Give some examples of everyday vibrating obje x4iczebk dd7xmvag/8 ;6tk s16vt00l cts. Which exhibit SHM, at least approximately?k0 x1 vt ;m/i0kazdst64 b6d 8v7gecxl

Is the acceleration of a simple harmonic oscillator a v 7aie(q r+ ) o5vz*xpqwht)f)c fh:j3dw1q(ever zero? If so, where?

Explain why the motion of a piston in an automobile;f/kntbj4w2h +ve0d . .ke/ abn2a xzp engine is approximately simple han t.fpe.b zhk/ekwj bx;4/2da 2v 0n+armonic.

Real springs have mass. Will the true perio5xj 9us5bu4j(hvmpm9 aq 7d6 md and frequency be larger or smaller than given by the equations for a s6mmxh9q57bp(u4 j5d9uajv m mass oscillating on the end of an idealized massless spring? Explain.

How could you double the max45yxvxpls nn+)j on+-o8x;b qimum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook ofa;5mkwxmaw10n)g 5 ln v/.b yd a vertical spring scale, and then is released. Descm. 510g;dwbk lamxnv)ya / n5wribe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gaoihm;z( nvg1)q 9cu: ain or lose time when taken to high altitude?zq; )o uvmi:gn1a(hc9 Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–48). Ho qswqvxltj-3+ -p x3s; i.z(dpw could you estimate the height of the branch using only a sto-t(+v szj 3 ;pw3 qqxlxdps-.ipwatch?

Why can you make water sloshn :inxfri--;hc6vrsgyg( plgwa v d(l) p, 103 back and forth in a pan only if you shake the pan at a c;x p31lgga(( v,pr-g:dsc fr w6i- nvyl h0i)nertain frequency?

Give several everyday examples of resona nm8zl y:ow4+v11:5apkvnazb nce.

Is a rattle in a car 8x vsd)tazn.4+f2pidever a resonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of its sou.),fa:ib.ey2si,t:x e n ch ygrce? Why or why ni .g, cnehy2b. )e: is,:faxtyot?

Explain the difference)3wrpr/si 5l u between the speed of a transverse wave traveling down a cord and tr us5 3/riw)plhe speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano normally ha; ;q7s uoivp0 gdvkhg0:fum3.ve wire wrad;vp qgu30 7 .mgoi0 kfuh;:vspped around them?

What kind of waves do you think will 0xkwx el so1sy- (5mb2travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) hori15(x 0sby2 - owskemlxzontally parallel to its length?

Since the density of air decreases wif pfx :)r, )1tofuak*oth an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperaux po for)tfk:,1)f*ature?

Give two reasons why circular water waves decrease in amplitude as they travefoml:4v xxl4,e+ fyto/ +;v jh9acm+bl away from the +xamf4of,+;vbxe4lho/m v clt+ j:y9 source.

Two linear waves have the same amplitude andcojywf,:li79if vlsy0 a n),- speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits more energy? By l f,jl yn:-wio9y0iv,acfs7)what factor?

When a sinusoidal wave crosses the boundary between two sections of cord as in F2b:eya0b0)peis6 l wk4 p, 2wd)cdt zsig. 11–33, the frequencde) bs 06iaetdzpy2pw,: )w0s bl24cky does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places you could tpkxa q ;wn/b.7zfbl.45av+ vn7 s au.fouch it with a knife blade bv.n;+7apk uaf x4vwz5ba.l/ .n sq7fwithout disturbing the motion?

When a standing wave exists :.l6quznm ilixm5g f2;k 7 h: ut-odm:on a string, the vibrations of incident and reflected waves cancel at the nodes. Does this mean that energy was destroyed? Explain.l-q7kiit mm.l62uhz ng om5fdx: ; :u:

If we knew that energy was being -vdr55 spxka)w 0 mid*transmitted from one place to another, how might we determine whether the energy was being carried by particles (mkdpx*0ims5 -v d war)5aterial bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.9sqtl xt (n9i)7 6ueu. tlvcj a+bt86l18 m, what is the total distance it travels in one perji tqtt ncse)la tu66 v8 .7+ubxl99l(iod?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs frxv6 9:nk. kr p3ak .ivht.kbd0om it but is 85 cm long whend6h pv 3ib0:kvk.kxkn 9.a.tr 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 compj4ckeq/w c d2s8yo2) sress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump,oesckcs4 /2)2qjyd 8w what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale str okupgwjr+wcm9:k/ w*4m+9gnetches 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffness constan mjw/*w++ mgkrk4o9cwngpu:9 t $\approx$    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 frequenc,m;ha0 assl5+jc0ilxj pjv+- y of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if o0a-p +m+jscv0,i l5 h;sajxljnly 0.38 kg hangs from it?    Hz

