Give some examples ofih.dr0e:n znl lp2z2 9 xz1rx9.f r4yu everyday vibrating objects. Which exhibit SHM, at least appzhn 90 fy14zx. r9lirrzdu ex2 n:p2l.roximately?

Is the acceleration of a simple hapg*b5gtr,b .n9d f*o uscvdxi/)f,1crmonic oscillator ever zero? If so, where?

Explain why the motion of a pistonq i5xbgju.cb7vq*;rh0b5 2 q pxux t:2 in an automobile engine is approximately simplevihxb xq7qc*q2bx 2 :p5ruu5j.0tg b; harmonic.

Real springs have mass. Will th bwwdhpnp ; 5*8uivrc/4zfi 9;e true period and frequency be larger or smaller than given by the equation;iizwh;*4fp8c5npvw9 r dub / s for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the matbgg*zk (wb7cb i5v 25dy r6/atqp /f1ximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a ver7z ;9o;z *lcth zyd(wltical spring scale, and then is released. Describe the scoyz9w7l ;l;ztdz( h* cale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose tidno( z;bxq eev uv*/.o91 riv7me when taken to high aro;9dev7bvq ou(nixv e.* 1/z ltitude? Why?

A tire swing hanging fromd.;j m,nil9 cu a branch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the branchlm 9jicd,.;nu using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake the pan aff0ki1,;fc s0rxgk t -t a certain fx gcr-1;kf ,is0t0 ffkrequency?

Give several everyday examplef ih+/joa:f0t(oggt+ s of resonance.

Is a rattle in a car ever a resonance phenoo5qe irbn1qzmv4,bgj 8q- 7c7vk;ok/ menon? Explain.

Is the frequency of a simple periodic wave equal to the frequencok q /m76zgo- ei4 fph*:sv*3 gx:nyeb:sk 2rdy of its source? Whdz*3k-hg xo *:qn/k7reg :ms v6ifoyep42bs : y or why not?

Explain the difference between the speed of a transvert )sf2k: znqbzk;kf6/se wave traveling down a cord and the speed of a tiny p;f2 b)6sqkk/n:fz k tziece of the cord.

Why do the strings used for the lowest-frequency notes on a piano nor0hv 6dvi5zgkn xc-xip;s(/k 3mally have wir5isk3dxn0zg -vxch ; /k6pi (ve wrapped around them?

What kind of waves do you think will travel down a hori4n fmp*mgv 0(l 3pxtm*-ul+ lhzontal metal rod if you strike itsl4fmlp- +**mxgp hl( mnvu3t0 end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase ij(5 ow(1ys hxcn temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound wavewo(1s(jy5cx hs in air to vary with temperature?

Give two reasons why circulao,/9ivudf.9 fz zzlzld5:u n4 : cfc:tr water waves decrease in amplitude as they travel away from the l:99nffc ozu:ciu, z /5vldzd.z:t4fsource.

Two linear waves have the same amplitude and speed, and other:n:j 41ijkb1gta6o9hm n 3lhbwise are identical, except one has half the wavhl ah19b gtjno mn:j314:i k6belength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boun9f d-sa7tz 5qf-q6.pw xhzb* rdary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and q5hr-6x pzs97b.q- fzd f*wt avelocity do change). Explain why.

If a string is vibrating in three sdnhrh-l4 8vgci5t) +yegments, are there any places you could touch it with a knife blade without disturbing trt-y nvi+hl58 4d)cgh he motion?

When a standing wave exists on a string, the vibrations of incident and re2-iei:ksc ,jo bryt(l;d6 u,p flected waves cancel at the nodes. Does this mean that encyulpbksrid2eo-;it,6,( : j ergy was destroyed? Explain.

If we knew that energy was being transmitted from one place torx-( 5fjy v2klgr05 qc another, how might we determine whether the energy was being carried by partic2kcqyj-r(r0gvf l5x 5 les (material bodies) or by waves?

  If a particle undergoes Seiba8t;/vz wap: ..-b y p4epfHM with amplitude 0.18 m, what is the total distance it travels in onpev84tf-/by;i abe zp ..pwa :e period?    m

  An elastic cord is 65 cm long when a weight ofe.0*s vengqculz/: 9h 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. Whahguzne*:9 e.qcvl/s 0t is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500cnju5t a/ glk2*y+ h)g-kg car compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the freque* n+gc hgl52tjy)ka/ uncy of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.680rx i 0w7nevc:or-tr cm when a 2.7-kg fish hangs from it. (a) What i:wr cr ei 08tr-7noxv0s 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 frequywm ji 6,8d6qnency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is it jdqn 6,6m8iwys frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. blvug7cuv +,gblb: r-c1r b.3 11–2 at times t =uclg,rb1:-lvu +gc 7v3br .b b 0,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web. The web vibrates pref9i, z4dpa, ,1o t4hdzng*uc wdominately with a frequeu p4diw, ngtfo4, *a1c,z9hzd ncy 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 Hz. When an a79y tah4y br8u /4ungw-x.vtqdditional 680-g mass is added to m, the frequency isn.bw rq79yxtt4vh a4 ug8 /-yu 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 nu)v kohsmuiw./m; x4,ce9wb t+y7g:times per second with an amplituwnksx4ty uovi,;be .wg):+7/hc u 9 mmde 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 equilibrium is the speed of a SHO half the maximum va cn/nzllvd (7.x:gnbi7l6x)ilz.c ndlnxxvib7)l(6 n 7:ig l/ue?$\approx$    A

A mass attached to the end of a spring is stretched a distan5mu*ysnh) 4rvpp:g-tce $x_0$ 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 stretcsddx .11q:xh9l4gwg vhes a vertical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilidvs9x4 lx hqw .d:g11gbrium position again?    s

  An object with mass 3.0 kg is attached to a spring with s(*t* 4iovns qgph)ueq, vrz+:pring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m fr 4 p)hs vqetu:+n,g*zrqiv(o *om its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the sp6(+.gipi3nxs)w74p *h pkk e, qcl dhmring of a toy popgun 0.200 m to “load” a , x7mki(q*chld 6+)3hswekppg i4n p .0.180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surflo /9n cl0k-7uqw p 0/8hqoanrace is attached to one end of a spring; the other end is fixed to a wall. 3.l l9 h/ou/q n-q7kna wo0p08rc0 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.xon) mb c)ho pcizmk9hn2* pe/l:7; w;45cos6.4t where x is in meters xoi*e;zw )h k2pop hc7cl9;m /)nbn m:and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the en ynzqb6wk6t 9,ergy of a SHO half KE and half PE? ,6 zk9qn wty6b±    A

  If one vibration has 7.0 times the energy oq20ttjt q:q) rzo7 no;j6zcu/f a second, but their frequencies and masses are the same, what is the ratio of their amplitu u qnott6j2rqzjqz)/;c 07to:des?   

  A 2.00-kg pumpkin oscillates frozi1mj v/o; m(:nar:ag:v-9) m sc5k omebnlr4m a vertically hanging light spring once every 0.65 s. mlvn:v9z oc:;mrona4- a: i(g bmsj)m5/r1ke
(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 by4k/(sj s(jqa 80v-esej9 iil0 x qkj-a two identical parallel vertical springs, each with spring stiffness constant k (Fig. 1(9lijs-0xq se4(kkj8a / jaeq-j s0iv1–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.7kmn (+ck v5rhc7 ak-l77bx.y jtkd m-5t where x is in meters and t is in seckrtb v7jk-75nml7-c(kxcdk myh7 +a .onds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labxaxw9g0f n u8 3n2z)yjeled 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 horizo7h ss56w6p pkpntal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s 6p6shpp w75k sDetermine
(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 :eo;s1-(gbodh5y qwek h6 mc8spring stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes thghb6 dq ck5eh-mo( 8;1wso:ey rough the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring stiffness cons)nbe2e-)uu syb )cbx ubfc. dmi*2( 6ktants $k_1$ 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 horizontag/ oxqi8-wkdlbj46 3 vlp::er l spring whose sprpv d:4rqbgl/l - j8xeow3ki6:ing 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 jumps from a high bridge. After reaching yo4i/fzw ;e/-boxbsw em3/2 fhis lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unss43 eombi /x; o2/bfz y-w/weftretched 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 vibrationsw j9b z:9f9vjd 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 makg5cicw 4 a/,nde exactly one swing per second? (That/n c,wic5da 4g is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0eer7k9m4 uy 0b.80 s on Earth. What is its period on Mars, where the acceleration of grav9ebrku40 em7 yity is about 0.37 that on Earth?    s

  What is the period of a4,mkonxuk; (x simple pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pel7vbsm ;7 q8zlndulum is 0.760 m, the pendulum bob has a mass of 365 grams, and it is released at an angle b;7m8zq slvl7of 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 pendulul4*c6ly0 2yndzcqk/bm has a length of 0.9930 m. If the clock loses half a minute per day, how should you adjuslq0k6n d zycbl4c/* 2yt the length of the pendulum? shortened by    mm.

Derive a formula for the maximum spewf0 rxvo+/ssaa krm:t/*-t -eed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates )vs4pgo2z:od 3yec+ fufyg3 2at a frequency of 2.5 Hz. At it is released from rest stare3o32dpys4 2v :g fu+g) fzoycting at an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchored boat eusig13zv vjh4bzg2(n6l(5 g yvery 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the w2uj gnz s lz(gv53g1yi(4bhv6aves traveling?    m/s

  A sound wave in air has a freque-*ivati*q4m6wvkl-r k2fj 2 kncy of 262 Hz and travels with a speed of 343 m/s How far apart are thjmkf *viv l6-r-2i*kw 2t4aqke wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and br;)bt6ieab7vqe5 q) 1600 kHz (kilohertz) an)bavee 65q)qb r;7tbid travel 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 longitudinaa bq dnadg57ezza23l62qt 5e.l waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have thex1rz m5;ehm8tpp8ix* same elastic modulus, but one is twice as dense as the other. In which rod will the speedx ph im1zr85 p;txm*e8 of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart.cnbr5/sg: 6c, 1bs ga/(eoqdjlf;m: b If the tension in the cord is 150 N, how long will it take a pulse to travel from one support to the othg bmb,da;qe bf os(lg:c6/r1s /c:5 jner?    s

  A ski gondola is connected to the top of a hill by a steel bk. g0yol 8f lzmj(gln.86 z-pcable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It ismo(b. g. -f6gjp0z kl8nlyl8z 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 shi 4i n3ppq+tdns2. b3ki-cur r9p just below the surface of the sea. He hears the echo of the wave ref3+ it q irn-sk4 rb2dnucp9p.3lected 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 earthquakeleaqxeker)..hl 5r 0o*a)pf 3 travel at different speeds, and this difference helps in locating the earthquake “epicenter” (whqlae5errx.k30)al )e.hp o *fere 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 apprrv * 8f 1gjghk4g0aa.roximated 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 tr40 fk1a.vh g*8gajg rhat objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the ialqd 9,(ldoe sm9b3t 8ntensities, and (b) the amplitudes, of an earthquake P wave passing thro,qm dd(bt esl8a99lo 3ugh the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquakeem)5 )dg* m0mbi,(.pbfo tuxs wave passing through the Earth is measured to be 0o( exmmb.it*bp5,dfgs) u)m$ 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 t* q:8wvpu -hanhrough the same portion of the Earth, but one is carrying twice the energy. Whatv pun*wh-q a:8 is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, but onu*h v(l;w+npo ;esslz4b5p m/t4 f;lee transports three times the polzp(v4lns4mu;elf5 b+;ts*e wh ;/power of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and doszu;/7houh c2 )zn(aa wn a total vertical distance of 6.0 cm, from th;czaoz(h )su7 uan/2he lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each czuv*v4 mod.u 6ob+l1other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments vm*dubooc41. z lu6+vlater. (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 krt1vr )na wy0n8l h)n4cejcj)k 86,lHz as its fundamental frequency, what are the frequencies of the fi ) jcrlneck4tknh)j81 ,r0lv68 way)nrst four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unbtrwlgb:( x 9 bos;rl)6w*o g5fingered. 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 vibrates as a sl 6b brxso9g* ;t)blw(wgo r:5tanding wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz. Nac7 4t o(dsej2hme at least three other frequencies at whisoj2dte c7 4(hch 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 ,bmc0 o0fply/waves is 475 Hz, how far apart are two adjacent noy/ m blp0c0,fodes?   m

  If two successive overtones of a vibrating string are 28ui4k(4), o .ypndw 8be ) pud)zolbj7 h.p5oyz0 Hz and 350 Hz, what is th,opyi.pyh ou4) k lzdo w)8)pb.5ndjb4e7zu (e frequency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distanb +c;/cexnln8u xkw4 9ce from the bridge to4xc;celnk n9u+xw /b8 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 r(nxy ;ci5td,.3fob pl f)on-supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the lt bc5oirf-yxo.n(np,f;3d )three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate av+6aw h3z-kn 7ro yna5t 200 Hz, but it is measured to v7z5av 3n6 yhraw-+ko nibrate at 205 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 attached to a small-amplituaj- c 32p0d4ytx 2pe-ekpt5 ojde mechanical 60-Hz vibrator. The x py-j3 05pdttapo-4j2kce2e string’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string+w,hrywmb:d)ayu27dfnx .x wn 4.a )o may be adjusted by moving the pulley. If the hanging massbdy7an x.w ,u24)xhwd.ya ) w ofnm+:r m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just s-yhp n t4tw:ytw(c./ the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-t (-4cnw./th tp:swy ycm-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 within the Earth bn tdoq26uez mc;r6+2l etween two kinds of material. If it approaches the boundary at an incident angle of nocu; tz e 6d6rlqm22+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 , 7 -8s;6( if(yul-yi 7;bxsco*izqfbt dwuqxvelocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests make a siu;oz(ibb8 c fy dw*-;y x(6 xf-7q,qsu7tli34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in w0hb0e rvsm h ev-f7:w/arm air when it hits a layer of cold, dense air. If the sound wave hits the cold air/f 00-e7rsevbw mhh: v 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 z +lgcq(1u)fr 6aypbi6gh-1kbo m8.k types of rock at a 3u (6kf.l go-zik qa8b1m61+rg yhbp)c8 $^{\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 d6/h( -xyziu etys*6tc iameter. According to the user’s manual, the dish has to be pointed in the direction of the satellite, but an errorut* - xi et/c66sh(zyy 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 Pa5 /fkzm, 7cpkqcific Ocean. As it approaches Hawaii, people observe an unuc,z/7kq5fk pm sual 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 them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 550 kN:)act*)qj hd / ;pomne/m Find the maxda op)c)n*;tqe :jmh/imum 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 wind f2voym0 zqt(3ow to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves lo3fvy0z(t2 q mike 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 endg:anw2r6m kdt uq 2l)4 of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency lgkdm 42t nuq2)w 6:raof the oscillation?    Hz

  A 950-kg car strikes a hug3j:+rwnhig/8 /al,j/apb hwv e spring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (8 :r3iw,nhpj jbvawl/g h// a+a) What is the spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (dia *gb+ hxnzj9q/-* 3h;d bahcfxmeter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffeenb;z f3ga** 9qh+jhh d-/bcxx.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-rpm phonograpcadu m9-r(3gx h recorm ac(drgx 9-3ud have a wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the eqn7y bvlnwws73r ns). ,uation x=0.650cos7.40t where x is in meters an 3,ssn7w. bnwnrl7) yvd t 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. What is its frequency if iyq,*8r8ht(w, x x g8mof c..oubg0j)5hkfk hmt acceleratgh .0hf q5ubrw*. , 8(omxm of)cx y8g8tjkhk,es at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man s/ :s;8gvxbop c-ccb 9mtands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for a wcb:op8x/cvsc -b ;g 9mhile.
(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 musicalod7.b 5ddz9b-d m t4dg instrument are tuned to play at 392 Hz (G) and 440 Hz (A). bt-7od. gdb dzd4d95m
(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 tr1 lh /pea-j sdtkdob .(+x-k0raveling down the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of / k (phd-0t-ads1l +rjbx. oekcord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and thedds- nd7 , e xjomur).;cn+9:ae6gzrw tip of each prong moves 1.8 mm to either s7sodx z gud.cdne;n 6m ,e: 9+jaw)rr-ide 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 x is n4 xb812be:qtdt9motion of frequency 1.5 cycles per second.4tbtxsdeiq2b9 n 1x:8 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 thwiu.*k.(k ekg ,h 2osx)9nbgxat end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine theu)e. biw ,.ohkxgg( n sxk29*k wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has aup8pq,ph;.6 hom)30nkjlwp b period of exactly 2.000 s — each one-way swing takes 1.000 q.op86h wpp u)h,0lnp bm3;kj s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertical directjt f7r,1xoo. fda71m qion 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 horizonr j7,m atq1.ffod71xotal 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 stnwf1cj+g g)ym7 3h gih (rnt44retched 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 end. Wherem +34rwcjy )7 gghtni1f n4h(g will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with spr3 yua3ab5of mx.b,ni 8ing stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations thanb 3b.8ox3y ,iu5fmaat will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. Thfi8 i7 :(*nbk/,rn)r oq jzhuye steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to i,bq k *z 8h:ry7oj)nif (nur/Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58pmm taoi 6t) 3crxegk21b7m62 (which also gives the dimensions 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 oxigmt 6)b7o2p2 ktca3m16 emrf 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