Give some examples of everyday vibrating objects.61 5.7j s wgjmci jrv8zdmkm+5 Which exhibit SHM, at least approximate .ms81wm6jjkzv rgc5+7 jd5mi ly?

Is the acceleration of a simple harmonic oscillat qjp9gx w.*so5or ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approximatim)j3 vy m/x/wuha;1vely simple harmovuw)1ymx /hjm;3/a ivnic.

Real springs have mass. : m-7gyomo i.zWill the true period and frequency be larger or smaller than given by the equation g.i:moym7z-os for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximumh5+u.v:xkq9gekp *m lic 8 d7y speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attache,b0ncup9 gf k+d to the hook of a vertical spring scale, and then is released. Describe the scale reading as a func0g9+,uc np fbktion of time.

If a pendulum clock is accurate qr4r a lpwxnqt1npt-/1 7 2u4aat sea level, will it gain or lose time when taken to high altitude14u2r7qntt n rplp1wq4/aa-x? Why?

A tire swing hanging from a /; g8dyq c-;ipfj;:yrr)pgy bbranch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch using only a sbrp; gcr -ip y/ yfj;qg)dy8;:topwatch?

Why can you make water slosh back and forth in a pan only if you sh.six 7 ).wtm wyis27r+t+ueg make the pan atirs) +xm 2y+gi.tw7. 7uswt me a certain frequency?

Give several everyday 5f oc *52akwsfexamples of resonance.

Is a rattle in a car ever aa d3z)kimxk 9* resonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of itso3ovo5,.2 t b,0p miykjypz i+ source? Why or wz5o, 3pkb20,i m .pijo+ytyv ohy not?

Explain the difference between the speed of a transverse wave-z mo,a8g5hd z.zoy(e traveling down a cord and the speed of a tiny piece of the cord. - do5m(.,zyez 8oghza

Why do the strings used for the lowest-frequency notes on a piano norms5n*cuqp.6nh vcs 2j,s(. esqally have wire wrapped ar.6.c s(s2p,sncnhv qsuqj* 5eound them?

What kind of waves do you think will trwr bjjm):+ kb2avel down a horizontal metal rod if you strike its end (a) vertically from above and (b)b)jwm kb j:2r+ horizontally parallel to its length?

Since the density of air decreasedr(9c /qwf aok.h b9f+s with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in ai+d9faho(b9q /r.cfw k r to vary with temperature?

Give two reasons why slu(r,gfoxz- ks 68 .tcircular water waves decrease in amplitude as they travel away fro.z ,g l6ssrko(t8u-fxm the source.

Two linear waves have the same amplitudw-09 styjua1i4a 7cq tm(x0 yde and speed, and otherwise are identical, except one has half the wavelength of tha y-ji xyq90w1 c0mtu4(td7s ae other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sectio5 n 97fcmvael/ns of cord as in Fig. 11–33, the frequency does not change (although the wavelengta5/fc 7n9 vemlh and velocity do change). Explain why.

If a string is vibratinwt z:pen)3qb fo7 sq(vch;*f1g in three segments, are there any places you could touch it with a knife blade without di)cq3e1hpt7o v fwqb;*n s:(f zsturbing the motion?

When a standing wave exists on a string, the vibratdwl iokp 5kna /2+;w4k *:oaqsions of incident and reflected waves cancel at the nodes. Does this mean that energy was des2q id+5ls ka no4w wk/;kapo:*troyed? Explain.

If we knew that energy was being transmitted from one place to another, how migvnva,dg//6 s bn-ko c+ht we determine whether the energy was being carried by partng vvba ,s/+/6ck ndo-icles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, whao /u(zkvarj72t is the total distance it travels k( 2j/o7uvrzain one period?    m

