Give some examples of everyday vibrating objects. gn n3fx4b* .s 1zlnqo7Which exhibit SHM, at least approximatez n nox1.ln*3qb7 fsg4ly?

Is the acceleration of a simple harmonic oscillator ever zero? If so, wher:yq,s mlg k58rq3yhx2e?

Explain why the motion of a1qzbuvck,*t:/dq rhi3w 0*s v piston in an automobile engine is approximately simple haq3*k0ciuzr :1 shw/b q,vv* tdrmonic.

Real springs have mass. Will the true period and frequency be lx ogf1yrkl/3- kz(x( larger or smaller than given by the equations for a mass oscillating on the end of an idealized masslekxk 1yf(l3zg(rx/- ol ss spring? Explain.

How could you double the maximum speed of a simple harmonic tmf3lb)k*uiw cc) : j8ew,1jposcillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spr):clzuf, . amr:+r soring scale, and then is released. Describe the scale reading as a function of timersc+um, ar:o).:zfr l.

If a pendulum clock is accurate at sea level, will it gain or lose time when t//j5z vu(7neiyikb9r aken t9rz ub /v7yn5/( kiiejo high altitude? Why?

A tire swing hanging from a branch reache2j)wxt34rg du )eozek5gm c),s nearly to the ground (Fig. 11–48). How could you estimate the height of the branch using only ar,2eg4mok t5 )je3cd) wz gxu) stopwatch?

Why can you make water slosh back and forth in a pan only-kr jye.n4iix z- ppvnw(m x(4;h.:xu if you shake the pan at a certnjku-xmh4i4xe .:vwpn; rzy( -.( xipain frequency?

Give several everyday ex 6mx p(1 kev7- nhms+4fp*zzugamples of resonance.

Is a rattle in a car ever a resonan-0tdxpo t3u6w ce phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of its so,ud i/a-l)mv0u .z3ux, +lrn0 aikx ksurce? Why o ,a,. / xil+unu)mkv0k3a0rl-suzxid r why not?

Explain the difference between the speed oif9 g-l2yio* eb+6kzpf a transverse wave traveling down a cord and the speed of a tiny pib6i +2y 9p*lgi- foekzece of the cord.

Why do the strings used fox2 0o;j+pk(n xpskdf8r the lowest-frequency notes on a piano normally have wire wrapped around thn kposf xdp0;8+2xk(jem?

What kind of waves do you think will travel down a horizontal metal rod if yok o,vl: g./c5 ku3 g:tsk7wkguu strike its end (a) vertically from above and (b) horizontally parallel to igws3ut:o / g7k,.kk vk5cgl:uts length?

Since the density of air decreases wij73 s+yreie( twdnzqf:- 0gv3 th an increase in temperature, but the bulk modulus B is nearly independent of temperature, how wrdw3evqtge+ 7i-j0 n 3fy:s(zould you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude m **.0g.*jzfqvxtuq81 cqiicxu(0 vn as they travel away from the source tqxz*mc*uv(qxc.niuv*10gi 8f. 0 jq.

Two linear waves have 8aou0 .e ql,5 lqj zecd2.bn8kthe same amplitude and speed, and otherwise are identical, except one has hale 80a je2q,.n .blo udlqkc58zf the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of cord asgjal:j qx /igswt)25*wxc0umim.76 i in Fig. 11–33, the frequency does not change (although the wavele 05x/mux*jigm:.i6al2)ctjwsgw7 qi ngth and velocity do change). Explain why.

If a string is vibrating in three segments, are thered5wmbxwpyu06kh 9at 6h) 1 j(n any places you could touch it with a knife blade without disturbing the motion?nj() hwxdm 0ut96 6b5whkyap1

When a standing wave exists on a string, the vibratio.5o, .u/veyxdfcdko u z2i0b7ns of incident and reflected waves cancel at the nodes. Does this mean that energy was desfo d/5 .7o,ecux2v0.u iy zbkdtroyed? Explain.

