Give some examples of every-+e -5muk wz xukiyq,ohx9ms-5g3 bs 7day vibrating objects. Which exhibit SHM, at least app -g5he-xm5 +3xi-bq,zuyku k m7s9oswroximately?

Is the acceleration of a simple harmonic oscillator ever zu79s0yx b3fb gero? If so, where?

Explain why the motion of a piston in an automobile engine is approxim yuvb4gz63 r+zately simple harmy3r6 +g 4zbvuzonic.

Real springs have mass. Will the true period and frequency be larger or smalle.34ggg zyior dq s(k8. 6)o+8uou d;aahm4txrr than given by the equations for a mass oscillating on the end ofd 3 s+4 yggo 4uak8oqut(r 6.hadxgr;o)8mz.i an idealized massless spring? Explain.

How could you double the maximum spee+01gukc f4 xjs0dtzmtu89 (ibd of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and theb:tz56j5jsa7 tm1igs9 tl l8on is released. Describe the scale reading as a fu 15s68 jzlts7abtl9jmg:5oi tnction of time.

If a pendulum clock is accu0 lt2l x k.t4oov0otn3rate at sea level, will it gain or lose time when takxoo3 n2 4klttol0v.0t en to high altitude? Why?

A tire swing hanging from a branch reaches nearly to the yar s*.+hp)rt ground (Fig. 11–48). How could you estimate the height of the branch using only *y. srph+r)ta a stopwatch?

Why can you make water slosh back 38r-kx)5buhr; can+rf dm -l jand forth in a pan only if you shake the pan at a certain frequekxjma uc5+rr-lf;hdn -b3r) 8 ncy?

Give several everyday esg pqv(q4n 63dxamples of resonance.

Is a rattle in a car ever a resona1irnsr**t z/ntuf 3 1nnce phenomenon? Explain.

Is the frequency of a simple periokd/r1x + q:ddm )vq *57hsgzwo+(nd rgdic wave equal to the frequency of its source? Why or why qrh7+:d /nd1 +gdxmvqsozg*w r()5dknot?

Explain the difference between the speed of a transverse wave traveling d/llpi0 q4faqqalk/w (v)i ;,nown a cord aqlf/vl(4/,ik q )wla qnip 0;and the speed of a tiny piece of the cord.

Why do the strings used for thes.di+ts755 ikqw kx-j lowest-frequency notes on a piano normally have wire wradk+iis75 qs5k-t jw .xpped around them?

What kind of waves do you think will travel down a horizo3qf:vjta5 -cy- nks.f ntal metal rod if you strike its end (a) vet3-s:v fck- fqn.jy 5artically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperat)bsy )e;.epjrure, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperatpr;ee.)sb) y jure?

Give two reasons why circular water waves decreasejpj73/bf ir5pqz u. 7a in amplitude as they travel away from the s juzjb7.a pfi5 q3/pr7ource.

Two linear waves have the sam.onvnh u2(r f (ky-44 6ccyjjse amplitude and speed, and otherwise are identical, except one has half the4.-u2yy nkjcjrv(hf6n (c4 os wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between vc v2dqhi0e(gt0w- 0d two sections of cord as in Fig. 11–33, the frequency does not change (although 0ic2 wtvde0h vq0d -(gthe wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any pciil ,w;zeys0rhiu(+.b1 s 2d laces you could touch it with a k;(w2rd.eilyzhu is+c01,bisnife blade without disturbing the motion?

When a standing wave exists on a string, the vibrapl 74qtfst,4hi ,: zsstions of incident and reflected waves cancez ,s4q7p,t4l isthf:sl at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to anowmsit8+4nwhovi uc 359vu +i-ther, how might we determine whether the energy was being carried by particles (material bow+ timuc-hs 89wiv 5uonv3 i+4dies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the tgzqi 39,-*dqf7v g/g dtud8wiotal distance it travels in ondt/uqi*igv gd97d - g,zqw3f8e period?    m

  An elastic cord is 65 cm long when a weight of 75 N hanl:zl:fc(25csuh, q(8shjb p fgs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constantush8 5fbcs:hlf p2z:(,lc( j q k of this elastic cord?    N/m

