other end idc81dmq ( xhrh t6jy,3nlwn(:10 ivs is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x = 0.eonwc(ocp fj-a*n898wl)af f5h s 5 q345cos6.4t where x is in meters and t is in seconds. Determine (fso83c- 8nj e 5)f5fpw cqwn9ah lo*a
(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 ;z )ndh+ir:yv:rn . wawiik:/energy of a SHO half KE and half PEiv)n;:r: wkhazrnid .+:w /yi ? ±    A

  If one vibration has 7.0 tid,ibfo.8f ,oa mes the energy of a second, but their frequencies and masses are the same, what is the ratio of their amplitu bioaf,,o .f8ddes?   

  A 2.00-kg pumpkin oscillate)z( 0wsx pdeab)jmx6)8v ,j jkm)qy-ds from a vertically hanging light spring once every 0.65 s. ( )8)xk 0vj6jmzw)qed)m-j,axdp s yb
(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 suppo4 r; iy68dsqzlrted by two identical parallel vertical springs, each with spring stifd6i8zy 4lrq;s fness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to thec 3b l(+(1f:nxgxtquln-/zm b equation x = 0.38sin6.5t where x is in meters and t is in seconds. Determin1fz(m l n3tu -:b l(bx/+xcgqne
(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. Fo,1 o f j,2auuh.8it0 aylioh/rr each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a j mh- t+:qjiilk+ j;p1horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Determine m+hlkti+1;jij jp-q :
(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 vibrates wit p75ukv:.tw5x1li f yzh an amplitudifz:v5p k7. lwxuty51e of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with sprrc ,l/9 dv.5ek a4rssying 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 horizontal g ,hpel/i.pmaj (no g .)abwyrq j8879spring who9gq jjbpahenwyp78a iorm )8/ .,.( lgse spring stiffness 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 jumsoeup0a8nn5 9 ps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the leve 5 a9en0p8suonl 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 vibrationl9 4pkvcu(c 4qs in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swing per second8 3newa2: sq.jxbflt 2:4p1* mvuvbwm? (That is, one complete vibration takes exactly 2.m v22n b:tmel 1fubqs3pwwxa.*:v8 4j0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, where g7y7put (z.ejwm7 bke)- .o.f8abjcvi9+z uc the acceleration of grzjoc(7.+ m uib87-kyt.wap)u7vez f.cbjeg 9avity is about 0.37 that on Earth?    s

  What is the period of a simple pen-(vvja )m d*ee e.r5oddulum 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 has a mk.7tsui7mmpm 4 nv7 d1ass of 365 grams, and it is released at an ang dmtis 7 4v1k77um.npmle 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 loswwbb-0xc, )bu;o w;hu es half a minute per day, how should you adjust the length of)cw, o b;u;-hw ubxw0b the pendulum? shortened by    mm.

Derive a formula for5xw.ayfot/hi 2ghcbn0 y1ce. mht:- i) 5.ury the maximum speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. A/ iz0qy 2)71fe be(yv:fqbuhm t it is released from rest starting at an angle of 15 fyiyb v:m1qe/ qbe27) fh0z u($^{\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 pa4pmi nh 4e/mny.8v2*qpz6vq sss the bow of his anchored boat every 3.0 s. He measures the distance4e4268 p mvvi*ynqq/ mphs. zn 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 travel2rb 2 d.ewmu/67mkyv8 9mhyob s with a speed of 343 m/s Hom6uyoby2 b rhkmv7 /d28 w9me.w far apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between xw ecx h usl47*6gbj* t(ww3t6550 kHz and 1600 kHz (kilohertz) and tc 7*s6ut w*whtgxl36j (bxw4eravel with a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal wa a;-ru-thwckq:i 6gfih, 9tf,k8/ykw ves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as dense as the o-jrz6my t4c8 th5v62 bbkh,kbther. In which rod will the z2-bjctk 5h 6t8b mrkh,6 by4vspeed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg;( cb- +qxqaus g1oo2t is stretched between two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse;u xgs 2t1-b+oocq (qa to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable1weq ):zv d mku*,pa6e 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 alon wvm*, qzu1adee6k)p:g 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 ship just below the surface of the sea. He 2rgbtduol re .ta2g+n(59t7i hears the ech+a tot erbt7d.niru(9225lggo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different sppu( q rb:lhrp 506vd)meeds, and this difference helps in locating the earthquak(q bvr0durm6: )l5 phpe “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 ;w9p1j,kungqr/2 nq japproximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the k ;j gnw2p,1/j qnruq9acceleration a>g]    m

  What is the ratio of (a) the intensities, and(6u+b+ku-w m szsksb7 (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20+- zwus k+b6sbkm us7( km from the source?(a)    (b)   

  The intensity of an earthquake wave pare7ichk (-, osssing through the Earth is measured to be ir e7, cksho-($ 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 of42ehfpfm jkja6 abyzqj-1(*1 the same frequency travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the ampli -pjeakybj4qzm(1*fh216f aj tudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency+5(fd; o ij+yx 9psmy8w-mqkuc2ee)y, but one transports three times the power of the other. What is the ratio of the amplitudes )yyw5cudkypeje s+8m9; q oxmf-(i2+ of the two waves?   