If we knew that energy was e-uaqe6,qhc (sd w)d+ being transmitted from one place to another, how might we determine whether the energy was being carrsw hu )(a,+- de6ceqdqied by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the to, dal0s1/9 eigti,mx utal distance it travat / gi0,ldem9iux, s1els in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs fq /vtpran nl ) 5/5vr*2xu2pkcrom it but is 85 cm long when a weight of 180 N hangs from it. What is tp rqv2a5t2nlu5x p *k/vnr)/ che “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver gekj) ixr +e6b3sbsv; kod,+jmv56b1 lu ts into the driver’s seat. If the car goes over am1kj5ji)b+rul6v o6k+,x besdsvb;3 bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hah po-chp lr -ccb7vpx1yno*s8 /048longs from it. (a) What is the spring stiffness cop8hro*-co pnoll08ypv1x4b -s /7hccnstant $\approx$    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 0.6dx-nw3 3)geh1s/t jdqj6x q 6rtp-s3v0 kg is hung from it. What is its freqw)qdq3gh n1/s-x3xsdvj tt-3re 66j puency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x o)cksyy )e:; lzf the mass in Fig. 11–2 at times t = 0,t = cze )y:;k)y ls$\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 wl r)yrz8 s6in:1 gniu7g 0y-w- c-o8vi -gyhfteb. The web vibrates predominately with a frg0f6s8y7yyr)o1wng ivi -z-lin ghu- :- r8ct equency 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 02bj.j*r/yfw*:bmb h*h fol .um 0n/gl.88 Hz. When an additional 680-g mass is added to m, the frequubj by/.** n0o m*w:fj lfl.brhm/h2gency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spn,*;l,g6 z9epltj rh yring vibrates 3.0 times per second with an amplitude of 0.13 6;jtryp,n9,* lg hzlem. 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 ex+fd oz- enl4ke( x9cmfd *2s:v; ft)rquilibrium is the speed of a SHO half the maximum value xx9 :* )z fdefmrd2e+lc(kn;ot-f4vs?$\approx$    A

A mass attached to the end of a spring i t kz.dr,upag(g- r6.ws 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 *xihpup1s;ra s5e3 :-tx( gzwspring 0.315 m. If the spring is stretched anap-;h5sr i w*: sez(x 31xptgu additional 0.130 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 spa2tn vt) 8d;d 6dsjqq,ring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is movi8 va d,t6n2;dsdjqt)qng 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 8t50.nvzj xei :0.0 N to compress the spring of a toy popgun 0.200 m to “loav 5t e:0zijn.xd” a 0.180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontao qvkr0o2/ bcxv,gt57l, frictionless surface is attached to one end of a sprqvbot0 /,ocxk75rv 2ging; 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 compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x = 0.45,9yh z7dsr+:ag:jh l9hs py/ +c;pcx dcos6.4t where x is in me sgpj/7:+alz+dp: hs ,yr;cyd9h 9chxters and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy/lns-s1z:(tj+ 3 s( qf7rfw6mpib/tq qz 8ace of a SHO half KE and half PE? ± 6t aestml7+ f3js1s/8 (zqbrq i:wq-/zfc(pn   A

  If one vibration has 7.0 times the energy of a second, but their8-u1r3t6ab a8ypx ndm0m jsu+(; jsyz frequencies and masses ary-mu8r8j1z sdu (bp+s nx t3ajma 0;y6e the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hekit,9yeq7 k3 anging light spring once every 0.65 s. 7q,e 39kk tiye
(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 suppod +jdifvr vov r44z07*rted by two identical parallel vertical springs, each with springv*vf7d4+ir4o 0vrjdz stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x =9i zo4 q6ee)pfe0;ztx 0.38sin6.5t where x is in meters and t 9z4tozf;e)q6xp iee0 is in seconds. 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 Sh w c:k6schs41HM, 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 end of a horizontal spring (k = 124 N/m) is stt:jklu 3dz kf1wh *0s1ruck by a hammer, which gives thhdl3k01 jkt:zf*u s w1e mass an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness / d78wzf p4kiw8(wthz 8clnn*constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibr *( l fzw8pwznkc8htiw847dn /ium 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 connectejc/x2/(i.s (su bruoxd to two springs, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed horizontal spring wy c u*c0j :oc.dli-vo)hose spring stiffness consta0*o-yccld )c .juvoi:nt is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high bridge. Afts2dehxrr e48np31iv /m4wa7 o er 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 spi4 8r3dxr4 / mse71a2pe hwnovring 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 exactly 60 s. What is 0 sec+put t)kwfu 04lg / xd7:u6jzm*vits
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be i10xx vf h tw/xrfmr 70c.iau,7h5/nmmf it is to make exactly one swing per second? (That is, one1 n hm,m57rv.f7 ca0 wtihx0rm//xxuf complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. kes:- mi/ar he 4wa+ tr2va76y)ea)pjWhat is its period on Mars, where the acceleration of gravity is about 0.37 that a7 e4 ) yh:ak+m)a-r6sp/a2r veewtji on Earth?    s

  What is the period of a simple pendulumhnk n,phm4s 0t-wfz7- 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, th eb2y5*jiver1e pendulum bob has a mass of 365 grams, and it is released at an angle of 12.02y1*ejibre v5 $^{\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 ph9np 1p d8mn obl4,e6sendulum has a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pendulum? shor 4lp9h ombnnps81, e6dtened by    mm.