Construct a Table indicating the positio5( lk gk-1tipe/; w8zoz (udkun x of the mass in Fig. 11–2 at times t = 0,t1zu/t 8owk(g-ilz e;(5dkku p = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 vibrates predzs9-55;rfnx9n jybjo ominately with a frequency of nsxzj 95-;9ny5jbfro 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 0.88 Hz. v 0-2)x; ikks)zcy v)xq*uolv When an additional 680-g mass is added to m, the frequency is 0.60 Hz. Wh ) x xvvsk2)0o)*q;yikl-cuvzat is the value of m?    kg

  A 0.60-kg mass at the*s,g:ka.h)b y7iw ujn end of a spring vibrates 3.0 times per second with an amplit) ,ijawng skhu b.*y7:ude of 0.13 m. 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 SHO half the maximu*oayv e6f) q6f*n*kpg -b12epd ie o.xm valuib nxfq1)2e - *ev*kop* .yd 6gpea6ofe?$\approx$    A

A mass attached to the endgnw5x8,83 tl4 j ;tdf2ghr dlx of a spring is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. If the spp(gxc,n3un1 a ring is stretched an additional 0.130 m and released, how long a3x(p1ugncn, does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached nt*.v3u q bp5b .kjhj.to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium3.bbn k5p hu.j.qvjt* 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 spj 11-wfk: * e 1/jx5ytmsampvyring of a toy popgun 0.200 m to “load” a 0.180:xf mse5jj* a1y1y/-v wkmp t1-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is atn 6 blhy/odkg7+yf0y;tached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 n0 b /oyl+7f6dhg;yyk$m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates accordingovodx5l9jjg7 bw;y8xhzfz.f5 ; 8;wb to the equation x = 0.45cos6.4t where x is in meters and t is in ; x.9b 8 jdfgozhz 8l5x7;b w5;wyofvjseconds. 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 th2eb*g xm8.vt ge energy of a SHO half KE and half PE? ± gm tg*.2bvxe 8   A

  If one vibration has 7.0 times the energy of a second, but4lwsr z9*x1dqjb / 8px their frequencies and masses are the same, what is the ratio of their ampli/q rz194x pdxw* slj8btudes?   

  A 2.00-kg pumpkin oscillates from a gfk3v (h0wem *; a,xrhvertically hanging light spring once every 0.65 s. ; mw ,*gvk(her3a xfh0
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallel vertical springs, eac(,9+opgze .gtnqq(o ph with spring stiffness constant k (Fig. 11–49). What wiz.( ,qg netpgp 9o(qo+ll be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.3 dy.a13m8 gnnn8sin6.5t where x is in metersm3adgn nn81y. and t 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 SHM, labeled A and B. For eachpk7o- rv,d7/9;1vkrlyogii9 a6 y rij , 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 rewyofq:(zi9 bvcf+ 3 n)fa2p-k st on the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an invocf kn- p9q+wa:zf y23)i f(bitial 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 m),d 6nxbsc0b;yf uy0stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilcf x6n b;,0s bdy0u)ymibrium 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 u rgv-s00ffox9 :b 03zdij , nntz:4p9 x6wikgto 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 y9 9 kc2+4,ftbw1aiuqepya )pblock attached to a fixed horizontal spring whose spr),butyk 4qeafp9ya+ 1 2 9iwpcing 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. After reachintno4 qvc0n)* a0n7fx wg 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 theox)n t n4qnf0c7 va*0w 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 vibran/r* 10q-,a8mpqca. ftitw5z y k 4jgutions in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to makch,xsy,6;hnx i:oz +s e exactly one swing per second? (That is, one complete vibration takens+ x;hicoh,yx s:, z6s exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mkc b3svzawgk nxr2/0 0u,cd611dt et +ars, where the acceleratiogr13d0t20x,zt/+sve61 kcn bwa ucd k n of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulucch:0 7wx 2uxvsj r3e2m 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 p5 revf,u67kg h e,b.cee9p0a7wxy *tvendulum bob has a mass of 365 gra6e,vytefcg xp7a * .bw,u r79k5vhe0ems, and it is released at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 mkv 4f0hux004lwu0ioq. If the clock loses half a minute per d 4wfivh0k0ox 4uu0q0 lay, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maxwr)f5g6/ck i0cxl.l zimum 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 ih*3 s-ycjzwk 5t is released from rest starting at j3y*ch-kz 5ws 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 t )yj k53vvnl 9s2(bulsx7fa2phe bow of his anchored boat every 3.0 s. He measures the distance betwe(nlvjf7 kuy2blsa 925) xs3vpen 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 spefrsj)s oxdpgb) o0/g/)xux 00 ed of 343 m/s How far apart are the wave crests)x/)o0/0xfgsxdo0pr j g ub) s (compressions)?    m

