Give some examples of everyday vibrating objectsb6zh+kpice+ mw lk248. Which exhibit SHM, at least approximi 8kb6k+w pmzl4+2 hecately?

Is the acceleration of a simple harmonic oscillator ever zero? If so, wh2 * r bndiu-6qzfu;bm9ere?

Explain why the motion of a piston in an automobile enufi)zfyx )tqmw /:rn5d18 )oyzl,4efl+ s 6ymgine is approximately simple harmoniciytsf)uofz6y, d4mzy1 )/ )lfqnl:+xr mew85.

Real springs have mass. Will the true period and frequency be larger or f:*g0g;f* gk -qznm9ra.5 rgcnhs9 wh smaller than given by the equations fo: h-w g9.90 knfrhsc;mfra zg*gg*n5qr a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonfr ,i+*anv7.n yhnwh,f-oc l4 ic oscillator (SHO)?

A 5.0-kg trout is attached to thvi9ookq ul ,**,pieamob4 7 l-e hook of a vertical spring scale, and then is released. Describe the scale reading as a funcop 4l*oaleo ,7qm-vk9bi u,i *tion of time.

If a pendulum clock is accurate at rqok:9g3 axj; sea level, will it gain or lose time when taken to high altitude? W39a qoxg:;k rjhy?

A tire swing hanging from a branch rea80a9 8og gmizyp030lbmg h+jvu s.(ilches nearly to the ground (Fig. 11–48). How coulgg0ai0g+z pvmhl sb 9l(jui o8 m.038yd you estimate the height of the branch using only a stopwatch?

Why can you make water sloshh3 cbdodcp2jwz3xum9iqv)j :, 67 o: y back and forth in a pan only if you shake the pan at a cer9po3 ddji7zvcxw2)6 : byjq,oc:m3 h utain frequency?

Give several everyday examples jvp*b:m*j(9noouv v 1 of resonance.

Is a rattle in a car ever a resoml3-lgajo kz va1z s2n5bo80 3 +i(e2qwe*k innance phenomenon? Explain.

Is the frequency of a simple periodic wave eq g :kab1:p rin5;-wkofual to the frequency of its source?o;1g:kn kp wbi:-afr 5 Why or why not?

Explain the difference between the speed ofzq2 6sto6sc 12*un ykf a transverse wave traveling down a cord andsut 6z*k6y qnfsc212o the speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano normalld. ixvtpi5*ut3 6hruj.-y, zmo 1n .fuy have wir p-3x,y ouuj5zm16ur.hnivt*ift. d . e wrapped around them?

What kind of waves do you think will travel down a horizontal mey 9f8 asvr-utl-(h/ zio)m ap)tal rod if you strike its9a-)fum rs8h(-y) zoitpa /lv end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature, but the bulsn.0z8os uwg q /mz;/h3.qijek modulus B is nearly independent of temperature, how would you expect the speed nqz.u.ezijh s/owm sg/q30;8 of sound waves in air to vary with temperature?

Give two reasons why circular water ws .ti:i , qq*oxo46jjb96nqavaves decrease in amplitude as they travel away fromtsq.o,*66iq: avijq9ojb n 4x the source.

Two linear waves have the same amplitude and speed, and otherwise are identic3ezf+qzb3 h u 647fdrnal, except one has half the wavelength of the other. Which transmits more energy?f7 h63erunzfqz+db4 3 By what factor?

When a sinusoidal wave crosse.bnh*7 .6rn vwsysoz 4s the boundary between two sections of cord as in Fig. 11–33, the 6.4w yvs.zs*hbnon7 rfrequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three h7ed)(y cm,n lsegments, are there any places you could touch it with a knife blade without disturbing the motih,y (d )7mclneon?

When a standing wave exists on a string 8xf: 4dj55;6dbg c.nqqjiwcu , the vibrations of incident and reflected waves cancel at the nodes. Does this mean that energy was destroyed? Expl ;jqu5d5 fj qignc4xd86bwc:.ain.