Derive a formula for the mas) gyx5otv2 h*ximum 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. At it is n,/cvt. fpk+n released from rest starting at.nvkc/ ,pt+nf 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 bo/-5*:a7)ipsjtiyo5io iuyvv bdda/f5 0b3cnw of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the waves traveling?ivus7f d td 3bo*5va jo)ca-i5i yy/0/n:pi5b    m/s

  A sound wave in air has a frequency of 262 Hz and t*vyni q3ad3bvc 9-m ,z5vj l0oravels with a speed of 343 m/s How far apart are thl 05,*oiv3c mz3 a9b djqvy-vne wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kiloherttm 5,5zxnxq 8wdi eu7ef83 7gjz) and travel wj8e753f7qi,g xz tnex 8um5dwith 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 longit+.o c9u+oky aj0j cs8wudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have theevro86 mtr d23 same elastic modulus, but one is twice as dense as the other. In which rod will the speed of longi63 ror d2tmv8etudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is sp;j jyk7 jhd,t43ukk :tretched between two supports 28 m apart. If the tension in the cord is 150 N, how long will it takktk j ,y7kjujp;43dh: e a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of length 620 md n)*p,cfmqh . and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sendp, .d*cq nfhm)s 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 fx.liykp.;y xk0lkbhhqgoii ; (*- 9 2surface of the sea. He hears the echo of the wave reflected from the ocean floiyxi ykki.q;0ohl b *g2.k xl9pf(;-h or directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and this dip-)+nl4 rwg y-g .kbplfference helps in locating the earthquake “epicenter” (where the disturbance tookgpk-lp-4+ w.) lybngr 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 v,ld0ye x 7f rvd;;u-xbe approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (tur-;f d 7xdve, y;xlv0ypical 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 of (a) the intensities, and (b) the amplitudes, of an earthqva fdj7:tyn4e6d13 cauake P wave passing through the E fve31cna46d:a7 tyjdarth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through ths3oy 1gxhvd/me l9l,-f;tm 0h8:zs5vusm5 awe Earth is measured to be ,gy;dh: v/-s axzeh81msvm5359f0 lmlo wu ts$ 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 of 6 ;z2cnghz(e/ kyrps7the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of the two waves? ;/z p (e7c6hrgn2y zks  

  Two waves traveling along a stretched string have theuuce)j-upp:/cg m(;m same frequency, but one tra-c:pc/)m u (eup jgum;nsports three times the power of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of / n n:e (;mcfvnenvs a(1u-cn5a pond is observed to move up and down a total vertical distance of 6.0 cm, from the ln ;-anccn(e n5fv:1vum/( nseowest 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 towardw;e*obqp *xm . 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 eac*emw* ;xpbqo.h other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fu8j7*veh . cpp*wuute) ndamental frequency, what are the frequencies of the firspj) cew *vu*phtu 78.et four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frsz wj,5-ta w6qequency will it vibrate if it is fingered one-third of the way down from the endjw5s 6- tqwaz,? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz. Name at amf5, uin 6*wbleast three other frequencies at whicfim *u ,6bn5awh 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 frequizh; odezt5tu .fq/+6 ency of standing waves is 475 Hz, how far apart are qh+;.fe o/uid zt6t5ztwo adjacent nodes?   m

  If two successive overtones of a vibrating string are 280mz2n axe 9z,cjmx 9f 3j(f ,*9hnrj8tx Hz and 350 Hz, what is the frequency tf* 9a3( n8cmf,2 xx9 j mzjexhr9zn,jof the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance from the bri s) jd18tr v7(gk/khdndge sk17) dhv8(j ngkd/tr 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 overtones?    Hz