  (a) AM radio signals have frequenciks9.79 zt9kg eyaoex 8es between 550 kHz and 1600 kHz (kilohertz) and travel with a sp8 9.zake7e9go9 tskxyeed 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 loz0p -ltv wwht7d/9m d*ngitudinal 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 tk*: q/sjc lic5wice as dense as the other. In which rod will the speed of longitudin /cc*kq:sl i5jal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supporsxos4 0 5*nwdtts 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one suppd stn ox4*w50sort to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable ozeiq9enn 3d g *m07vg +k44afuf length 620 m and diameter 1.5 cm. As the gi*d+ gkuzeg4 m7039q4avf en nondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 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 shi9nqdmb(t :0nn p just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directl nnb(tmn9:d 0qy below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different spdas zt2s-q7 b7eeds, and this difference helps in locating the earthquake “epicenter” (whers7tbzs 72d -qae 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 appro:7sx/03 f--f qhoeufio, ml5j rl h(xopqj5y3ximated by a sinusoidal transverse wave. Assuming a fre,oflp j5h ix 3huyq-/eo-j q0s 3ox5 (7lff:mrquency 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 intenbl m op go58r)bx9 zu+cop2,n+sities, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from zpoo+8n2ox+ rpg) b,lm5c9bu the source?(a)    (b)   

  The intensity of an earts;qoy(i 0x ta+hquake wave passing through the Earth is measured to be yxi0+s( o;aq t$ 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 frequencymf5fc(snq 7usv)kf sl48z; 9b 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 wavescu q97s8zl s;fsf( 5 v)fk4mbn?   

  Two waves traveling along a s(* iwyi;af) byg2 gfa6tretched string have the same frequency, but one transpoi(iwy6ffb 2 ;aagy g*)rts three times the power of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to awthd * *ldm;x3sgax4wd54*s move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wa*4w;d*4xgs3* xtdas5da mw lhve passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each otheroefql0cd (8 ,m. (a) Sketch the shape of the string at the momentd,8 (lofq c0em 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 each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440) 2* ucdpr/l b3qz2gxc Hz as its fundamental frequency, what are the frequencies of the2lbg3qr)ccpzd */ux 2 first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At,*ugji jmmp1z., 5p pfu6gwp/ 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 aspjz6g p,p1, wmg/iu*ju5.m f p a standing wave.)    Hz

  A particular string resonates iapea:.w)a 1r :3en0-suovpam n four loops at a frequency of 280 Hz. Name at least three other frequencies at which it will respm u ow:a)a1r.0-enpsa: 3veaonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on wh: uy5t87mhla string is 92m/s If the frequency of standing waves is 475 Hz, how fh8hwy m75u: tlar apart are two adjacent nodes?   m

  If two successive overto( 97 mppld -3zmrrqcy;ikr( c:nes of a vibrating string are 280 Hz and 350 Hz, what is the frequency of the fundamenimr(c prp3k9yc ( ;mr-:d7l qztal?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance nlrt-t/ny* 7rgu5e0 qzu-ze )iz b5w* from the bridge to the support post is L = 62cm and the strizuz/ tri)70 rwz n -ne*q5uy b-5gl*teng is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar ojgn + k, r a)9e+udleqm1xh*9string is supposed to vibrate at 200 Hz, but it is measured t ,gl eneoa+ j mruk)99q+dh1*xo vibrate 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 Hzh )lnbv;+vwb* ..p yf /xtp5bp, but it is measured to vibrate at 205 Hz. By what percent should the tenxf .+)5pt/bvl*wp bh vnbp.y;sion in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal strg* ;:,esgtmuv ing is attached to a small-amplitude mechanical 60-Hz vibratvt; ,s ug:eg*mor. The string’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length ofk- i1 kub.jpu( the string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing w b. j1u(ki-kpuave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water)q*4p4;j i)bt * ylybt6mxgnn back and forth in a tub 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 w )jpb*mbg;n*644l nx)tt iyyqave?    m/s

