Give some examples of evermn od.m8nsf,yk 9n,uc0q 59b fyday vibrating objects. Which exhibit SHM, at least approximates nn.cdmq ff9y0 m n5k8bou,9,ly?

Is the acceleration of a simple harmonic oscillator ever zero? ic/cp dg1r5s1 lfh.:rIf so, where?

Explain why the motion of a piston in an automobvt qun0w+ o+e+ile engine is approximately simple+oq+0 +ewunt v harmonic.

Real springs have mass. Willof;d gs w)v1;g *sj3wn the true period and frequency be larger or smaller than given by the equations for a mass oscillating wg g) osd* wvsjn;1f;3on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmoniusba, 5:07h h1 cxyyysc oscillator (SHO)?

A 5.0-kg trout is att 3pw qv(6n)inyyd8hn:te) , ix.hhf7 mached to the hook of a vertical spring scale, and then is released. Des7),wd6y8f3 mp.ihi etnyvq)hnhnx : (cribe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose tqku qe9; 2d9dpb* ex.8vd3vup ime when taken to high altipe;3veu9 9k. ddb*dpq2vu8 xqtude? Why?

A tire swing hangingb:h0f4+/dyp :/u* kljfmnu)zx: pjdtz1gql 8 from a branch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch using only a stopwatchuq0bgf p4 t :1nkyj )m fldd /:lp8uj:xh/z*z+?

Why can you make water slosh back and forth in a pan only if you shai)v:ph pfo*o ,ke the pan at a certainhv,pip o *f):o frequency?

Give several everyday examplesl :.;5n vr : u82oa4rcemquufv of resonance.

Is a rattle in a car ever a resonancek -6b qe1weztzaq )k:.ywl5a6 phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of its3f vxd;1absp 0 source? Wx10vd spf 3a;bhy or why not?

Explain the difference between the eqxc/+tf,8fwwir nk4sz) oxlje x 44* *8hc7 pspeed of a transverse wave traveling down a cord and the speed of a t8) 4ex+wxzl/8itwfjcepf 4*,qn sokh*cx47riny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano n1 azx *vi)dpgjjxct(v 3 ;qzi8q0 +as2ormally have wire wrapped aroundz 1 0cqia;jzxt2i+ xagp* vj3)qsdv8( them?

What kind of waves do you think will travel down a h,smd +60r bb: a h/bk-shnci 1jsb9,uporizontal metal rod if you strike its end (a) vers:1nb ,cr9jp/0i -s uh b+bhkbms6,datically from above and (b) horizontally parallel to its length?

Since the density of air decreases /2 *eowgb; j 2*perua x;egnplm 3n5o6with an increase in temperature, but the bulk modulus B i5jlgr/ eee*ouw 2xbmg p; 2nnop6*;3as nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in + )0t gek6mreqamplitude as they travel away from+gmqer 6t0) ek the source.

Two linear waves have the same ampl*(6s.rttrk yv y2 yjz3itude and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits more energy? By what factor.yttsryj v(*y6 3 rzk2?

When a sinusoidal wave crosses the boundary between two sections of cord kkt ce g-2q3pvz ox nm3;hb(*4as in Fig. 11–33, the frequency does not changq2z k g-*;vn3o b hm4kxe3ptc(e (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places you could toucf xr;.6,au eo kirs/u-h it with a knife blade a ,us.xrk/f-r;6ou e iwithout disturbing the motion?

When a standing wave exists on a string, the vibrations of incident and reflec(rndc cgb.z2-5l/ evm+oy5wxted waves cancel at the nodes. Doeswlbcoyrm5 d/zxn ( gce.-5+v2 this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to anothec g,*.lc fgn,or, how might we determine whether the energy was being carried byg,. nlcfc *og, particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitu)u2; xutwvh6f- jlww/de 0.18 m, what is the total distance it travew/)vlw-wfxuj;u t6 2 hls in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs f;hzaa5zp f0qcb l/mkv)y+:9 from it but is 85 cm lomyp/a5k0;+)z hff9zv :qabl cng when a weight 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 its 68-kayizg3 *efii 6 fu+9das.47 blg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequency of vibratd.bil+9fsai6 ey3u *7gazf4 iions?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. tq 5ib0cpkg1 w o;y -z,1xk6ae(a) What is the spring5,qkzgb 0ck 61 w;x ait-ep1yo 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 wy4or kuazjt,kj4) myew*e8- ,hen a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg ay zm uk4or-we)*,,tjeyk 84jhangs from it?    Hz

Construct a Table indicating the position x of the mass i/+ni2zdjyp+x)z u em )n Fig. 11–2 at times t = jp+e ))i uy/zmd 2xnz+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. The web vi4c5qu 4)oa*3n yeuny gbrates predominate o q 5y3aey4ngun)cu4*ly with a frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequ)bierrp+v7 j*ency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the valre bpv7i) r*+jue of m?    kg

  A 0.60-kg mass at the end of ai:d( ru qcr(l;syy;m. spring vibrates 3.0 times per second with an amplitude of 0.13 m.c;y :ry.(ldi;s(muq r 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 a SHc2-zz ui(ekrmt k 9.r+O half the maximum value?r2t rz.cm-e9(k+ izk u$\approx$    A

A mass attached to the end of a spring is stretched qss(c o*r* ls4a 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 stretc3 b1 2w:t*:ladz(,c/ pbjb gb)avi qavhes a vertical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long db*q3( l atjb21a,i/d:cgbw:v) apbvz oes it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg ii5c),u4xc* rr9cip jns attached to a spring with spring stiffness constant k = 280 N/m and is executing cp54cr n) j*,i ucirx9simple 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 po rv (,sf3z ya d+m0gqi35hpgj;pgun 0.200 m to “load” a 0.180-kg ball. With whagmi(y ,0s ;5+gzfhq3 rvj3apd t speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one endvni04mokin7 6 of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.4 7nivnki60mo 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 = 0.45cos6.4t where xff0z3lo:x -qqry; /sj is in meters s fl/y0xqzj:3qf- ; roand 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 equilibriuidc/dac/iy: zh5do.v ux 75rh:6en h: m is the energy of a SHO half KE and half PE?5c 7y:.d nocdu5ih z:hre:i//d ha6vx ±    A

  If one vibration has 7.0 times the energy of a seco:a,qpj8qcfm7 y2ej. vnd, but their frequencies and masses are the same, what is t:q2a e. ,j7vqfj ypcm8he ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillahq10yu 0mx9 t;) ,,dt81mouo2f rnvxe xt:fijtes from a vertically hanging light spring once every 0),f2,to tx0fx:xe9nr1 0iyqum8ou1jvt d h;m .65 s.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two m6x b)i qvl0ocrh:7plwxc s5:0,f )jy identical parallel vertical springs, each with spring stiffness conqiw h ylb7scp:)cx06r 5,m:0vxlfoj)stant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates accordi *xm5 l3g.ow guoqq5p4ng to the equation x = 0.38sin6.5t where x is in meters and t is in seconds. Determine o5pq o4.g*w ulgmxq35
(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 A n. 4wi9iacen luk/4 nk: z1o,gg1c(oxand 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 horizayx )bj;g rhj)2w+l-lontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Determg jlb-)jlhw)2 ar; y+xine
(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 305 N/m vibrates with i;.kib 2 6hxgnan amplitude of 28.0 cm when 0.260;g. h2bnik6i x kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with sprum7, zh ur;rq;0wviyhd+h- ; uing 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 fia ug.7u,x0a ifxed horizontal spring whose spring stiff0uxa ug7,.iafness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high bridge. After reaching( (zco 9) +kjpzhwnw.k 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.w.+ (pko jc 9z)nzkwh( 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 exactly 60 s hj bdbk,53 nl5-,uckwjt-;em. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exvd+v 2 l6dyirzgqz h)-cf:)4d actly one swing per second? (That is, one colz+g-4i vyv q d:zd)df2 h6rc)mplete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, wher (tpca sfzqjmes+4w-s; ( k./olw7vg+ e the w+p +-zol4;7 cm.qs gfevjk wa(s(t/sacceleration of gravity is about 0.37 that on Earth?    s

