Give some examples of everyday vibrating objectudh yx0x 7l(r3+ jucg7s. Which exhibit SHM, at least approxi0 dyugcu7ljhx 3 +(x7rmately?

Is the acceleration ,wm1 klpino.46; vefjy;sz; rof a simple harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is apprjxkbaq j v*i2 k 6hweg4 4e:gel21 cv1l16lqg/oximately simpl 46i1q4egh1xkecj:wlljqv l1 a /e6g 2vgk2b *e harmonic.

Real springs have mass. Will the true period and frequency be larger or smas/d e0hgw+ -j /xbgp6f q;ejx)ller than given by the equations for a mass oscillating on thxgjf/ -h/x)ds 0ebej +w6g p;qe end of an idealized massless spring? Explain.

How could you double the maximum sx lmm*:jze0 c+x 9)4eltpzle *peed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring svci4pn yg3l1au vo5,; cale, and then is released. Describe the scale reading as a function of,nvc35gua1iv;yl4 po time.

If a pendulum clock is accurate at sea level, will it gain or losea nec: dwaa3t: r vox01iu7nflx*9(,y time when taken to high altitude? 0 anwxef9r:*ia(nx3a:y,7otv duc1 lWhy?

A tire swing hanging from a branch reaches nearly to the grjp.34vh( x 6v *uvxcqsp), nvsound (Fig. 11–48). How cou*j uvvsxnc .hp 3)pv46xq( ,svld you estimate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you sha,4w*sy,dxe lks3 5 as2 g+xulike the pan at iwysl5lg2ekd,4 +sx3s ax ,u* a certain frequency?

Give several everyday examples ov19(ykh ft4qoe: 3*mdx+x b xbf resonance.

Is a rattle in a car ever a resonance phenom qa,)fz0atwe7enon? Explain.

Is the frequency of a simple periodic wave equal to the fr39ka 2 ue6q,g- daokwbrrt y9hu5q7-gequency of its source? Wu t-,kduhk r w5ba-23gr7a69qey qg9ohy or why not?

Explain the difference between the speed of a,fa 5neu f96vblu6 oy/pnwqy4g m8 +* /nag(qt transverse wave traveling down a cord and the speed of a tiny piece of the/nlqgf(a4+oe6p ,g*/b v6tqfay umwun9ny 8 5 cord.

Why do the strings used for the loc p. mc+w57vfwfr1m t+west-frequency notes on a piano normally have wire wrapped around thm7mt.+fcrv1c wf +w5p em?

What kind of waves do you think will travel d0pm*h: 11 wopfi ktj h*np9t*vown a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally paralle ohhf11j* ppmwkt**nv09:itp l to its length?

Since the density of aiqhe;e i m7tcx94-dt 2ur decreases with an increase in temperature, but the bulk modulus B is nearly independent of te;t9tiqecx4hm 72-eudmperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease izd9 c9q)-s tdin amplitude as they travel away 9sq td)i-9zdcfrom the source.

Two linear waves have the same amplitude and speed, ancnx*flvg,qzxn 1r so3 19fr7d1lax(7d otherwise are identical, except one has half the wavelength of the other. Which transmits more energy? By rng,*szxv 91ol3xnx rl1caff(dq1 77what factor?

When a sinusoidal wave crosses the boundary between -zhgm 6keg9v*q .yj 5wtwo sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and ve6.9zm hwy*5 -e qgvgjklocity do change). Explain why.

If a string is vibrating in three segments, are there any places,e jq0 dfiqxk0xr *1rpth, yo):ew+u ) you could touch it with a knife blade without disturbing the h1yw q,rkeop)q u:xr0,tf) d0*x +eji motion?

When a standing wave exists on a string, the vibrations of int6ovaq,:hg 1w eguww)/ r;4jh cident and reflected waves cancel at the nodes. Does this mean that energu a6jgwhv/o4:g, w;rq e1tw)hy was destroyed? Explain.

If we knew that energy w0es8qzea)l cts(7w. tas being transmitted from one place to another, how might we determine whether the energy was being ca7 et l8wq.at sc)ez0s(rried by particles (material bodies) or by waves?

  If a particle underg/f7 n9bjx t.icw4a3+g mygh4 koes SHM with amplitude 0.18 m, what is the total distance it tr3mkgtxf4 i97y bja.h+4/wc ngavels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs fz)s4pg (by e*lube,.f rom it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constanl pf*b)seu.,by4gz (et k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver gets into t+tn:: yuw pw;phe driver’s seat. If the car goes:pnpt;w+:yu w 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 hangsgkt;l crh 23(l4fgv 7w from it. (a) What is the spring sti2; ctvf37lhglg(4 rkw ffness 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 of 0.60 kg i 55zveojt1 *cbs hung from it. What is its frequency if only 0.38 kg hangs from it? o5v5eb1 *ztcj    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at times,i86 fyqyot:biveuswcz(d334y - 3l q t =ceq3 y y-vbi8fd6, o33uwyz lstiq4:( 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 ssc)lj.- e*v1c*scy3mf l xgq3 pider’s web. The web vibrates predominat3j*.3)sgy cmxclcl 1f -e*vsqely 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 0.88 Hz. When an ikdkif y j3*k: kx2u98additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the value of mjx:u k*fik ykdi289 3k?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.f+v l;;t,5 s bu2aevab0 times per second with an amplitude ob2;fbv5vsale, u+ a; tf 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 tm8,6bu czgy - i0ra1yuhe speed of a SHO half the maximum valum, y uc -y0gbu8a61zrie?$\approx$    A

A mass attached to the end of a spring is stretched a dista ;azek 5oi5 .s,jykv3mnce $x_0$ 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 0.315je2pasmxfo/ 7n,)8 bv m. If the spring is stretched an additional 0.f v7p8 aoe/s,n 2)jbxm130 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spm 4nm1z2x cvva gc;o5a6 q360+gczajaring with spring stiffness constant k = 280 N/m and is executing simple harmonic 4az a c5;gv+3 6n mocjmzq1g0av62 xcamotion. 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 2sr9(lz o 4e9ebvp rvf6r9d088o sjvy to compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what spee62 obdz88r9re sj v0syvo vrlf94( 9ped will the ball leave the gun?    m/s

  A mass sitting on a horizontal, friz uf9n:wzzsh9hfr)a b2;+vnp3h f1 0fctionless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If tf)zh9fs+; nhuva 2 0h3nfw9bfrz1:zp he 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 = yy05o m-tucf :n4,rwo0.45cos6.4t where x is in meters and t -u ot:5r onw4m0,cf yyis 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 displacementw)a,n4z 2d yxzn sjcfho1vs(9 6 6lcc/ from equilibrium is the energy of a SHO half KE and half PE? a/hnsw6c fcv29dz,nz1lc(xj 64o)ys ±    A

  If one vibration has 7.0 times the energy of a second, but their freqzq /mh;)yjm*4s3 ,d z j.dsj*. ;saiq;y jbumnuencies and masses are the same, what is the ratio ys d hyn3mj.)./ ijq;j*aqujsbsd4z,m;;mz* of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring once evdo.ocp:6y e n4it(eo 1+xz1t gery 0tzo (ony1t c4+:eipo g1.6 xed.65 s.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallel vertical springs, ea9q a 6ggj1+jcdch with spring stiffness constant k (Fig. 11–49). What will be the frequency oj16aqg+c d9jg f vibration?

  A 300-g mass vibrates vgkvi ev-d65 gvio x+8 lop6,1fjf6n+according to the equation x = 0.38sin6.5t where x is in meters and t is in secopk j 1vfodex gvl8f5ii6-6ov +,v 6ng+nds. 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, lo75g8x ka1w1d , u qf,i;x6nm5zuhog mabeled 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 = 124 N/ecm:y06 mfr- :ajyh( em) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Deter-60em (f rj:h:aycyemmine
(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 constaq 8l 8un8ww, 8.yyj6zx 0tubljnt 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the eqy lq8wwu yz68,u.j nl0 t8jxb8uilibrium 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, witho(*ughvuk 5n-h,wym -iatq1 .0cc 6 +;ubtg qj 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 uwip;eg 1 k7 /pd.5fmrfixed horizontal spring whose spring stif5/k mfd w71r.upgi;epfness 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 hiyr.z8 2-o0*iowgu7 ykc xtm9e4ef)hm ,k7rh j gh bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched lengthu-,wfk829 mi)z0k 7g. ty o mo7xhcjh*ee r4ry of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 60 s. What is itsaxrc qi+ h 76;z ey4w(e7ji9yf
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is ticvvs o2d6oph3x p0a2d )ubo 8)r6qj 6o make exactly one swing per second? (That is, one complete vi)d66u v pav j 3rh x8)d22pqosoboc06ibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, whevo; 3ks*idpv7 re the acceleration of graps*i;dv7k3vo vity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm lonivo 3fl3h tg( elik*: g66pop1g
(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 0ov6vzg tft9zab 54*ependulum bob has a mass of 365 grams, and it is rel*g te9 o54fab zzvv0t6eased 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 hlq d5tuu2cme;vdi 80(as a length of 0.9930 m. If the clock loses half a minute per day,tqiue825;d v ul(0md c how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum sul0 l;cwj7o w8peed $v_{max}$ 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 akegyob,68gs -w;* ovc0 c fb)2.5 Hz. At it is released from rest starting at an angle ofg*-a8f owoe y;g0v bc)k6,s cb 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 oku2+o;nln25dnf i o9 8mn ec.that wave crests pass the bow of his anchored boat every 3.0 s. He measures the distance nonkoumenlfn9c. i;2 +8d25o between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed o-z l,hxwm8 le.f 343 m/s How far apart are the wave crests (comp8,.- wlzxmh elressions)?    m

  (a) AM radio signals have z-r,zh camvh0y;4ff-frequencies between 550 kHz and 1600 kHz (kilohertz) and travel w h;4yf-m0cr,ahf v- zzith 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*w 2, 08w4cfcrxs g0nq 3dixyt longitudinal 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 twicq)h oexxo 4v i.c-1wjwf09g8re as dense as the other. In which rod will th-o 1jx) vo9h.w0e4cw8ifr xg qe speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretche: czzlbv 7+,-yxd5n zam(jf*j(o 7ohsd between two supports 28 m apart. If the tension in the cord is 150 N, how long will it (lz n7+bdf 75j:zz *,hcm vy-o jx(asotake a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top 0w 6nlpjiawr*t7hm )0 of a hill by a steel cable of length 620 m and w6n) amw pir lj*t070hdiameter 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 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 bel+sacg0xc3n aoc bc;09w7c0p low the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean a9+;7 op s 3nw0bcaclc0gacxc 0t this point?    m

  P and S waves from andt ) tf8;dgw,-j3uc 1bqdooqjns 1it08m ,8wc earthquake travel at different speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbance took plg,01t8,d tsnuocm;tbwj )- jdid 18q cw83q foace).
(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/kc q.:to, rr a( pmp0p8povi* 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 rp .o*/oiap0:,kpmq(cv rpt8begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of an earth,w e1q )4 mrlwhx:8uulquake P wave passing through the Earth)hemw4xl8 ,uu r: 1lqw and 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 to bhmvg/cs8 yj +;q(ngy .ri; 0yhe gyhn vmjrg8;q+/c(. ih yys;0$ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency travel through the same portion o;ac(,lx;avglk:*itoewz r x(;r fc)u (;kz4 cf the Earth, but one is carrying twice the energy. What is the ratio of the a(l klox(*c ,zg 4 (v z;ew;)cuc;k:;rxiafrtamplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, butltc94 pv vhs3331 en)wr-vwl i one transports thre4l)hepsv twl33w 1nv-9rciv3 e times the 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 am (rsf:qz.ex;0 w:o7e3kza rynd down a total vertical distance of 6.0 cm, from the :m0ekzx wr:eyrfqsaz73; . (olowest 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 inro* -4jahj4 sn Fig. 11–52 are moving toward each other. (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. jjn*ao4 - hsr4What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as a0i)2ow ;pu dxie 0j4nits fundamental frequency, what are the frequencies of the first four harmonicsjp2duao w )inx4 ie;00?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency will it v6rzlg /wylz4n 9/j 1znm c67zyibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wagn njz6 zml /7crlw41yz/ y69zve.)    Hz