  The springs of a 1500-kdn0 kgz0gjuv:d121kfg car compress 5.0 mm when its 68-kg driver gets into the dri kdvngf :z0kdgj121 0uver’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 whenc 8bymvhq 0xdvxg(is;.,7yov fjb/7 ov53p-b a 2.7-kg fish hangs from it. (a) What is the sbhb cjo vov7-xifv, 7vydsy3;8mb.(pq / 0g5xpring stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mass of 0.60 kg,od xj.0euvg* is hung from it. What is its frequency if only 0.38u. d0jx,egov* kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. by q4m :-6.c)ulc89vv) r5fwlgnwzw j8;vjsx11–2 at times t =lsy wcwbj 8; 5 )x4- 6.fqvv)rl:8z u9cmwvjgn 0,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web. Tp. h 5dn-x0vwzhe web vibrates predominately with a frequenc xn5zhdp.v0-w y 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 vibr3m* ,re9qurno ates with a frequency of 0.88 Hz. When an additional 680-gn3erqumo,r 9* mass is added to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second wiyu yn4ke.6/e k6k8vphth an amplitude of 0.13 m. Dete .8h6kvnyuep/kk y64ermine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed of a SHO half the h v4-rjbcih,:6ovza 9maximum value ji,h:4brvzah vc-o96?$\approx$    A

A mass attached to the end of 2 q 1r1k3;u*q**xu3f9dcjie rarwop p a spring 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 0.3157d:ni e7 ,jdhf m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equnjf :ded i7,h7ilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stin--xm)w1qqjx 65 q+ga8zxs 4uudt -lcffness constant k = 280 N/m and is execuxu5 qd1 jmxtc 4z-qu -+gaqw- x)8lns6ting simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a toy popgun 0.20027kyu9uq5ib ,q0 gwxj7st5yw 1cr(er i4 f. br m to “load” a 0.180-kg ball. With what speed will the ball leavei wq.r15yiyrqetxfs9g ru 4,bcjw7 uk7 b0(52 the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is a;7pj21b2rve 6kd dzvdttached 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 released from rest with the spring com7kz p 1;2v6ddjre dv2bpressed, 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(ljdjus(-v* q .4t where x is in meters and t isq j-( j*(vdsul in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of gmfs9 wp j;1a9a SHO half KE and half PE? ±f9 amj 1;9wpgs    A

  If one vibration has 7.0 times t.nwvg)2 vmb2/x-dtip he energy of a second, but their frequencies and ma-/xvtbn gipw.2mv 2)dsses are the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spkv7+flgde, vo/j o.3e5 hxr n+ring once every 0.65 s. e 5djl3kho,/o +gn7v+ . efrvx
(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 sp 81 w95euxe0vj0r ;svm+nukh rrings, each with spring stiffness constant k (Fig. 11–49). Wse u vhwu+x 0 5mj098rvek;1nrhat will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x is- 0x c,,j5p*ful thjzvi o,.vo in meters and t is in seconds. Deter ji-fux h.*j5l, ,v0vp,oot zcmine
(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 examplef1s myue7i/v)s of SHM, labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the ene:*w sjlx3x8kd of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mask: *jle 8wx3xss 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 30pp v- lrwj)avg-u ldo6+a3/i 65 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 velocitypo v /-uwl a jadr+)v6l3-6igp at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring stiffjx+v;-y*) ra mtg,wdhness 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 attachwjyv; pfa8-o1 ed to a fixed horizontal spring whoseo p8ya ;wf1vj- 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 high6 fu-,t j,goph bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eig h,g,uj6t-fo pht 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 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 exactlq4*a- m:y y xlnuv-;evy 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simplza0xzr-p f2 e8) 11mbfuvpj(ke pendulum be if it is to make exactly one swing per second? (That is, one complete vibratfavz81(m)jek 1x f02 p ur-zpbion takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. Whalw+tww 3zf:) hk.dl 8yt is its period on Mars, where the acceleration of gravity is about 0.37 that owyk hll fwd+8 .):tzw3n Earth?    s

  What is the period of a buh(f)s61mqq0ivkc , simple pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulum bob has a vesou +stl:5wi *)oct qmj+.2mass of 365 grams, and it is released osmlts2.v+t c:+eu q) w jo5i*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 lengti8(k +*mgqbgwf l6ov/h of 0.9930 m. If the clock loses half a minute per day, how should you ad/b+ (6i gkgv8w*fmoq ljust the length of the pendulum? shortened by    mm.