  An earthquake P wave traveling at k4f//h zuj4- .pu pslkt.0 km/s strikes a boundary within the Earth betweh/szlupk -.4p4f j/tu en 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” wherem);s6joro *jb the velocity changes from 2.8 m/s to 2.1 m/s If th6bmo)o *sjr;je 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 uk9xu xo.5 /nl(f7b+h 8u:stbbs(m yfit hits a layer of cold, dense air. If the sound wave hits the cold amb:yukxfsbf 5n7+s b.(8 (hul x/tu9oir 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 twf+t3j9dv zi bje7s 42vo types of rock at a 38+ sj 397i vzte2dv4jbf $^{\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 u wl25v8bn -h .sr(czad-,v wain diameter. According to the user’s manual, the dish has to be pointed in the direction of the sat .vvb-la (z8cdruha 25w-s,wn ellite, 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 anjw- 7-dluaod ;z att(nc6sl;/d velocity 750 km/h travels across 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 absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes anda o/z -sa;tldtu;-( wlcn6 7dj boats.)    min

  An energy-absorbing car bumper has a sp. yw x.a+vpskc(-4qnw ring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energx.pwcn 4(qy wv.+-ak sy.]    m

  A 65-kg person jumpss9 ;f14+oj7v uyaszsf from a window to a fire net 18 m below, which stretches the net 1.1 m. Assumu4 +syz7jfof; 9sv s1ae 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 freely hanging spring. Theb q2oqr71 cdj 4m5d9wo mass then falls 33 cm before it stops and begins to rise. What is the fb o5791jrc4q2 wmdqodrequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 7-iy;bdw qju*22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) Wha; wd-q*y ui7bjt is the spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter ym*0 e0 phukai7 )fp+lr+ 2ucz8 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 7r +m+)h ka0yuufclp i02e p*zof waves in the coffee.    cm/s

  The ripples in a cert q27tm zg:d *d8i-ag+bg smc3xain groove 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the stzds mqa28xbm:+g c*d- g g7i3ound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0 bw.*wvp/ jb;eswg 2l:ys (u; h1(xicm.650cos7.40t where x is in meters and t in seconds. Determine :sm.w;g( xvhs/*iw 1;cpu jlbbe 2y(w
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. What is its frequency if it ajb2+1 ef kdc ,(wv /fi5ujajg,9c a;tcccelerates at 0.50g (a) upward, e;tbif cj gu59c1fd/ ,jcj(2aw+ a,vk   f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. Wht9t fxtrh,.o (p. )ul*cgksfcwd1 x1h0 -cyz7en a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates fwt x.fso tf*9h.c klcp,ty(g )7 h1cz x-10duror 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 47 niyfy e1n94fai- y+ zu1tj.p40 Hz (A)..94yfyjint-f z1 neip7u+a1 y
(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 stretched two-part coruiye :- fdv4;xc 0gyh 0b;d8kqd 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 freqihyuk0f8y ; dg:4d;ex bq 0c-vuency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of each prong votsoj4 -q9 p5gk+t 7vtpow35m:/ oqxmoves 1.8 mm to eithtqtvo oj: 7/wq 9x5po3-pmko+t 4 vs5ger 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 oscillates with simple harmonic motion of fre/ vyqh.se,kg7 quency 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 contaq e,gv/.yks7h ct with the board during the oscillation?

A string can have a “free” end if that end is attached to a ring that can sl*pw -inwu// h6dingi1g18/af 5j wnhlide without friction on a vertical pole (Fig. 11–57). Determine the wavelenw/n*luafi h6gh 58jd/n p/w w i-11gingths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.00,qhaox7br g qz)-o 8gy c1.5uu0 s — each one-way swing takes 1.qo78b oc1quhy. ,r)za5x- ggu000 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 f9c9gisn/quvb aq i7n68- m2 ogblq5*spring can oscillate 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 the horizontal swings, and by what amount? [Hint: Lecbn9mg9 o8g u67q 5qiqin-2sbfl*va /t $l_0$ 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 tensgri3.t agctm(da *uf5 an,:o5ion of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generat,df5i*tu( a3 aangocg trm.:5 ed at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended ;z81j uq.opixt nd d d+))un9rfrom a ceiling by a spring with spring stiffness constant k. A)ju)9dnn; .p8ux +diqt rod1z penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted 5 )y:u bo8 j.ee*olpvra 1200-kg car at the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A *oop yjev5.8rlbeu) :breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plar (/+z joryn4vte as shown in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, anrzv r(4n/joy+d 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