  What is the period of a simple p-kq: uk m;3rxjendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple/pbdm0g9 qki(*tx sq; pendulum is 0.760 m, the pendulum bob has a mass of 365 grams, and it qbm;s0i/x(q9pkt d*g 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 of6)2nxdcwwx;bf0 o/fjnwq +8 n 0.9930 m. If the clock loses half a minute per dayb+f njnd wx;)w xnq8cow/20 f6, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for thx.ce:*q*vgh8 cq jf ml);g4ixe 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. At it is 2dltnmk77l+la7 nqe0ozy +yv; *wpa. released from rest starting at an anm77l *0ynaql .y;dpzt27wnk++o v eal gle 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 tpbvatno (k*:x4wqt ;9hat wave crests pass the bow of his anchored boat every 3.0 s. He measures the distance between two crest4 vt(b wxkp;:tanoq 9*s to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency ofi 9*v1hs1oc y0jbtv- h 262 Hz and travels with a speed of 343 m/s How far apart are the wsthbojhv10 *-c91yv iave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz peo-p -zlxv4 q(nn),pand 1600 kHz (kilohertz) and travel with a pxqp,(4no v)n z -l-epspeed 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 oq2d,*9r z igu2mru2hlvqx 9 4xf longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic d s vm(s9.dc9dmodulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be greavdd (sdcs. m99ter, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apyt/8- +htgt*jpxargzb xw .3 ,art. If the tension in the cord is 150 N, how long will it take a p* , 3rpy+axwj.gx zbtt/-8hgt ulse 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 leng+5y8uuayt* my cz q8r50:icgeth 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps intu0e rcuz8yq5yim85c : +tgya*o 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 se4n61 *v:i y/etjyx 2it ovc:voa. He hears the echo of the wave reflecivox /y1:t 6ijec*t vy :2ov4nted from the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and this difjv*4nqei psk13e x9 v9ference helps in locating t k3es1 vvixej94pqn*9he earthquake “epicenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approxima 7ye0bl 8jgx4yted by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with th 48l0 y7bjyexge ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the ag flp99)a1 -iko2(akrngbz a+mplitudes, of an earthquake P wave passing through the Eal(ngik g- )9o+a pk29barzfa1rth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave p(l+/.,lwi2 h zth ese*v7 uyrpassing through the Earth is measured to be plw+er2vise. z*/uy, hlh(t7$ 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 samt )yf+q w5nu2be frequency travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of the two wavesn5y+qf2btu )w?   

  Two waves traveling along a stretched string have the same frequency, but one jdrx f i;+ er:ngl5+n+transports three times the power of the other. What is the ratio oig:dlrf +;+e nnjr+x5f the amplitudes of the two waves?   

  A bug on the surface of a pv.ou dr.e8s3aond is observed to move up and down a total vertical dist.ds a3 r8vo.euance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in n8h kvd -:rud-wb5i4t7n7on b Fig. 11–52 are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string atrik-587- 74b ub ho nn:dndwv few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, wz)lwmvqg8 r;2zo9 z g/hat are the frequencies of the first fogvzz2w 9zr/m;g)l 8o qur harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 ph(t,:fr/ax0j, fnjn Hz when unfingered. 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 standing h0ft,j/ (,:narf npx jwave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hzi:4 kcqd -u/l (x5kdyh. Name at least three other frequencies at which it will rehuc5 x4kdi: k(/dyl- qsonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of standing kec2 du ,5obvra 6qe)8waves is 475 Hz, how far apart are two adjac,2krvba6o8 eud q5)ceent nodes?   m

  If two successive overtones of a vib73 j7pk 6dikh(i/enarrating string are 280 Hz and 350 Hz, what is the frequency6h3i /iakk7prn 7e jd( of the fundamental?    Hz

  A guitar string is 90 cm lpfiie.64.osurhl 17 t ong and has a mass of 3.6 g. The distance from the bridge to the support post is6uproshf.1 47l.ti i e 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 t cw :zx5a,v53 i)j 4ca wnxxaxd1h4np4o 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 the5a ahad514i,cxz:pwnxj wv4 cn4x)x 3 frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vlaszrnug. *1vu.d 35tibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be chan1n.3lst.z*rd uu ag v5ged to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mechanicatd,59 * snkowa* r37:ky(erwczz7o j ml 60-Hz vibrator. The 79k m 3zcotoz*rry:w ,ws (ej5*7dnka 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 strt+7ye(jt3f 7vxoytlmr+ :aya9i .ea7ing may be adjusted by moving the pulley. If the hanging mass mt(a v 7yly+it+7ae x 9jyora3t. :em7f is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a t:o+x. 3ulryw xub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water waou:xly 3 x.wr+ve?    m/s

  An earthquake P wave traveliocun 3 4dl8kx:ng at k.0 km/s strikes a boundary within the Earth between two kinds of material.ln8o3 k 4:ducx If it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velocity changes froq5 pu9 e.,i7sdpj mee5m 2.8 m/s to 2.1 m/s If the incident wave crests make a 3475,j9qe.iupd se5em p $^{\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 layer of cold, de. z4wnol6(ied kk *tf*nse air. If the sound wave hits th i(kltzd*ef nko*.w64e cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary b/ w+l lzm+gab9etween two types of rock at a 38 +glza/ +wl9m b$^{\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 abouml hqs;k1+(4,1 rdhwls(keg wt 0.5 m in diameter. According to the user’s manual, the dish has to be pointed in the direc1sw l(g+;s (weqhk rk,hlmd1 4tion 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 acros i.4 iio163ehgj7hiesnvlo +5c- p1was the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the a3el1 hp ogv4 5aji+ise wiic7 .6-1onhbsence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffn5 d hrq;)2 vujtay1u7d3eibw *ess 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)hyduje rb3 2tu 5*d q1vawi7; m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps frtwtjrz4r xzi,. u*da 2*2 k9ixom a window to a fire net 18 m below, which stretches the net 1.1 m. Assumerx w,uar dji2 2tk. z*zxi49*t 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 onnexto b7)ea +-ai2 e wfit inr2q-5*6q;mvfg4 the end of a freely hanging spring. The mass then falls 33 cm before it stops and begins t65m7rqf*ait; 24 fee+gnn-b2iev) iwo qx-ato 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. 1z p i95c+,pkeki+iyo)1–54), compressing the spring 5.0 m. (a) What is the spring stifiyp5opze, 9+kc ) iki+fness 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 +:v0ngo t/ 6cf 9jdiy3jkd2 taqm80yk (diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffek0v8o / yqd:cij 0 f6n3kj2mtga+9tyde.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33ut2)lauhg+p8fv4 nlr x24mh)sb4j/uqf ,e q4-rpm phonograph rel4h+rxaqfg 2ufvup )4m t4,l4)bsn8u2jqe/hcord have a wavelength 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=0.6 l7p-q5taj g2t50cos7.40t where x is in meters and t in pq52jltt7-a g 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 oscillatebn. 6: 0xlnak) tyfox9s with frequency f. What is its frequency if it acceler o.x6yxk:nt 09b nl)afates at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lctgmxl;lww )qba ;ln;p /26 .fake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft6)lw;mln 2 apq;cgfw/lb; .xt 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 ak 8h+kmp9 z7:s j(krlmv/oz1play at 392 Hz (G) and 440 Hz (A/ka(r8mj +hzk zv7k:1o9 l msp).
(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 stcf3 p5du-krx0 retched 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 ifx 0dk3p-r5uc s 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, b1xgq2xxklzvli(5 ,x 2s- n.czrw6o)and the tip of each prong moves 1.8 mm to either side of ce61g lo 2kq2xlx5x b,-zir. nxvw)zc(s nter. 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 ha kkp)n*d/1ykex9m +qs rmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebbleqy/k pk9*+e)k1xn sm d 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 rino +fs+fhp nb4 :.ekwciv5ku*e 1 o1by:g that can slide without friction on a vertical pole (Fig. 11–57). Determine the nvub iehfoboefckpk 154*: y :w+s.1+wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — ea wtfa4c.fm/,:. gbrobch one-way swing takes 1.000.r bob w,fm:/4g.atc f 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 i hqs.xh8qcv40n the vertical direction or can swing as a pendulum of small amplituxhvc8q4 q0h.sde, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123cknj*m;gaq l; u qbh 0kz6qb4ld .o68ze*n8i8 g is stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second puls8 qqlb;z;n4k* i bjh66o8g0 dnamkz ql.8ec *ue is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended fwhp49/ex7yo(kp3gj jnhpt7)6t p e 1arom a ceiling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to jw)hoj (p pt 7etx/p3e g9j71 4pky6anhust stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cable is y;mg) aciv1bw9 7mu:b22 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? [Hincm:y9aumg ) 1wbvb;i7t: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 1(sb6: x ;kn:eiqi;yvh1cyt y 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello spr xib:(y1k ; qtn eis6c1:yvyh;ings 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