  An elastic cord is 65 cm long when a weight of 75rjfa tx::jp -a z.it*bv2/f5k N hangs from it but is 85 cm long when a weij:ia-fv5t xz:t/far p .k *bj2ght of 180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when it+px2(-dqj c.hxm hoa +ryeh+*feo; y)s 68-kg driver gets into the driver’s seat. If the car goes over a bump, what ohe +yajr* xe( m+dh p;qo. 2y-+c)fhxwill be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 fiy7xir8-2vzt+x+a n kgm z2y v;+3avcm when a 2.7-kg fish hangs from it. (a) What is the spring ;2f8 y3zay+k im x+vvi2n+vztg a-rx 7stiffness 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 u4/ yxz+rl2io 5ch.azof 3.0 Hz when a mass of 0.60 kg is hung from/xrho.zuy alz2 4c5+ i it. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of tvsvq3d,zvn( 9he mass in Fig. 11–2 at times t = 0,t =9vvvqnzd 3,s ( $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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’sgc e(x/gve .-pms 3fr67fjbm - web. The web vibrates predominately with a frequency of 4.b/cx7s 6jge( .3fmrvg-pem-f 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 0.8uf14 77 etz g1wdg6hhv8 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is t1u4 f7gwv h 6gd1h7etzhe value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times pl9 9s6q2jvkjv v 7ov;1un/rlaer second with an amplitude of 0.13 m. ql9k2 ojauj 71lns;96v v/vvr 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+tss.4cyn )- fx4wny.w-oqrq a SHO half the maximum val -sy nx.qcqf t4os yr)w4+n.-wue?$\approx$    A

A mass attached to the end of a sprn* qlu nbdh50p rlir8dc r :1(5v+vhq5ing is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. If the s+-)nkxokl5ksvea;n 0ina r )t -*)o 3no (kqhbpring is stretched an additional 0.130 m and released, how long does it take to reach the (newaolnqeh3t-*)0 s+b)k nn) o(v-xin rok5 ;k ak) equilibrium position again?    s

  An object with mass 3.0 *y 9 19cjcizj/cufh1q kg is attached to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When th j*fj 1yiucz1 /9ccqh9e 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 to compress the spring of a toy popgun 0.200 mq1b4wliq 5 d6md/oj)x to “load” a 0.180-kg ball. With what speed will the ball leav1b/4 dq5)joixw6qm dle the gun?    m/s

  A mass sitting on a horizontalep).k8pr5s xtr ,:mx u, frictionless 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 the mass is relrtue .,mx)psk:r5px8eased 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 tx-x1 ( k4 mjrap8vf pwak7)qxa,*n(wshe equation x = 0.45cos6.4t where x is in meters and t is in (n7(w 1xkpqa-a v8rpsxf j),aw4*m xk 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 energy of a SHO hae m2leb2khfi6; )(8 jmbc.jl6wmg tz9lf KE and half PE jmc.l fzel) k2b m982;6ihewbm 6(tjg? ±    A

  If one vibration has 7.0 times the energy of a second, but their frequencies and2yiv0nzdg(-9s x,tc z masses are the same, what is the ratio of their amplitudes? c iz0-9gsyv 2 nt,z(xd  

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring oncev-zs/h/c9k1 j,tk h2r0h, ols st-mzr every 0.6t-2-0s/1r/ rkz jhz hkmh sv,s clt,o95 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, eve9-g. u ua y8ji+blm5ach withl85m-bue a 9+vyu. gij spring stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equ4t o9j hc(y9 1a/ltdebation x = 0.38sin6.5t where x is in meters and t is in second e4 t hb9l(o/1cdtjay9s. 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, labeled . 8ltqn x5kww 1ludw/4A 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 end4 qkl2espj)+f nln;6 a of a horizontal spring (k = 124 N/m) is struck by a h;nf+l ) k e6jnspq24alammer, which gives 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 st4j:cnk r.4:vhw qra:,zhf7lhiffness constant 305 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 positivkhnz4 qw ::.4jrvh7: hc,frlae 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 sprdcz uv/lp- -(z;wx1ow ing 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 stri, kdh/qwodskf7, /nwm6):u t mkes a 0.600-kg block attached to a fixed horizontal spring whose spring st mhd)knm,t:do/q/, wkfs w7u6iffness 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 bm1 7dj 4np7rbhigh bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight morrb pbnd1477j me 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 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 exactlb+1gfnbjp 3a 6y 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendueu x7vp6 9zkcgsmdl/p: 2+tq3lum be if it is to make exactly one swing per second? (That is,2z6:7cudq3s9vp mkel + gtx/p one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, wheae i/)l; 9if5arx4 syhr rn:u*re the accr/ur5f)a9ies r4ya;: nhilx* eleration of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendu we-xf r7.5hj-f; yzsnx2n /wwkp6dk9lum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulum bob has a mass of 365w i(q 2lfd / iqkq6ss ;j6ieg,s88.uhd gra ii,;8wdq6u2iqh.6d/j f(ksg 8elq ss ms, and it is released at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 krnld3j/r ngaa 50y: :i0bi/ym. If the clock loses half a minute per day, how should you adjust the length of thbn:/0yg5:iy a 0k/nliadrj r3e pendulum? shortened by    mm.