If we knew that energy was being transmitted from j+ urr-+ ix/dqe 0elxfh4ge ,*one place to another, how might /jfg x+* 0erhexiduql +,e-4rwe determine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplituzsv,y 6s u(2kv g)lc;6)ls28as xcogkde 0.18 m, what is the total distance it tra;v)s2yso , (lzagx)c s862uk ckg6vslvels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but is am0 dv6 s8gblat/zbg6 :vwl / 8vy7eq685 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this/v:08t6y ag6zvedblqw b8/76ga vs lm elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg 6 par rsmdy /+p l0nn;*mq7-cfdriver gets into the driver’s seat. If the car goes over a bump, what will be the frequenc -6+pqm7s*drnf; amr0ylc/n py of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fis(al/ux uc0ka/h+g fp4 h hangs from it. (a) What is the spring4u/x/ga+cluf p ( 0kha 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 mass ofh skp :8 t4k2m(r+yssc 0.60 kg is hung from it. What kss8ysht:r mc4+(p2k is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicamb:yam/r 5(c sn5a p0twsx86y/sc l0tting the position x of the mass in Fig. 11–2 at times t = 0,t sm5war5 t:s( x/y 60tbcsnpam 0y/cl 8= $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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. The web vibrah,.hg q ez(b (v98dvjt/1o lw0n5 oygmtes predominately witgv v1,d jy80o(m hl5egzh t.9wqo/nb(h a frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a freque0vlo+4t*p y(3lzq w/* ogwtjqncy of 0.88 Hz. When an additional 680-g mass is added to m, the frequ( *j 0zgol*qoqt wp3l+/yt wv4ency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a sprinz9:eqk-tlu 6 dviyk ,4g vibrates 3.0 times per second with an amplitude of:-qt ,4evuz96lydi kk 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 spe 3/uqog40ce *hr3l 5hniz 3scned of a SHO half the maximum valun c uls 3c0*rehh34g/oz5q3 ine?$\approx$    A

A mass attached to the end of a spring is s cb) kmqa9yx6c,m*r *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 sprinjpo.1: zdth (wg is stretched an additional 0.130 m and released, how long does it take to( 1woph:z.dtj reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is lp -p p(-n;u0ot6waefw4je* v(vu/vaattached to a spring with spring stiffness constant k = 280 N/m and is-et eav6j/up* una p;lvfwv((o4wp-0 executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N 7tg x4iq ana+h7 w/l-cto compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. Witi- +tax l4wahcn/gq77 h what speed will the ball leave the gun?    m/s

  A mass sitting on a hori8d 5gnl )irdcj.1yg. jvc +(tazontal, frictionless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work i.)5l+yt.( gjvr nd8cjc 1gaids 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 = 0.45cos6.4t where x is ih 4,.+qsvx(mf ku:hml n meters and t is in seconds. Determihsvlmf :4u hkmx+ (q.,ne
(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 fromwqyx vcdzi.*y/i6)7;1 n xxmj equilibrium is the energy of a SHO half KE and half PE? ;/xq*ixmd )1zvwci jy6nyx.7±    A

  If one vibration has 7.0 times the energy of a second, bc n6;h0kz op/rut their frequencies and masses are the same, whapk;r h60n/cozt is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillateslweky, a45o:n1obbv7um d 93 b from a vertically hanging light spring once every 0.649odo1 b7y e ,lbwkn53ab:mvu5 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 identical parallel vertical springs, s3:x3df/zzw w fpb s8 qbz5l0,each with spring stiffness constant ks/qwpf3l3x 5b 8w0f zds bz,z: (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates acc p63pbo90 lwhlording to the equation x = 0.38sin6.5t where x is in meters and t is in seconds. Determine po3l90l hb 6wp
(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 ofivac 8gm:h8ll 7hvt+( SHM, labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal spring (k = 1+( o 8mue zplpt9l8)ga24 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s De p(9t 8o )alp8zlug+emtermine
(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/mphns4q xsvn0 -t a1+a3 vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes t +pn4 0- 3qa1shtnaxsvhrough 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, we:rwlis 0iy zq (d8v(.0 kqi8kith 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 horizontal spring :lns ;q li5.jkwhose spring stiffneslk: n;q.5ji sls 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 jumrt* ,3,2lb7 jdb icrsmps 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. lb* 2mi,d, j 7tr3rcsbHe 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 viwncn m0car f.hag;n559 j hl)hg;,8xq brations 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 hy sk4fejnry4ib+jq985 l2s5swing per secondf9yebqh4 58j 2+4rsknyl j5i s? (That is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, whe0diwmkskisxw,ow 05a0nt 5( b y w-h,8re the acceleration of gravity is abtkb0,0iy5n0d5i xko ms h,wws(w8-w aout 0.37 that on Earth?    s

  What is the period ofp zq f7+lcfls4:rc8 .n 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 u1sw 2 kgpr2y yr+)0wnpendulum bob has a mass of 365 grams uwy y)w210rn2+ksg pr, and it is released at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum hh 66jukp-;xkp) cp9s- e e,deeas a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the ekpep66 dhu-;,-x9jpe)e sk clength of the pendulum? shortened by    mm.