  A bug on the surface of a pond is observed to move up and don0itrx5/3bws (k jhg)wn a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples 05nr/3tkbi(x)s wj hgdecrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–5813koa 4vpk0kdx/l -b 1d elou2 are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Skekdl4 1oao xu308k-vbkle pd/1tch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its funx zlg sg5 vfkti;v;26: 4)pkszdamental frequency, what are the frequencies of the firg xs)slg pivztk 46;vk:z;52f st four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hzsvh0t(yn0 :e l when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string 0l( vynhs0:e tvibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a freq c;i+ : +nur70wtlyxcuuency of 280 Hz. Name at least 7+wu;unlc0y:i c +xtrthree other frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of standing wv 00s8aww/df*8yds d zaves is 4ww0dv* yf8 ss08 zd/da75 Hz, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrazg/.g1xdq:rh7fef 3nj .f+wwting string are 280 Hz and 350 Hz, what is theq:x7 j gezf.w3 rghd/1nw+ff. frequency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance from the brzbilr6*fkyvq 8k 3 p6lf+1/h sidge to the support post is L = 62cm and the string is under a tension of 520 N. What are t6 k81bh*z fp3rfys+v 6lki/qlhe frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is mrzl6mby 4g)h x0-a d lgrh9d.3easured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the tyhd6hg.r ) -x0lb39r zl4gdam hree frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrawv.h.ctc yx g4 2xgi;,te 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 thvg cc 4;xx2,yght i.w.e frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mechanicalfm h5nv(l ufg5 tzo6+ r)lrsla0u 9f)7 60-Hz vibrator. The string’s mass per unit lenr (gl+90 fsarffloht u5n u6)mlzv7)5gth 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 mkl+h;b psj7e4ay be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achis+;ej47 hkplb eved by varying L between 10 cm and 1.5 m?   

  When you slosh the water on0 qn /jq2u in1qm)0qback and forth in a tub at just the right frequency, the water alternately rises and faqmn) nnq o/1 i20qujq0lls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k. t sxh*5orgvt8n//7jo0 km/s strikes a boundary within the Earth between two kinds of material. If it approaches the bot8x* /rngv7tso5 jho/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 9p p.-k)xna zg*x1xdg -au )i (,fbcfxchanges from 2.8 m/s to 2.1 m/s pn)x--gzcx bxkgu)d*. i1 fp( ,x9afaIf the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer of cold, dense air. yg4btmk.31v n egoa2geg*s59If the sound wave hits the cold air interface at an angle of* kv41byg5egn.2t go3g9m sea 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 type ,dc+4 , 8g.edoeu khal3i1mpqs of rock at a 38o8l +, 4ee agpc,ihd mk31duq. $^{\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 di;srtjr)1svt3+j fyvn jz/8q8 ameter. According to the user’s manual, the dish has to be pointed in the direction of the satellite, but an error of about jtyv jn18q zv3/rr8 +s)tf sj;2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 km/h travels across czw//wyzdv .)cdd; ,bthe 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 and warninw,wv./d/) zzd;cyb dcg, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant o htis1w 5hj0l*f 550 kN/m Find the m *wi1hlh5sj0taximum 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 windo/z**o7y3mvzzhh/ u huw to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a simple3 *zu/ h v7zhzmoh/*uy 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 enf/+ de8;yju)m r*hcu nd of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of the u);nf c*eh+ ruydm/j8oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/st nhbr46g91nj (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness consta r46 ngh1tnb9jnt 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 co(4hx rz:zt jt7ffee (diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more unti( rtz:thzj47x l 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 10.8r//u z5ssz5h l cm from the center of a 33-rpm phonograph record have a wave u5 hrs5s/lz/zlength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equ-x*,sp7b d1v jhpx5gw 6d+me tation x=0.650cos7.40t where x is in meters and t in seconds. Determi petwdg x5-+db,61spx* vm7hjne
(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 frequen;o e;rstc c+r1cy if it accelerat re +scor;;c1tes at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raft, ixi*cd9m 9 l0/lz1rwxkt sinks 4.0 cm deeper into the water. When he steps off, thekxil / x*dmz9c19wrl0 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 tunepuloft.s16-qoq. jg 6d to play at 392 Hz (G) and 440 Hz (Aj-u.l1 gptosqqof6 .6 ).
(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 cord0er pmu.ih49bt :hf3q of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus tt.r039upem4 bq:fhihhat 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, and 93/e l1 vjvnxythe tip of each prong moves 1.8 mm to either side of center. Calcuv1e v9jl3/ ynxlate
(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 hvks);o *k uv2)ofk . gty,0lhharmonic motion of frequency 1.5 cycles per u.kg k))ys hh ot2*vl,vof;0ksecond. 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 during the oscillation?

A string can have a “free” end if that end is attached to a ring that.dbm;uh:hp fdar v (-6pqb7y( can slide without friction on a vertical pole (Fig. 11–57). Determifhdypm-6:7p .hdbbrqu v (;a(ne 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.cq 83brhl8y 5wwg j,y/000 s — each one-way swing takes 1.000 s. cwy rl88gyj /5qhb,3 w
(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 dir.lc9y a6uu c+tection or can swing as a pendulum of small amplitude, but not both at the same time. Which one is9uu a 6ycc+lt. 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 strrs)-uwxuhplcj/+ lo/) p9jpj/m9 hep)ea2,p etched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite /j9r osm2 e-chh px ppw9ullp ja)p) j)u//e+,end. Where will the two pulses first meet?    m

A block of mass M is82ea2o m0w/(peg 4ptfi he xg9 suspended from a ceiling by a spring with spring stiffness constant k. A penny of m2/48goetw0 mxe 2ag ip (fe9hpass 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 9d n2qt((iybi2qd;kjce)is( 7inr+m 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 cablei9(nk+csdb(ed ) 7 imj 2q i2(qnryit;. 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. 11–58 (whichswh r)e, ,iuv. also gives the divi,w)s,he.r u mensions of the block). You push it sideways as shown, and 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