Derive a formula for the maxjc:kyh/ n aw24o k6pe)imum 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 adox3r)1sxw a 2 frequency of 2.5 Hz. At it is released from rest starting at an angle ofrws do3x1a )2x 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 every 3.0mrx;zg/ yqc 49 s. He measures the distance between two crests tmz;4c9x/r g qyo be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz andsq-a4.t g ma/uw4t l+ax)+ikq travels with a speed of 343 m/s How far apart are the wave crests (compressions))xw 4 takuml+atqi/+- gq.s4a?    m

  (a) AM radio signals have frequencies between 550 kHz and:wom ntxm1 y+1ddo0,l;eq x2d 1600 kHz (kilohertz) and travel wd1 xtx02ld,nd1 yo:;m q+moewith a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal waves in .*rautjo9 fr 4dvw-m *,2dugx
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same ;doxa;5p;k y celastic modulus, but one is twice as dense as the other. In which rod will the speed of longi5;c kd y;pox;atudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If the temgsa6*g) qwf;ynt6w7 nsion in the cord is 150 N, how long will it take a pulse to travel fg;y) msgf66 twn wa*q7rom one support to the other?    s

  A ski gondola is connec+ 532;2i3dtgge 5p9 czil,bhn hhyjxrted to the top of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of p hd ,h5+95itxzn32rj;eggc2l3 bhyi 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 hvw8yetw mit5r: 592peears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this yree5tm5ww: i28t pv9point?    m

  P and S waves from an earthquake tracy1fz dym lb 3,ze39z8vel at different speeds, and this difference helps in locating the earthquakm, 3 e8z3zbzylfdc 1y9e “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 sinusow1f vrzd *.:vjuclx+ deb-6xs7 49gcaidal transverse wave. Assuming a frequency of 0.50 Hz (tyv6fjbz1v 49s+x:-g*w ca u. recl7ddxpical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio ofk jnvn(n:2skbgi09 .lfoxg8: (a) the intensities, and (b) the amplitudes, of an earthquake P wave passing thrfvik g0:82n:g lk9(njn xbso.ough the Earth 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 measurcd)bqe .ubfk/up2h- 6ed to be uuhkeqcfd.- bb6 )2 /p$ 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 portionx*nafcuc)h 6d q;wjh 8 *.nn+u of the Earth, but one is carrying twice the energy. What;auh *+8cfh x u)qnnwj dc6n.* is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequjm9d 1 pqpjp/g eds/)0ency, but one transports t0ppg 1)jpd m/s/e dj9qhree 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 oby/ i1n dm*- c:ieoabk9r1g .683egczqdn to c:served to move up and down a total vertical distance 1-.ind6zi:norcbde octky ge1: /c 8*a3qg9mof 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward eacq9w7vup 9t z* +e( li+xvy;pnqh 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.e9 ;7pt*u9qlqnw+ y+ x(pzvvi (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 frequency, what *y ,; u;uy vmp*iji3gn*o. qseare the frequencies of the first four hv yis q*;;*nmj*p3u, ug.o yiearmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency wil5by-p )4 etfaxl it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of f4) pet-abx y5the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops a3*35 jrz jxq(4ctd trpt a frequency of 280 Hz. Name at least three other frequencied( c*54tt j zrpqx3rj3s 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 fre gxw60 lck p/g42vheg4pb+z9o5cz5tjquency of standing waves is 475 Hz, how far apart are two adjacent nogg54h j/cczo l tpkp0z 4vb 9+wx65eg2des?   m

  If two successive overtones of a vibrating strit ns4ek4x9ya(t9 f c/ bc(8kss k4-ccgng are 280 Hz and 350 Hz, what is the frequency of the fundamc/sbks-txs kf4k 9cec(4c (9gy8t a 4nental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The dista kayw5w)u9ev vxu2, o9-mu v/cnce 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 the fundamental and first two overt92-,uuvvuk vx5o /9)y ww ecamones?    Hz

  A particular guitar strin27gsv+ p,we(a9a xgmq g is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent sho9sm q7pg(a+eg, w2x avuld 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 gkw/tze0z8qs25 s 5e bvibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the 05b2 et wg5e /kqzssz8tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached t63ko:s c l+dhq4xzta hw8hn25o a small-amplitude mechanical 60-Hz v 2s 8a64tw+c5d3: lhxkqh hzonibrator. The string’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be adjust o8(7hpx o)tpoed by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved p oop7to(h8x) by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the right freqps.fl1 cq-8crf m2ch: uency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to cffr m:lp. shqc-218 cproduce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s sk eh79 v- op0h;gfn7gqigo+9.mj6 hvstrikes a boundary within the Earth between two kinds of material. If it approaches the boundary at an incident angle ovg +fjsmqin9 hg7e0kgh9vph7 o;o6.-f 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velocity chk04tl q 2ro2loanges from 2.8 m/s to 2.1 m/s If the incidlq o2ot420 lrkent wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warmcsvnm 49xo. xi 6m(9wq air when it hits a layer of cold, dense air. If the sound wave hits the cold air ins.4wimoq (vcxm 699 xnterface 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 of rock h5plqa1krks 94 - w)jzat awprks z4h-)j9 1al5 qk 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 about0:u9 oj pay2ijq o3r3i 0.5 m in diameter. According to the user’s manual, the dish has to be pointed in the direcuo i:ia33 qj90pojry2tion of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 km/h travels across the Pacif 0i/mea+lc s0aic Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them0ml ca+/esai 0 attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffyo y0 4ixq zd7os1v.7iness 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). [i 0is7 dy7o1xqo v4yz.Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire netuim8 vzb:(ky4 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a simple spriv 8bz4mk: iy(ung, 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 sphci7-sw +auj +ring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of ts7h +i cwa-uj+he oscillation?    Hz

  A 950-kg car strikes a huge spring at a sp ;dd/z)ri0 .*3gv0hzeyrv* f msr+yhweed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the yhs* zmegirvr0*vyw+;f/ d0r3zh d. )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 (diameter 8 cm) at just the right pa mwdi .z2w x8;c+vxz xia d0q406d-fhoce 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 in4;ziwz+a8hwdmco .fdq06xi dx2x-v 0 the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of g s21hr tlf x-(4w)yro(iqr sy6 b)i;ta 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sound emittedoys(r()h)wf4lyi r 6xbr 2qgi tt;s-1?    Hz

  A 2.00-kg mass vibratek1l*hp fdl.wv2v7 kfllk5((w s according to the equation x=0.650cos7.40t where x is in meters and t .1h*kf(vd5lplv72wlk w lf( kin 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 isji2jyz+ tuff1n v1a( 2 its frequency if it accelerates at 0.50u1na(ifj21 z+y2 fjvtg (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the rafza* +ssaa w)t1t, it sinks 4.0 cm deeper into the water. When he st s1z*staa+a)w eps 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 instrumw1gqq*x( wg k*kl((ww ent are tuned to play at 392 Hz (G) and 440 Hz (Akwwqgg ww(ql1(*( kx* ).
(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 travelinir1e2f j*0kl-ug ; )a2lgwfyeg down the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of uf2i g k-*l)wfeej ylr;02g1athe 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,e9gx,u. w oef of each prong moves 1.8 mm to either side ofwoegu .x,f ,9e 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 harmog .gce(0(w o1tyxh pwx peap1z+,gb52nic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in or 1pgyt0xa(g (woz,. whb5g+21eepcpx der that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a ring thas/4, a3 y havgxx(pq.dt can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the res3p/x4q g vy.axhsd,(a onant 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 swing1fgh7-x+r yypt1lg m0 takes 1.000yghft m1-r7g y0l1x+p 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 direction o l2s5cvgyh2*w wm 5swm6adj74r can swing as a pendulum of small amplitude, but not both at the same time. Whid5 h67wlvsm m* 2sgj5ca2w 4ywch 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 tension of 255 N. A pu;cn b;sedvog80u1h d-lse is generate-0c;;bd ogu1n8 dhv sed at one end, and 20.0 ms later 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 spria3+klaox ;v 9mng stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amakmo; l9v 3x+aplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyaj;z- qzaj,.clz:v/9f gyk .vtrd. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car .fvlk av9zjjg.y,c /: -zz;tqbouncing 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 (whicsetmm,lq 1z 1:h 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 of this vibration, given that the shear modulus (Section 9–5) of jello mqem :,l 11stzis 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz