Give some examples of everyday vibrating objects. Which exhibit f6womz ks*g0+2vbt,f 2bj.wo SHM, at least approximats+bzo2k6g0 fwv,2j*f .bwm otely?

Is the acceleration ott -75jisz d *ve0tqf,tgri5 .f a simple harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile e.s /1ew8rwd kcngine is approximately simp r18wed.c w/skle harmonic.

Real springs have mass. Will the true period and frkj d/c/ym- vb) a4dw*qequency be larger or smaller than given by the equations for a mass oscillating on the end of a//kddq4w)mb-ya v*jcn idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillator (SHO)n fb3;wi7 bq(m?

A 5.0-kg trout is attachedxhzvpl i; .7p9 to the hook of a vertical spring scale, and then is released. Describe the scale reading as a function of .pzxi9;vhl p7time.

If a pendulum clock is accurate at sea level, will it gain or lose time z)pjnxl,-5: erez+j*f/ /ee5poa q crwhen taken to high al:e q nx ze ,cjf/l*rreppaj5- e/5)oz+titude? Why?

A tire swing hanging from a bran-a +w c)cjo*1pfv -effch reaches nearly to the ground (Fig. 11–48). How could you w* c- +foepaj-v1f)cf estimate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if youb on6b3gdk0 jph b87o2 shake the pan at a certain 2phob0bg n6kb83 7d ojfrequency?

Give several everyday exampletcsm5aj o3jq hl9e61)s of resonance.

Is a rattle in a car ever a reso) ,tui s,dkd78o /dir;rofrw8lz:5q inance phenomenon? Explain.

Is the frequency of a simple periodic wave eq 4:4 ncy q+g2twcqfbm/ual to the frequency of its source? Why by/wc c fm44+n q:qt2gor why not?

Explain the difference between thid s .2smv4eo h))z;d +t7d;g/dwmwmf e speed of a transverse wave traveling down a cord and the s4mm.mids h+ 2d))/fw 7d;evwst o;gdzpeed of a tiny piece of the cord.

Why do the strings used for the lowest-frequo0v+g( c;:akxp ;6m1bcuxq dz ency notes on a piano normally have wire buq:0 c ga1z ;xv(cmpdxo+6;kwrapped around them?

What kind of waves dg9t(yr3fl h *a w5 n9fztbwe y9a-a-.to you think will travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parallel to its l y9 a-3- hw5*9trn.zgey9taftw afl b(ength?

Since the density of air decrey)l pclrb *k9873 zedsases with an increase in temperature, but the bulk modp)dr8*93 ybszcke l l7ulus B is 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 decreayw..w c,p*(s y- ed3enusvs9 yse in amplitude as they travel away from the v .3( yw scs.-9,n*swyudpyee source.

Two linear waves have the same amplitude and speed, and otherwise are i13 iw-qk zx 9sl)iv 8,rlkakv)dentical, except one has half the wavelength of the other. Which transmits more energy? By what )i w,v)ql a9kk8vlz-i rx1 3ksfactor?

When a sinusoidal wave crosses the boundary bsfu w,omf6g+c*0 h ;obetween two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength *w6f h+;csu0mob g,fo and velocity do change). Explain why.

If a string is vibrating in three segmeb:negj;jn 0.d nts, are there any places you could touch it with a knife blade without djd n;: b0j.ngeisturbing the motion?

When a standing wave b38cxo; gd/s afe ).zvexists on a string, the vibrations of incident and reflected waves cancel at thezvs3 o8 bd;) .xfca/eg nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmittedfw6 q2 xee7s :4atn)6mnl(ngh from one place to another, how might we determine whether the energy was being carried by partf6 n2hee64)7 ns qatxgnw(ml: icles (material bodies) or by waves?

  If a particle undergoes SHM*0ov,v *gn*p p (l7xck5eqqp d with amplitude 0.18 m, what is the total distance it travels i*gn0 ,d l(pp ckxq* pe7q5v*von one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from h +l (el(3tr qt9gent-it but is 85 cm long when a weight of 180 N h- (3e9hle+tt(q g ntrlangs 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 w 9en7nr:ppx t y60kr1ujkc3fg ,ds1k4hen its 68-kg driver gets into the driver’s seat. If the car goes over a buj639sukn fn: y41kxckreptrg,0 7p 1dmp, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs fro7og ) 0irsfe 7ptrk4,mm it. (a) What is the spring stpo)ti0k,r e7r4g smf7iffness 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 mas tj8 yy5+ va*fvol(d/os of 0.60 kg is hung from it. What i* /v+oya8vj t5o(flyds its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at mnjy7kry zcemr.v5 17q f-40ye+vj z8 times t = 0,t = kr-e77my+5jcv1q8 nejvyf0 y rzm.4 z$\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 as2.-o62tkqmn /o ajt-ydil0 kd ;os w+ spider’s web. The web vibrates predominately with a frequency of swdk-oyso0/nm d+ ;kl6j i t-a2o.2qt4.0 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 ;pn*i,)clts qa frequency of 0.88 Hz. When an additional 680-g masp,*siclnqt) ;s 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 spxrebz em9)a4+3v wy5xring vibrates 3.0 times per second with an amplitude of 0.13 m. Determi3ary ez9v xxew5+b4m)ne
(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 isto1f8hf 9tw6r the speed of a SHO half the maximum valuewthr 8o 1f9f6t?$\approx$    A

A mass attached to the end of a sprbm4i ,fxqc0 *dli+g*ming 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 st3s,ll/an0p 4 atxsmffa 4v;;sretches a vertical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how /v 4 smsflx;0t3; ln,a ap4faslong does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring wiu2 n)duvc 0ha5th 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 moving witau2dcu5v0 nh)h 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 comp gi.6tu(f8lt5wf s r2press the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed willilg. fu(ts2rtw f 8p65 the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attac*ot..vetbz; uv e qsth;8(suf6qiq; - hed 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 q6t- s*ttu ;(.fuz .seqi 8;v heoqvb;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 / lj x5emm)-u, bt7ffrda(/ho according to the equation x = 0.45cos6.4t where x is in meters axhrt)u df/jm/ , ( o5efl-m7band 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 th:)8*jrqyfsxp l6 jbai2gq6l 5r;den6e energy of a SHO half KE and half PE?pfbi 8jx dn*;r2 6qlg)5lj:r6qe6say ±    A

  If one vibration has 7.0 times(av) sqco2y(c(:oijwqv 0a( o the energy of a second, but their frequencies and mass()si aao vovj q( 2qco:w(c0(yes are the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring onvbpdbs te7 ddg;5qj*xn a5,9h v3bf31ce every 0.65 s.vv5xb5a*b7e qn bgd 3fp ,s 1h9;3dtjd
(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 orf4lqd : 4.zyparallel vertical springs, each with spring stiffness zf.lrqo:44y d constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t )szan4*s;r al5)jk;0vtmghc where x is in meters and t is in seconds. Deter0 )jz v4t*k5ha ms g)n;r;calsmine
(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 All dar1 wi;,r6.blg l3 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 oex p hsidcvt-fz9/. -)n the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed ofvs-efditcz.9p x h)-/ 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 stijyh-xno7l s-;ffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes thxn yhjo--7sl ;rough 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 sprin-mg(:zftbxs*n9 9wif gs, 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 xe s/tmq8or9c1fa0- da 0.600-kg block attached to a fixed horizontal spring whose c9e1moqs-8a xdrtf0/ 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 high bridge. Afte01 3k sunrj1vhr reaching his lowest point, he oscillates up and down, hitting a lskh 03 n1rj1uvow point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched 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 r 05rli tkvi-f k/rw7t*/tl 6bs. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one +nccjsjz0 .jk pbr5(2swing per second? (That is, one completcsc2 5r(n.kjjbz0+ p je vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.*/ nyj;kyp zx k )0.pabpvpfvc:d 8-w880 s on Earth. What is its period on Mars, where th*8p8-cpk/. xk:p;v)0yzb jva n pfyw de acceleration of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum /l5uwgpk44mn 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 pendulumd1 gxymn 2;ks7fy-;eq bob has a mass of 365 grams, and xne y1s;qf yk7m2 ;gd-it is released at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has:/ een vgg .exd2rg+e3jqlo68n vs:t*ro7l8f a length of 0.9930 m. If the clock loses half a minute per da:neg r3q7nlrg v8 2vs e.*eexo8 6f/t:do+jgly, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maxisr,lybdxve+ k6 sp,8b16a 4 gzmum 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 freque6ay,2xo f4swvfef.6e ncy of 2.5 Hz. At it is released from rest starting at an avw,6. yxfoea s46 eff2ngle 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) .v8(ebx;.ww6baozvf1 rqm cw of his anchored boat every 3.0 s. He measures o1bq ( ra6) v8ezxvcm;.f. wbwthe distance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed of 3435jzma 5 jev;2gzuc+b. m/s How far apart are the wavgv;jj2zb+.uc5 e5mzae crests (compressions)?    m

  (a) AM radio signals have frequencies be). c mmsm 8howikmxe.njs m,5v2o9y-) tween 550 kHz and 1600 kHz (kilohertz) and travel with a spee2 mwmn- x.k,s m9 y8ome)c5ov.jms)ihd 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 longitud0h zi(o/ (l e2fwbw okboo5a67x wsc90inal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twi23okgp p0odbm,cp* t1yp6+ sp ce as dense as the other. In which rod wil*pgp ,d0tmypbo+co 36kp ps21 l the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If th+ quc7pxx:0t he :fgi:e tensi+ eqx70phc::g x u:itfon in the cord is 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a stee9iunu59 u +vq d.xw:7btb8r ysgx; -zel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into t9 gxb+uzys9u u: d5v7qi.;x twn-eb8rhe 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 oypk; *wdv7w+ cxii:v1s/dx3 gf his ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s lapsk+:/gc*dwx 3;v yiw1dv xi 7ter. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, az15ug7:tdftxo 0 5 xbind this difference helps in locating the earthquake “epicenter” (where the disturbance took z157xt:tf ogb50ixud place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated bx ;)os7jxh ;oow87rnsy a sinusoidal transverseow7; 7o8;nhr )sxos xj 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 the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intye w bt)-js4u3ensities, and (b) the amplitudes, of an earthquake P wave passing t-t 3wj eubsy)4hrough the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measuru9 9hn pq3xo9)dhzw+wed to be qxn)d pww9 + oh3zh99u$ 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 waves3og fh 4cea;0h of the same frequency travel through the same portion of the Earth, but one is carrying twicehf c;oah4g3e0 the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, b k3t5fvdc vu5rpm99.j 8n3hzbut one transports three times the power of the other. What is the ratio of the amplitudes of the two wav339t k 595 hvjbpr8f.vn umdczes?   

  A bug on the surface of a9zy5bttd ; wz7b66(h0mh kna*h* :xf w.upprd pond is observed to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wby wfmb9h7u.6 ;dzd*6(nh ta :*hrxt wp0zp5kave 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 o l-wehnz7-hl* yb;k( are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Figlw bz *h7yn e-l(k-oh;. 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 freq 8zqadx:c31q k(witw*uency, what are the frequencies of the first four harmonic ta*8zwk x1qw i(c3d:qs?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingeh.dzq)g:p p f)red. 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 wave. z)qpd ):.fhpg)    Hz

  A particular string resonat5 ; lgvqjbfpbw8gqdh25 7q 2:sds;1ur es in four loops at a frequency of 280 Hz. Name at least three other frequencies at85pqfdrs v;5ub : q27;2 1gwlghsbqjd which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of standing wa9x2jzfu,ky,jm 1y5 tk ves is 475 H ,ujxkym19jktf ,zy25z, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 4a a /moser//aHz and 350 Hz, what is the frequency of the fundamental?r o4a/ae msa//    Hz

  A guitar string is 90 cm long and has e7i27b +yqtpz x9l-vqcvu0b * 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 520 N. What are the frequenciesl9q7xvvqt- ei 2*0b+uzcb7yp of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to v3eng2 41 dyhdps ,ffe9ibrate at 200 Hz, but it is measured to vibratfsdgdy32 ne e41,9 fhpe at 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 200 Hz, but it s vciir9tftxu*+7 ) s(is measured to vibrate at 205 Hz. By what percent should th9)7s ti (vu*+csxif tre tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitudek:t 0v9qh 26;u3mhbb jumy +ae mechanical 60-Hz vibrator. The string’s mass 29um+k63hv0;hm:e b aut yqj bper 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 movin eq.o6v kw.u.g wdq)/lg the pulley. If thewq.6 /gd . uqwv.e)lok hanging mass m 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 tunx42p4 fol 5ywb at just the right frequency, the water alternately rises and falls at each end, remaining relatively ca2w4onp xl4y5f lm 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 strikes a boundary t:veteenx)ht07 8)ajwithin the Earth bet)na8t0x:t eeve7 t) hjween two kinds of material. 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 from 2.8 t ji28fc *gq3sm/s s*cig2f 83tjqto 2.1 m/s If the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hihpe4zf,uxl /( 5cv +n 3n.)klop kcu uncmt5,.ts a layer of cold, dense air. If the sound wave hits the coldn(.pnvkok/,z 4 ,ln l.huuec5cm3ftup5+c x) air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary between two types oac7/oxr q8 +y qc6iuab-3rc c1f rock at a ccr63aab1u xq87+o q -ci/ycr 38 $^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m in diameter. According to the :8k ehr1pxu/:j yw ;vtuser’s manual, the dish has to be pointed i xu/hjw8e:vp: r1; ytkn 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 travels y/k/wdc 44 nxtacross the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they 4x n4/yckwdt/ 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 car bum; ma4 5i6pcsmfper has a spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kmipfm654;ac s g, 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 below, which stretches g0f*ml9g3nrgls .h v b3 -sak6the net 1.1 m. Assumvb*.g aglrg30f -93mksl nh6se 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 the end of a fb,+,k9 21fczi mh() ugzulizvreely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of the oscillathzlzm(2c fvu9, +iugk zb1 i),ion?    Hz

  A 950-kg car strikes a huge spring at a1z b:om.:1 tcz my4qrg speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of the sprb.zc: 11o :mrgm4qz yting?    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 j+ +bm*i;kya 9avfgfo9oz/+y8 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 (F 9 *mafvbj;i/zoa++ +9gy okfyig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cmgk ;go tcej6;9l:x2ni from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sound emitted? g xk:cntg; 269;ojiel   Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x i9xine, wh-adryqls56 5 z;n(l s in meters and t in seconds. Deterdir55wnlxaz9n e( l y6q,s h-;mine
(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 frequencx (75knnxqux/so; a: sy f. What is its frequency if it accelerate:skn/x 7nx;xus(a oq5s at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lak0nam+*oflmw9 z3iid) sljj) 2e. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. Whedl)3ji)na+oijl 0s2z m w9f*mn he 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 atjdiop; ,i9 k )a6vacn, 392 Hz (G) and 440 Hz (A). iapkjco,69n a;,)v d i
(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 vz3u9ssw n*be8mv 62ndown the stretched two-part cord of Fig. 11–33. Determine a formula zwvs6s 2vnue9b83*mn(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 wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, a -kcs6 e3s/ ukw:(eqdnnd the tip of each prong moves 1.8 mm to either side of center. kd/kq 6uss(e-e : wcn3Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of+ fnawe ,:z9pe frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board duringn+ ee:zfwap ,9 the oscillation?

A string can have a “free” end if that end is atyk-;mfnm: x*.es lq 9ztached to a ring that can slide without friction on a vertical poles*z- k 9mn;mlx :eqyf. (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a periogisufb, . h4a2o4(th+ byig2sd of exactly 2.000 s — each one-way swing takes 1.000 .yt4 fas 2 4o,+2h(sghgi bbius.
(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 v 2q(o-e0tojk 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 period of the vertical oscillations or the period of th( vq0o ktejo2-e 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 unjlj wqgyi fv7d*v9w5bn7tw0+-jbwt 9 /3-j lrder a tension of 255 N. A pulse is generated at one end, anr0jji 9 w-9tl-n/*37 jwqwjlg5 fy +7wbtvdv bd 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 suspe*1s8auwn 7e,. faxey qnded from a ceiling by a spring with spring stiffness constant k. A penny of mass u ea . ,1yan*f7xwe8qsm 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-o(p3b .si9tvg8 sm+ twkg car at the 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 thwbovst .pgs t i+983m(e bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which also m 4wabx*leg-j2 -x)rda yoow4iv0 vt9)g90vygives 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 analov)gvt av)xgoyyd 9r4jbw il- wxe0am 0-294*ogy 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