  A particular string resonates in four loops at n.k zn7;xrps7 wzy+ :mx3b cu3a frequency of 280 Hz. Name at least three other frequencie rnzysmp u :x 3ncxbz.wk7+37;s at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the .+/uuo8h d hokfrequency of standing waves is8o uhu.+ kdh/o 475 Hz, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string ar02o(f yl;ctdle 280 Hz and 350 Hz, what is0y(od2llf ;ct the frequency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance from thendu/ t . ef x.x3ol8cac(a7tvcnh 17*h bridge to the support post is L = 62cm and the string is under a tension of 520 N. What ar .ht* 3 8(e/cx71ouxdnf cvhaacn.7 lte the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vigb7 dvd:cwlgh 5.hx z9:7qv 7tbrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percentzhw vqg7d9lg:x 5c.:bt 7vhd7 should the tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, bxf, 7d.72z ajgi 1vcglut it is measured to vibrate at 205 Hz. Byl1ic27xv zg 7agfd .j, 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-amp;a/dqy v-*ouh o4l ty3litude mechanical 60-Hz vibrator. The string’s mass per unit lengttv4aoy d-/*l3u;qo yh h 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 thd )48oq11cm c3e thldte pulley. If the hanging mass m is fixed at 0.080 kg, how3e)tccth4d ldqm8 o11 many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water 7 84ae .8p 9egbaywaraback and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. a 479gbw8p8 aaey.eraWhat is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s stri6pq/0ms /fsymkes a boundary within the Earth between two kinds of material. If it msm6fs0p /yq/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 “shelnc ox2 bg6tuga1q6v( 1ofn l39f” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident c lng29t6f vaqunb og11x 36o(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 l si/7xffs/xc3ayer of cold, dense air. If the sound wavc/ 7ff/xssi x3e 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 twe(o 7, mr/b zqnkj:in+stiw5f(y1j9xo types of rock at amz in+:ys((f,iw5bqkoj/j 9et n17x r 38 $^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m in diameter. Accolkt*f fn5fy,i w6uv9u- -cug6rding to the user’s manual, the dish has to be pointed in the direction o*56ynu6,9tu - cv-uw fk lfifgf 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 hw m-+rv+puc7 4,gygdvelocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run tmyw ,7g+-v r4g+pchduo 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 o2 lqvh phq:c u;-1esi.f 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a waqe.p-;sv c2 hl1:u iqhll at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fi 5 gvv /+9w++zrnvbb3 +wimwsgre net 18 m below, which stretches the net 1.1 m. Assume that the netbz5nv+wwbwsi+m+v9v g g/+r3 behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hanging spring.4)w)wgku:qs b The mass then falls 33 cm before it stops and begins tog)uq4 wswb) k: rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed* 6a9t)vffmqf of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness consfq)t* vf9m6aftant 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 cu ;19up a6nk dp.e8zlpdqe y71kp of coffee (diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more ak6 dud k11e.nqe79p;py a zlp8nd more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-rpm ph ;.dei3 cxks8oonograph record have a wavelength of 1.70 mm.sik;o3dx. 8ce What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x hua24r+d c 9mn:rx7z 57ipwmg is in meters and t in seconds. Determine acgwih r2 n4z 79+ x7mmud:5pr
(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 i8 -a,h3txxwjdp;j b 7d1cyl2 of it accelerates at 0.50g 1;h23 acx8 jpx7yb d,djltow-(a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands ong q4cz ak; noyr;l8 a7b-w.it: the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for a wtk;b -4:i czla .rya7qwog;8nhile.
(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 instr6zx+(:dm: b 8catizs-t ae4z jument are tuned to play at 392 Hz (G) and 440 Hz (A). a6j8zadsb4z-+cxeit t(z:m :
(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 +z.1- kxnbjq2k/cnxz8d gt7znf r6 u2the 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 section-kugk1j t/ zn zqcrnd762n.x2fz x8 b+s. 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 id6cqq*+h;l1sy h++wb rga6jeach prong moves 1.8 mm to either side of center. Calcuqqr+1gl+hha 6;cwi+sdy *6bj late
(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 frequ8cj1hm*.a t.ode zkm 1ency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble pmkae*cd.1o.8tmj1 zhlaced there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is dsfgbon/70 ezrk, ,4m attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengtk se b/,or7 0nf,z4dgmhs of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swicv: lq2/4kij2o wxvv 24j1kq -b+fuaong takes 1.000 s. ck a4v+f-vqwo1i2 2b 4kv l2/jq:ojux
(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 direction org :,0rejf -yp,0l :xg5),thx 3vci kvz- iitlb can swing as li:cz30bvxk),:er-5jtl0t-y x,ih g pgvi,fa 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 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 tensioni*9m+rhx+67e zylm (f l v7inu of 255 N. A pulse is generated at one end, and 20.0 ms lrim7 felv(yli+n7u*9 +6zhmxater a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with spring stiffz,/tqar- aioqs eh0 ,;ness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Asq ;ie zah 0-,t,s/arqosume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyarlpo+6xjjuidg*:b e /b q,1n-vd. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of thud1v-b+jjgb, o:pxl iq/ ne6*e 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 gives pd0;yk6ory7 ) +aktpu 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 toypt 7k0 +pud)k6y; aro 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