Derive a formula for the maximum speedu72 p8ojl+eaf05moc v $v_{max}$ 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. At it is release zdt;qq w5an4+d from rest starting at azaqnq ;4 w5td+n angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchorexp9xtjjq y m289) dbn4d boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the9 jx 9mpq4nx d8)bjty2 waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a sai ;9.xzws )a1akad + fuk o8lp-j3v0rpeed of 343 m/s How far apart are the wave crests (crjpzo-aw9k3sx ak0v;a1l8i).d uf + aompressions)?    m

  (a) AM radio signals have frequencies bc3vp/kxk+ udk8xi )owk ;ve p*qnew ,)7nz 6g0etween 550 kHz and 1600 kHz (kilohertz) and travel0g,kk7zkp)vv3 w;n8*k p wnix6/uox )+cedq e 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 ofk0hc6kv mrkp+ u:h 34x longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the sy. asz , 5wdbch87m m6a*n( lekvf/x(wasg. z0ame elastic modulus, but one is twice as dense as the other. In which rod will the speed of lo mc/e0z,7dl z8a*mvf6 bg(w(xna 5h.kswsy. angitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two suppori3 mc36t. yxhtts 28 m apart. If the tension in the cord is 150 N, how long will it xity3 . mt63hctake a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a st5 b96a;jz7r 7as6jql71n u hk0esqoezeel 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 n6l; ha6eaozu q7rjke97s7j51 zq bs0 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 ship just below the surface of the smccxfy2 ))+ kpea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at thcx) fk+)y2pc mis point?    m

  P and S waves from an earthqu;dyhw1 xxe: 9 pmavaa1+ v-z,nake travel at different speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbanceywhav n 1dam +ezxa9;-,1x: pv 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 l5 uu) xx 1zgnvm(1ez( fmm2,u ,o,cdpapproximated 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 witvnxc z2() uu ,mez1gp5xolm ,mdfu,(1h the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intens1o:m:lp2zy h: +k wmjcities, and (b) the amplitudes, of an earthquake P wave passing through the Earth ao ::kh +ly1zm cw:j2pmnd detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured tozq2kt zv 4;pj2 be t4 jvqz2;k2pz$ 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 througrg eqo kw*v1g;l)u2 9dh the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes ofwu)g*;q2ekr9 dgl o1 v the two waves?   

  Two waves traveling along a stretched string have the same frei:s k ls;45(9 -u c-ynqquir zigal,6mquency, but one transports three times the power of the other. What is the ratio of the amplitudes of the two zk i-4;u9rsliq ,-5csa mn:(iyl6 qugwaves?   

  A bug on the surface of a pond is observed to move up anu5ld om1td :u5notnyx6q2 5/ vd down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE cnx d21/5 ot5ud6:lt o5ymvqunhange?   

The two pulses shown in Fig. 11–52 are moving toward each o7cchbqs 9e mnnyg,hl 4;-g v;/rt*v e2ther. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened tyven,qgt9c;;rlnshb m* / v- eh2c g74o the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, what arc2a;i cf(a *duxct+n:e the frequencies of the first t; cccxd:n(f +2*ua iafour harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At gbfgo 2.1j c;jzo .-wwwhat 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 vibrates .wcogf;oz- w. 1b2gjjas a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz. Ndvc 3g sqpr:( n-++qeon j8:ftame at least three other frequencies at wjr:(epsg+otn - :+qncvq3 f d8hich 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 waveijsb;inc w (*,s is 475 Hz,w (sic,i;*jnb how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating stringnp:(u/du d cv9 are 280 Hz and 350 Hz, what is the freqdv(/dun9pu: cuency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance from the bg9pogp0sp e d3hlv+(6 ridge to evd 9gol0h (p6gs+3pp 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 overtones?    Hz

  A particular guitar string is supp.*, ate.b-j+b)az x8e gwjtdwosed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequenc e*bjwwt-.x g a8)az.b+ je,tdy?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, bu6bxe9yff*wz9+0t 4 :sqtqqaq f8cfc;t it is measured to vibrate at 2y8w:a;z +t4 s6 ff qqcf9tcfqe 09qbx*05 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attach,js, r. cjqaxg zb7-9xed to a small-amplitude mechanical 60-Hz vibrat ,j7g , bxr.csqxa9-jzor. The string’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the s2 w*+mk byb,dq: dvb(utring may be adjusted by moving the pulley. If the hanging mass muqvb(w :kdb+bm* y2,d is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the wac+ . xka 47 wjtas6a5uqaeq-h.ter back and forth in a tub at just the right frequency, the water alternately rises and falls .ahqwq4 tu x6 ak5aejs.7+- caat 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.0 km/s strikes a boundary s5wnfvvd5 1- :a6z;yn g1isbxwithin the Earth between two kinds of material. If it app5gvsdv16 ;:-z51ynifaw x sbnroaches the boundary 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 thecv861 lb u3qsga/ q3vbtufg.7 velocity changes from 2.8 m/s to 2.1 m/s If the incidentf.3u bgsq716qbu8 3lt vacv/g 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.b b0p0 aph2sd3j4t2 fe If the sound wave hitp4 ehtj02sdapf b2 3b0s 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 st6t k3,w ijis;hrikes a boundary between two types of rock at a 38ih k,;s3i w6tj $^{\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’s manual, k2+y1n.wuii ithe dish has to be pointed in th1wiy+i2k.nui e direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 km/h travels across the Pac ifsxke*-n/0 hific 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 warning, people have died during tsunamis, some of th 0xns/*fh-ik eem attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness coq 0wgmoj0,: ov ga;u,co,/ wgwnstant of 550 kN/m Find the 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/;og0gacj owg, v,uq:m/ 0 oww,h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps jn nn3fr2b:,afrom a window to a fire net 18 m below, which stretches the net 1.1 m. Assume f n na3,:njbr2that 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 aj s ) s7t/k1mksgzq z-6lpb4-z freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of the oscillatio)- 1j k qspsszlk 4-7mgbzz/t6n?    Hz

  A 950-kg car strikes a huge sd c0lc sn0/0fgpring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of the spring? dl0 /0fsccng0   N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just the right pace of ab,a/yeztv ggf9e)os 0* b0e h7uout 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55) 9y v0z, )*hu0beaft7/oeg esg. 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-rpk9qn:hwp3o2 jm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sw kh93oq:np j2ound emitted?    Hz

  A 2.00-kg mass vibrates according to the eq*q+o -aqgo zd 6t*ou;yuation x=0.650cos7.40t where x is in meters and t 6 ooqqy**g+-ztoa;du in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. Wh 1kuq9qrf6va( k0ar8 hat is its frequency if it accelerates at 0.50q0 8f kukh1aa9(rvrq6g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft flsk gnjo2mb9pw(lf(v 0lk5*a/oats on a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates fov5n2jwk(ak 0l/*9pb(s go lmfr 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 instr1) .cf.60zcuhr e-akvrfp 2mrument are tuned to play at 392 Hz (G) and 440 Hz (A.rfh um-rk fve2ca.pc10rz6) ).
(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 Fig. 11a: b+usthcab d;9ln )(–33. Determine a formula (a) for the ratio of th n:lc9dsta ( +)abh;bue 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, and the tip ofnf*f . 7zvi+us each prong moves 7fn+vi f*.zsu 1.8 mm to either side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of frequency 1.5 cycy1s/,p-dezthpld f22 t; p,zmles per second. What is the maximum amplitude with which the end ozlz2ft2ysp/peh dmd;, , t1p-f 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” en62i bvtsv-2a s/x 0fvzd if that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determinva0bsv f2z2 -6tv is/xe the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum z5n,3x0f .dtj60 joshz4yx x upf7bt7 has a period of exactly 2.000 s — each one-way swing takes 1.000 s. 5j.4d xtfj3 0yh7soz,zx76f nxbptu0
(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 ooa:*pmvjkf4;vbp t /*scillate 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 or the period of the horizontal swings, and by4 b/ f:vp pt;ja*k*omv 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 zjxil/u 0wp)3 stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pul)u xp i30zlj/wse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a cei4.a)c egvab 5v3lvwz 8ling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum ampl38 .ew5)av4 v lzagvcbitude 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 junkyar(i e cka)a(y,ur 5rb,gd. The steel crane cable is 22 m long and has a diameter, cy buir5)r(ae( agk, of 6.4 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 shown in Fig. 11–58 (which aloj ;53dy b*wcvso gives the dimensioyjwdcv *5bo; 3ns 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