  A particular guitar string is supposed to tk7(zgun-cw/yshp0ys 9t( f* vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequencikz/n7yh*y( -9gt0 twfp s(csu es are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is suppo)uvlt j+ck )*exoj(eqi5 hv)- ljx,5tsed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the strin,qvx -ieltu)tl)jv5c(e)k h*jo + 5xjg be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to 2 prubt3wut23a small-amplitude mechanical 60-Hz vibrator. The string’s mass per unit le3u2 rw3pt2bu tngth 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 bejqppuh2t45 +o adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may pqp+h utjo254be achieved 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 frequencyranhl -)e1:o q)l7g 0dopvh8i, 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.)hln0voiqo7d h eg-r8ap) l: 185 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave travewoczzux7 ( np1up4z gs ou5./:ling at k.0 km/s strikes a boundary within the Earth between two kinds of material. If it approaches the boundary at an incideg 5zuu os7n4 x1wz.up/op:z(cnt 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 vel/z xfaj;y2w5tkx8 h ,c: t9rynocity changes from 2.8 m/s to 2.1 m/s If the incid5 jyh2fnt/ :w; z8r9cka x,xytent wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in z6huv+ r2k v/7le)sn+jorj 2uwarm air when it hits a layer of cold, dense air. If the sound wave hits the cold vo) 2vj6r7uz/hrn+el sku 2+jair interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary between two types of rock at aqh6g hczl /-unrgwg r/8)d./.gh*euw 38 ng)-h/.c*h/6 dlwqrzuru8h/g e w g.g $^{\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;wbu; 0n tc1yyoseo4j9j ( o;c diameter. According to the user’s manual, the ;c0jj t41you;w(yos9 bn;oecdish has to be pointed in the direction 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 ti+8e9mcr5 b wkk; i kz.+x mmxmb(iz3gry*2z *ravels across the Pacific Ocean. As it approaches Hawaii, people observe an myi*k(rxz8m kez.b zib 23mg*i5;9c+mkw +r xunusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing ci l-wcs7walgsy 9+i*; ar bumper has a spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collide7+ c9y swi lsilgw*-a;s 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 below, which s/se5x1aj9b3b xvz uv*( bdhheu5e 58ctretches the net 1.1 m. Asseubcvsv 51xx(55b9/ aze 3 8hb*jd uheume that the net 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 ther: ( n7z2ywvq3)mr pdt end of a freely hanging spring. The mass then falls 33 c27n:rz (wr)tmd v p3qym before it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), compr6bqhx1i *awvcc p,6z8essing the spring 5.0 m. (a) What is the spring stiffness constant of the spring? axc8*vp hcw1i 66q zb,   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 r)tl 8k:fph90c xdlsx+0 jsevye l3+pr r(3ps-ight pace of about 1 step per second, the coffee sloshes more as3rjysfe3d00:vc(+k+)x xhpll8e p t p sr9-lnd 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 phonograph2 jmj*u u:nbg2j2 cn;k1 3xtiv record have a wavelength of 1.70 mm. What will be the frequency of c3tbxg1k* :v2 ;iuu22mn j jnjthe sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x is in p4+ tzu00vcn ometerscu0v o04+ npzt and t in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum os cudl ut6 g:35jug3,cjcillates with frequency f. What is its frequency if it accelerates at 0.50g (a) upwac cj3l6ug: d3 ut,u5jgrd,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands k6: 6anc9/a-mqrykga on the raft, it sinks 4.0 cm deeper into the water. When he kqa:c696km aar ng/y- steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play at 392 Hz (G) and 440 Hzhkqc 25aa; yn- (A).2 cnh kaa;-y5q
(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 travhzhr95 nx2q-y u;z 7maeling down the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) 975rquz2ay zh hx;mn-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 frequenjv1b6w;bdjf(yi,/d ocy of 264 Hz, and the tip of each prong moves 1.8 mm j/fbvdyi 1,bd ;o(6wjto either side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillatend x3-;bd ok.zs with simple harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of thb z3-dxk.dn o;e board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” envjis3(i oeh ov)/dt sz8b1 9k0d if that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of thet3)/ jz1dissi98bok( vo h0v e resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of wy+qb7 c*or5xrggwd (/nl9 t+exactly 2.000 s — each one-way swing takes 1.000 s. lwwo+5q*tgr /r d7yx 9+bncg(
(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 o53pv +fvbv0xt7q6 av 9nx0gmcscillate in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the mxx bv5vn76 0+vt 39 cf0qgavpperiod 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 pulsyq ur ,fz2vg7/e is generated at one end, and 20.0 ms later a secvr, fz u/qgy72ond 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 stiffnesa m4ds5j7myds,+zk 2k1ydicw/. 8 bycyr/w: zs constant k. A penny of mass m is placed onwmd .w c/ :z2bk+c15sz,k84 rdy7yy/ yidsajm 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 tpga7h h-) ax75sg jxt8he junkyard. 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 the cable. What is the period of the bouncing? [Hint: Refer to Tablh7j agt) hxpx-ga5s 87e 9–1.]    s

  A block of jello rests on a plate as shown in Fi4 frdqqiph+-k:k ub- +g. 11–58 (which also gives the dimensions of the block). You push it sqk f-r++:kdbi-pu q4hideways 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 is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz