Give some examples of everyday vibrating objects. Which exhibit SHM, at least oquj1 8d9xnt-qyr/ :w4f ir6l app jxqwtu- 8lq9ny ro:f64 /idr1roximately?

Is the acceleration of a simple harmonic oscillator dml6j/fy00+j pdn s12r qgs.y;jq3m rever zero? If so, where?

Explain why the motion of a piston in an automobile enginlp8,vp vhe-6t 1 a8fqpe is approximately simple harmonic.1 tvq- p,pev8fhl8a6 p

Real springs have mass. Will the true period and frequency4-eqqdg9v sm eu xyv(0dm1q 8:s:j9uu be larger or smaller than given by the equations for a mass oscillating on the end of an idealize-q :xsud9ugdmjsqv (1qe490u8ev: ymd massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillator z,)fdxn hu ;5l7skg/o(SHO)?

A 5.0-kg trout is at -05mvnn/6s yop*c aywtached to the hook of a vertical spring scale, and then is released. Describe the scale reayoyp06 n s/n-c5*mwavding as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose time when /k:qmy 37+v.dx1zihg7tu kbdtaken to higi kgmk73hyq d b+:v xt7.udz/1h altitude? Why?

A tire swing hanging from a branch reaches nearly mzn,8x ie-jde,k d(u, to the ground (Fig. 11–48). How could you estimate the height ok dizn,x ,d,ee- (uj8mf the branch using only a stopwatch?

Why can you make water0euao c59re - mwqa;d) slosh back and forth in a pan only if you shake the pan at a certain frequency0c;do5eaw eq )mua-r9 ?

Give several everyday exampll4y/qnjvu v/5f x 7mb.es of resonance.

Is a rattle in a car ever a resonance phenomenon wi(:a ./raj0vd6 nqdr? Explain.

Is the frequency of a simple periodic wave equal ldu 9;x0sqouh) w2y/pto the frequency of its source? Why; lqpo0u suh/29wxd)y or why not?

Explain the difference between the speed of a transverse wave traveling u- *x kelmv kd;tn:s+(down a cord and the speed of a tind:x mk+ tvs-;ek *lun(y piece of the cord.

Why do the strings used for the lowest-frequency note p8e3ab+bhy6ni-wh( 9xu(lf) t wej +ts on a piano normally have wire wrapped arh(w fet ehn8i- y9xu6ajbw+b p+)tl3(ound them?

What kind of waves do you think will travel down a horizontal metal rod ig-i d. f 6b cihs7t4arl,viyumlp9i) .v+f(l; f you strike its end (a) vertically from above and (b) horizontally parallel lifv,h4t 6.v p c7ur a+i;-imlyidls)g9.f( b to its length?

Since the density of air decreases with an increase in tw8md+ q(z,/j1*z6tc*fgmqowoi 9pg memperature, but the bulk modulus B is nearly independent of temperature, how would you expect z*,odoq6g/mq zg8mpwm1c+jtiw*9f(the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decreast j-z2tc(k4 aku/ba3 ye in amplitude as they travel away from the sou3ayukb/tk4az2- jt (crce.

Two linear waves have the same amplit0jrbb1hhy ;nh7m1 kngs2z4q: ude and speed, and otherwise are identical, except one has hhsk;rhn 04 2bjyb g qn1:m7z1half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses wl03j7dkm/mgqc dzg- .v9 kx5 the boundary between two sections of cord as in Fig. 11–33, the frequency does not change (altho.gd jk9wzv05cxg7-mmq 3k/l dugh the wavelength and velocity do change). Explain why.

If a string is vibrating in tfr4)j+tjj j)6lhot0 three segments, are there any places you could touch it w )t0r 6ojjl+fhj4j)tt ith a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incident and risdro2 a0 qok/o 2 3xtr;+hqp)eflected waves cancel at the nodes. Does this mean thati q2r khqod/)p;sto30 a +ro2x energy was destroyed? Explain.

If we knew that energy was beinglrsw;fk w;bv 00h fr4x)1:nhs transmitted from one place to another, how might we determine whether the energy was being carried by particle0 ;f rwf0hr:)shb41nk l;wsvxs (material bodies) or by waves?

  If a particle undergoes SHM with amplitudk jzw 4v8-,rage 0.18 m, what is the total distance it travels in one periodaz8,v4gr kw -j?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it bu 0c;m2zn7wf 1 cv :ubfu7,fznmt is 85 cm long when a weight of mnmz0c72zwfv1b, u7u fc; f :n180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car comp) o,7 9ixrr-*nyvdihxress 5.0 mm when its 68-kg driver gets into the dy7dx i rr9v*,xi-nh)oriver’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 from it. (a) Wha(2lruivh948.f-;f-fxxd rvtdx *+ o ou r6 ihht is the spring stiffness constaxhxrv;o l 29u. hdftir8dx6-vrofhu i4f*+(-nt $\approx$    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 of 0.60 kg is hush:n4 ope( av :z:-pswng from it. What is its fre:oze p(w4s hv sa::np-quency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating tsax r p+sas,ph5s ,8;dhe position x of the mass in Fig. 11–2 at times t = 0,ts8xa,pd s, s5rp ;ash+ = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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. gqrtqcb4 8q9 3l0 ksd04axp;2 r2nnj hThe web vibrates predominately;kqtna c83rj2s l0h4q0b4p9n rg qx2 d with 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 frequency of 0.8ne7nt hu*)p 4 zvyu35 mu/nax78 Hz. When an additional 680-g mass is added to m, the 5tu7n/mzn)u4 axhvnu p3e7y * 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.qyr pj 4ulnmtn2+s2/*0 times per second with an amplitude of 0.13 m. Detult /y4 qrjsmnp*+22nermine
(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 equilibriunq )w9zz9o3os m is the speed of a SHO half the maximum valuenqoz)z 9sw9o3?$\approx$    A

A mass attached to the end of a spring is stretched a dis7 r l 0doev9j+pevnw98a1l(hntance $x_0$ 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 stretcxc0k1o ;e wb5bbk2s l /y4nr+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 r5s0 vybc lex4+bk1 krw /no2;beach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached t8ga3udy /xf7.l4 bhm jo a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving wig.7/ufx84ma3l yb hdj th a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring7kam c1gs)n*r of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the bgmrk*71c a )nsall leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one end of a.gbd joz.g83obdfp: b* +:im d spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest withfz+gd:i 3dog..8p mdb:*ob jb 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 xus+6xm gqsd f;o 3j2+n is in meters and t is in seconds. Dets ; +qjnods+f6u x3m2germine
(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 * id2m0i x s o 9kuffa+5xl 9xy7cwq,-jqdf8i,energy of a SHO half KE and half PE? ±2,9-ifxld8 j s5 y0xcw 9uo7faqif+*ki,dxqm    A

  If one vibration has 7.0 times the energy of a second, dt8,hfq o 8eew z4pxw6 n rmpaibg0 z9*9ia;),but their frequencies and masses are the same, what is the ratio of theigdzzq)pfb, po x8n89;aiherai*wt,m96 4w 0e r amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically haneh+:n.wrp, c31qa d awging light spring once every 0.65 s. wad :1ew 3qra+,h.ncp
(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 verticab 26 vl hkh+.r0qi-:n rp/gqzvl springs, each with spring stiffness constant k (Fig. 11–49). Wh+2l kv: ih /.qp 0g-rvnqhb6zrat will be the frequency of vibration?

  A 300-g mass vibrates according to the equatnweyd h977n ng;je/r;z/a c) bion x = 0.38sin6.5t where x is in meters and t is in seconds. Determih g 7n r;nzdan;)c7je/9wye /bne
(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, lab mn* 2,i- qdjmhv(ie1geled 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 sprfis goh3t kiasl8- 8l0sl.34v ing (k = 124 N/m) is struck by a hammer, which give8 3 lt0-.g8 iisoafs hl4vl3kss the mass an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305ecey-7)mdu7*rn e+ (d bxqko9ezy- 4 t N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity attq7+d4 o)y7(e*-9emeune-dxzy rb ck
(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 sk 0atb3re:)5ca lhf5o(6vswto two springs, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixe6i(cb ovy; 3iad horizontal spring whi3v a(iyo;c6b ose 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 jumps from a high bridge. After rey09 abb;q vx4 fon3o1xaching 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 level of the bridge. Calculate the spring 9v;n q1xbxyfo 0ao4b3stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in ;+a;yptgg 1x 4x:pp cpxj)k7gexactly 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 on w v/orbc. hw)xl*m13ie swing per second? (That is, one complete vibration takes exactlyhmi vlox1/3b.wr)c *w 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period t 9zbsiwrwbc0)2;d;lgf4 x)d on Mars, where the acceleration of gravity is about 0.37 that on Eacbl wi;dtd0xfg)4w9s zb2r) ;rth?    s

  What is the period of a simple pendulum 80 cm long 0:,4xtoiwb:psln ql cvk 5 q2,
(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 peno:ciz /1d gb5+rviqz:dulum bob has a mass of 365 grams, and it is releasv /zbicdz:g:r 5o+qi 1ed at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 m. If the clox11bjqg4ly puw(2 8h ock loses half a minute per day, how should8ju1( bxgw pyl4qho1 2 you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the ,,ikwo f :q lgw5:fj46bqe mu4maximum 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 Hz342ftl79sybing9l0 54yscz yg9yio s. At it is released from rest starting at an angg049f5cli s3 tniyy9oy 9 24yz7slsbgle 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 bow0c hwyd2vb *iv)9fdm: of his anchored boat every 3.0 s. He measures the distance b0dwi)d2 mb9y*fvc :h vetween 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 travels with a sp+,prt g7uj(a aeed of 343 m/s How far apart,jpa( g+7 ratu are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies bet6qsk o,,;dpm iween 550 kHz and 1600 kHz (kilohertz) and tr,s,o;di k m6qpavel 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 longpe4 c+ 5jqgmuq:z,ho7itudinal waves 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 5w)5 c9albcekn5xqi,vh z:f.as dense as the other. In ibfavk :q z,x. )e5wcln595chwhich rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg zacf43ja0tgjw*ruh3 8i o ,k5 is stretched between two supports 28 m apart. If the tension in the cord isro*g w 4j8j u,tafa5zk0ci33h 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable oycvw17(pal : xj z 90v9z)uglrf length 620 m and diameter 1.5 cm. As the gondola comes to the end oflx gjzr :9)u9p v1(c0 way7zvl its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the surface of the sea. He hear xz 7sx/tqf+ rywwf3+9s the erf3+xywfqz/tw79+ sxcho 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 speeds, and this diz*n.q u a5 ngub9xv;b5id tj50fference helps igxb 90 jqn biaztud; .55*uv5nn locating the earthquake “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 approximated by a sinusoidal transver18 ghtfvv6 k3ad*n.a yse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually i1 fhy g8* a6vavdnt.k3nclude a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (l(qc52a :gjei6n*www3ume ; tb) the amplitudes, of an earthquake P wave passing through the Earth and detected at twowljmw 526iew a(g;n cu*: 3etq points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave pa5*zi* u cj 5d6gqnl0(ijl-lmvssing through the Earth is measured to be (5q5jzld*vg-li m j n6cu*l0i$ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency travel through thk22y wv2bm8 j4 0kfkbse same portion of the Earth, but o2kvy8 k2w0m b2kf sj4bne is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, but one gq3uyyzih.gfzl52yg.( 21fd transports three times the power of the other. Whygy 5.qg(2z2y1fdzfu3g h l.iat is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down a to kx8 )9acfaw8:ptu, tetal 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)xa 88wte, ua9ftkpc : KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) Sketch ther; wz-y3kmwnykt3ov y4 :(6kq shape of kz k ny(yqm to6;vr4:k-yw3w 3the 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 to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequevrrb t+ksx1in0i- ,;zncy, what are the frequencies of the first four harmonic+nb 0-itr ,k1srzv;x is?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingeredc, n8cbs*izs( . 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 vibs( bc*,zsc8ni rates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz. Namk.d kda)y 9+vje at least three other frequencies at which it will resonata9dj).+vy dkk e. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of stand8 pi psfibk14v6;*omving waves is 475 Hz, how far apart are two adjacen1s4p;8p6*ibo vv ikmf t nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, whaaap 3;q+tuv23qhkxz 2t is the frequency of xh ata p+u3 z22;qvkq3the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of sji;t7 a v4jg 17qut1h3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of ti17h1 vqt;s4gt ujaj7he fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is measq.h ul3yk,fk6.3tk no ured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the threelf3kkkh.3y 6qu t, o.n frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, by,os( y1qk*rq u2u;di ut it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency? dec*,uyqqy 2ik du 1r(so;reased by    %

  One end of a horizontal stxn+l-bh o9zj1bg) ): 7zn,:zwkt 3azboq0h l dring is attached to a small-amplitude mechanical 60-Hz vibrator. :z h:1gw-b 7b+ x a9)do)k3t zo b0nz,nlzqhjlThe 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 may be adjusted by moving the q , )oo:.ihnnsxh *evswbkqgo,.61u2 pulley. If the hangiqh* qoi en21k)gb,oh6v wuo..s,nxs:ng mass 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 ad1 lcdrpywrn4db)z + *f485yc209v a nije3pd tub at just 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-cm-wide tub is 0.85 Hz. What is the speed of t4 4 jd8p)a3zcdrn0welfrid yb95+* dcy1vnp 2he water wave?    m/s

  An earthquake P wave traveling at k.0 k 2 ch gn4ek8lnjq13j lrgy;.9xm/s strikes a boundary within the Earth between two kinds of material.lkyhl3. ;2 1cnjgn jr8eg4xq9 If it approaches 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 the velocit6geed88ur c*j*lw 5w4m ibfx-y changes from 2.8 m/s to 2.1 m/s If the incident wa ij8rfwde4x8el6wgbm-u c* 5* ve 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 hi :u 0(uyhj)yxzts a layer of cold, dense air. If the sound wave0z ujyx( u:yh) hits the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary between two types pw-*bqry uc4 +z/vhy 2of rock at a 3 zw cu+ybv4r/qp2y*h- 8 $^{\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 abou06rh.l kib:*phoo )vet 0.5 m in diameter. According to the user’s manual, the dish has to be pointed in the direction of the satellite, but an error of abou.bo r6hvk lehi0p* :)ot 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 Pan6 aa/6kc,t d. aw,)oqfu+pf icific 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 hav)p6w .tfoi/aa q,nd,ucf6k+a e 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 stiffnes *id)( dyzrvjulcn:0.d g0gz5s constant 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/h). [Hint: Use conse n(zrvuzji d*l d)0g5y0.d cg:rvation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, whiche.14z1kehbzqbp r0 8v stretches the net 1.1 m. Assume that the net behaves like.ez10b z hq1e4prvb8k a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hangingr6n+pil) x5i p spring. The mass then falls 33 cm before it stops and begins to rise. What is thr)ii6p 5n p+xle frequency of the oscillation?    Hz

  A 950-kg car strikes a huge)( cc 0otyi,xl spring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the springxo clci,0(t)y stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just the right pac070fnsnnaid1vt 3h yjj+q w6.e 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 coffee.+6dn jhvn wqj.s0f 1i 7a3nty0    cm/s

  The ripples in a certain groove 10.8 cm from tt5 r lic;9tk)khe center of a 33-rpm phonograph record have a wavelength oli ct9 )r5k;tkf 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.4kl6i)na; o 9;btbgvbrc g k;7650cos7.40t where x is in met; kb tlg ; a;6c7orvngib4)kb9ers and 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 osc 7o,udh* wk +*nipe- hcqp-y+lillates with frequency f. What is its frequency if it accelerates at 0.50g (a) upwarde*np-u lh -oh+q ck p7+w,y*id,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg manub2qyjs 6yi13n .m)t k stands on the raft, it sinks 4.0 cm deeper iy13jnky )i .sm6u t2bqnto the water. When he steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to plaatr2;o h ;s*hly at 392 Hz (G) and 440 Hz (A).ah*s2h t ;lor;
(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 o ke3)et.l 1lbrf Fig. 11–33. Detel rke1.)3bl termine 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 cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of each prong moq: d+v;uz+ z st+or-hmves 1.8 mm to either side of center. Calzqd+ u;zhv- s+: rmo+tculate
(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 fa6ftk 2ge6 j/drequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed th gdje2af /6t6kere (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that enrx ,h r+7zh zgm1ayhw)0h8c7 rd is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other hzh 10am87r,wrc hh x)y7+ grzfree.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way snc7e :9ycb3aaut ucjz; r,n1/ wing takes 1.000 sra3a9jbun1e ;7cn/z y, t:cuc .
(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 t,q kkm(ur.g 3zhe 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 tr kg.q3,mz(uk he period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched under a tension of 25:p f: (1dy:e)io jzb37 vyfqda5 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the t )jydifv:pz o3dby 7qf::1(eawo pulses first meet?    m

A block of mass M is suspended from a ceilismaf. c, +rs,:wfi:lws- zl g(ng by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations,lf( c:f.alr sm+wiz:,-ss gw that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 0 -(kfbhig*dt1200-kg car at the junkyard. The steel crane cable is 22 m long and hhg-bfkdt0*i ( as 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 Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which also ma.w2tbx3yip ziyh2*/*t xsvn;/p/ngives 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 a3ipbt/;nhxspztvynm 2 .a/y x2i w* /* 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