Derive a formula for thecj ;; 2rv+ pahg*rf:ix maximum 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 Hz. davo/d9h3 ;fl90ea*:q khwcawjq0n4At it is released from rest starting a 4lhoj 9 k9evha;cw0aa3 *wdnd0qqf:/ t an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchored boat 0oxr0ic9/7 j isj: amc nfx+ yr+gh7h/every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the /0 /+9gir7janhr+0 fymx:co h7c jisxwaves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels wi3zjb l:9/h /iimkc1v oth a speed of 343 m/s How far apartvb :i/ l/hjkcoz93mi1 are the wave crests (compressions)?    m

  (a) AM radio signals have f ycrryk s*3)x26i p/tfrequencies between 550 kHz and 1600 kHz (kilohertz) and travel with a speed ocrf3rs2yy6) i*/kx tpf $ 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 in4fc5 7i6/s6wsxu glmr
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modul1g5lt6y ez 0 7al0wkipus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be gre lyw6i7lp1zt0akge5 0ater, and by what factor?   

  A cord of mass 0.65 kg is stretched betweew1 nzogj+ae( a: 9p7tmzsq6,jn two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one supp w:m9pa(a z,sjgn7q+6ejzot1ort to the other?    s

  A ski gondola is connected to the top of a hill by a steel cabl*gpj d 8;rybg 2 :;i444iqc0gv m)whz olpd*gue of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 sl vq48 ; hgg )gzji w44ibd 0y*pru:ogcp2*;md 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 9j: 4smfvj4s (9 obztudt)kr-surface of the sea. He hears the echo of the wave reflected from the ocean floosjr9u (9m4dj)ttv b k-4s:f ozr 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 sp36fww:7nav,e m-u s jweeds, and this difference helps in locating the earthquake “epicenter” (whejva6 umww,7s3f w:- nere 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 surf*0b4nbr yt0jtmgb p;4 ace wave can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies),0j*r g;b0n pt mty4b4b 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 (b) the amplitudes, of an earthqz j8+5 *fg(owsph4 yhct9 zas0uake P wave passing through the Ear(4 9tj5a fs spc8zwhozh+0 gy*th and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through th fw)ry/m e(dd)e Earth is measured to be w/)efrd)( y dm$ 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 frequenc +b7vgq,q xdrv cn1.4k suex,7y travel through the same portion of the Earth, but one is carrying twice the energy. What is the+vxd s7xe,,74 1.bv kg qcrqun ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string hm+hl-,ab d smkx6*tp8 ave the same frequency, but one transports three times the + pmhkla86m dsb,tx *-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 my38oeme;hh:2 bq -txdove up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, bx y- teqed3bh;8:mh 2oy what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) Sketch ec46kro- o s29wdz4lru8ow:yea: ; apthe 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 pu9ruy2owc z ld p;4oa4:e-ars :we86oklses 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, w(wuu,7qt sp czlrl6n0vj85/sd:e k.uhat are the frequencies of thtu,k rw6p 5e udv/7q0ujlsz.:nl8(sce first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered4;/pr)h aoiro sk+5qu . At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a st +;uh/5 or)4r pkoasiqanding wave.)    Hz

  A particular string resonates in four loops at a frequency of 2wv-0czb kvg 3/80 Hz. Name at least three other frequencieszvk 0b 3cwg/-v 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 thed4 qdz 4p1d2vma h- s p:4b0yuo*sqz8p frequency of standing waves is 475 Hz, how far apart are two p8:4bv-*q01hz yo4p4ampqdsz2d udsadjacent nodes?   m

  If two successive overtones omkqjb+lxwaam):9q 6+ f a vibrating string are 280 Hz and 350 Hz, what is the frequency ox +qjwb+:a6qk mm)la 9f the fundamental?    Hz

  A guitar string is 90 cy 8u/2jezeh ;xy6 sn) 7z-ggssm long and has a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 52usesynz6 /ex)7g8z;j s2gyh- 0 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it ;vws(/3h9-8selsbsl py y: len1w d(vis measured to vibrate se p(l:ve-wn y9 ysl;l/d1s3 v s8wh(bat 205 Hz. By what percent 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 200q n 5 v2s+uyfj6-uq zd3vhr45p Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be chanu+3 hj4n-szyp6 5frv ud 25vqqged to correct the frequency? decreased by    %

  One end of a horizontal string is) a2d++ cbijzb fe8i;z attached to a small-amplitude mechanical 60-Hz vibrator. The string’s masa8e;zfi)d+c b2+j zb is 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 pulley ff f9h mnyc;2;n1dp)p. If the hanging mass m is fixed at 0.080 kg, hopfy9d;n hfn 2p1m ;)cfw many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the wate vjwtee983mj chlz.+ 4r back and forth in a tub at just the right frequency, the water alternately rises and fajthwlemz8 v3 e4jc.9+lls 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 the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strike1 dpy9q.yho1;7.j emh fx0zns s a boundary within the Earth between two kinds of material. If it approaches the boundary ayh0oqnmh9 .1yx.zp f1;edjs7 t 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 velocity c 8 il.xpbb5yt,am+o+changes from 2.8 m/s to 2.1 m/s If the incident wo i+amy b.+x,8lbtp5c ave 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 layer10 tul pnv :vfr4 uj04y77umm 7w(sldp of cold, dense air. If the sound wave hits the cold air interface amfyt0nsdrlu:p4wv 7uj0 (ml717v4u pt 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 t ef t1sew (jov +0gcif.1je:;wwo types of rock at a 38:w wjoiv ef0 1sj(1g;.fc+tee $^{\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 *t(biu8xhne4-7u i3dhv9b j sdiameter. According to the user’s manual, the dish has to be pointed in the direction of the satellite, but an error of abot47 ub*ix3i-dh8 s9jv(bnuhe ut 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 Pacif7ou:ssr m 3jsv-pj .t1ic 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 them attracted to the shore to see stranded fishes and b os:7j 3pvu1s .jt-srmoats.)    min

  An energy-absorbing car bumper has a spring2 fmbt p8*a-lc stiffness constant of 550 kN/m Find the maximum compression of the bumper if thept m 8*cflba2- car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m bebxf kid)ihz8jz* 4e5, low, which stretches the net 1.1 m. Assume that the net behaves like a simple spring),d5hj bz i*f8x eizk4, 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 w-t u5uz ))vurte a0- :h f(48mscparmspring. The mass then falls 33 cm before it stops (t:54u)ah )faw80rtsrv mz c- mu- eupand begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring ajet 3o55 /dph-l rv3r9mcuan:t a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (ao/eha3:j5-9p tnc mr dulv3r 5) What is the spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just the right pace4br xi(ub) :jikb6+ et of aboutkje6tbr: )i ixb(+4ub 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.    cm/s

  The ripples in a certain groove 10(6upq;-kv5ne,mz fl68lzy ejy3bhnn8 (q0 ee.8 cm from the center of a 33-rpm phonograph record have a wavelenk(b86 qhefqzum(0pn,e;ye -nz3l5 8n e6 jvlygth of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0w5bjpa-2ob ., s7jofi.650cos7.40t where x is in meters awb.5ofb-j,7p 2j sao ind t in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency 2qo0u)u a7 j n*bjt0hkf. What is its frequency if it accelerates at 0.50g (a) upwardaoj b)qtu k n*7ujh200,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raft, it b n)/p-5h ifyhsinks 4.0 cm deeper into the water. When he steps off, t yh ib-nfp)h5/he 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 a04 d.o;cdanvja.*dg7wrktd x 5b7dj+re tuned to play at 392 Hz (G) and 440 Hz (A) tv. d kj0xbn7dodcr.*jw 7;dg4 +aad5.
(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 stretchyp4x0aj*pnp t1 gv+/v ed two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavel y4p+1a*gptvvxp0n/ jength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequencyl 4b0f(p/t5 l;zfmo2q7orx 0/qoxkmy of 264 Hz, and the tip of each prong moves 1.8 mm to either side of center. Calcf5m o2tr /lpq0kobf/4lmox7 xyz;0(qulate
(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 harmonicnl +-)k6 abkmd5rvsx1 motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the k k 5)da+1v-mr6bsxlnboard can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a 0p )1xmvn*ug*ipfx:dm(i f 1yring that can slide without friction on a vertical pole (Fig. 11–57). Determine the waveu0p:mix1 1* )vdmyn* gfxif (plengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a periak/8( y6w3aalu2qbrkx c 6 y 67rq+rkiod of exactly 2.000 s — each one-way swing takes 1.00 ulba6k a3wqca82(k7ry r6yrx/k6 i+ q0 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 spuke7)b7j ga- mring can oscillate in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same tim je7a-mu) g7bke. 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 stretce s:ogv0x :hv.hed under a tension of 255 N. A pulse go0x: v:sh.veis generated 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 spring sti/ 2 9lkitj4ficffness constant k. A penny of ma2c9if t kjli/4ss 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? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. Tcv:t 439umr ;tu)xmmuhe steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing?tu9x3cr u tm;4umv ):m [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in 8jn7:.ay 9 ;ngv+gnyi w -fuwy ev/u0qFig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequeg+;eyv : y9n ngw a7-wnq8u/f0ui.vy jncy 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