Give some examples of everyday vibrating objectssc;lc l5 ,t6z.+ptcp c. Which exhibit SHM, at least appro ctcppc5;ls 6c+zt,.lximately?

Is the acceleration of a simple harmonic oscillator ever zero? If so, wxj 4z9umn. 9fphere?

Explain why the motion of a piston in an automobile enginewnvfd b** v hu39kfciqa)-u-3 is approximately simple hafb3fq u)n3u vi9wak *dh *v-c-rmonic.

Real springs have mass. Will the adkf b7 v 8fl69j- (gc9ac1naqtrue period and frequency be larger or smaller than given by the equations for a mass oscilla -9cfg(f a a91dal7jn6cv8 qkbting on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simz7 rs -lc6k9dwkq;oe goo.0 r5ple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a v44jijq*l53kn khme mts q+(9)ty an9lertical spring scale, and then is released. Describe the scale readinn mlj k+l39 k*4am9s )(qnjtih 54qetyg as a function of time.

If a pendulum clock is accurate at sea level, will it gobn (-qwquz 0p62r4m3gl u* uwain or lose time when taken to h-lgb3u6urq o nzm *upwwq(420igh altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–48).oqg3 e:2iuk4t How could you 23iot q :4gekuestimate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if 31) o.sgoc).ow .ohgus m etd3you shake the pan at a g .oeou3)too.h dg1c 3s).mswcertain frequency?

Give several everyday examp0 bq5d,e 3rglcles of resonance.

Is a rattle in a car ever a resonance ph5kpa,apbb :w hc9 *of(enomenon? Explain.

Is the frequency of a simple periodic wave equ+t3guumy 7cfdvb88*l al to the frequency of its source? Why or wh*vd 8u3mbfcgl +y7u 8ty not?

Explain the difference between the speed of a transverse (ad tgcs/xbl( 4e3fc5wave traveling down a cord and the speed of a tiny piece 3x tbc sal e5f((c4/dgof the cord.

Why do the strings used for the lowest-frequency notes on a piano normally haveid7zf2l;srptkhz y vm++-9 n6 wire wrapped around themv2fnl z;k h irzsdp-6t+my 9+7?

What kind of waves do you think will travel down a horizontal metal r5h mhjt xx2, ;wx3v1jdam)v,wod if you strike its end (a) vertically from above and (b) horizontally parallel to its length)mw j3xm;dxw,v2aj tx 5vhh,1?

Since the density of air decreases with an increase in temperature, but the bul1 9nsx:q/t te y+-jqidk modulus B is nearly independent of temperature, how would you expect the s intyq-q9d/xejt+1: speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves dec2yc0vuw io/ry /2* mhnrease in amplitude as they travel away iw0r22n o/yy hm*/v ucfrom the source.

Two linear waves have the same amplitude * 2b vs8v; 49bpkufqfrand speed, and otherwise are identical, except one has half the wavelength op;kqu*v 89vbbr s2f4 ff the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of cord8d7xzrdk3gi + as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Explain 7i xgd+r3zkd8why.

If a string is vibrating in three segments, are there an q /y,(k/c plzy2of8swy places you could touch it with y f(oz/8 y/sqcl,kpw2 a knife blade without disturbing the motion?

When a standing wave exists on a str e2o:h8)o7g nzcmru a*ing, the vibrations of incident and reflected waves cancel at the nodes. Does this mean that energy was destroyeuramc 8oge 7):zn h*o2d? Explain.

If we knew that energy was being transmitted from one place to anothok we+dega4b /94 wu(eer, how might we determin gbdeowe+u9 we/4(k a4e whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total distanc s x48bjbu9,wqzohza)1ino+mf .e9 u.e it travels in one pe89i )bu sjxzq+o oa.e 4bhw9n 1m,ufz.riod?    m

  An elastic cord is 65 cm long when a weight of 75 N hanj3fydv 198tyz nli lj4arir6if5;(w .gs from it but is 85 cm long when a w(35zf 9 rtvjy 1y dr4llnw.8i aiif;6jeight 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-kg driver getv 0rf:3an+oyuywkx j cif;2bm+i;z57s into the driver’s seat. If the car 02a+uf5zkin;yjor 3 xfc7vw bm;i +: ygoes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from) vh ag4 (4w7gt8qst1-qx77ew lvgx tf it. (a) What is the spring salgf74gx 8 qht v-(tt47gv7qx e)1 wwstiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mass of 0.60 kg w6*ikkp 7,iic is hung fro6* p,kiickiw7 m it. What is 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 timeoj*1e9 qr;2gp4b . jfmo huvq8s t = 0 qoep.g *o1 q9m2uj8 r4vbjhf;,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 cacq73no 92n hrbught in a spider’s web. The web vibrates predominately win73qnho9b cr 2th 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 vibrate)pj bq(cn9 v8v,tsj0:g dg) kts with a frequency of 0.88 Hz. When an additional 680-g mass is adde0 pj(9s:vgk8b,tgd n t q)vcj)d 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 j;ec 19ad4 qxu 0v;fj:mw1 jjospring vibrates 3.0 times per second with an amplitude of 0.13jv0wxq; j 1cf;49d e: jojmu1a 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 equilibriux.1phzkz 6o/w4te bsvy:c d(,m is the speed of a SHO half the maximum valht,y4 z besx(v.: ockwp1/z 6due?$\approx$    A

A mass attached to the end of a spring is stretched a dij/6j e)8tf61sdw3iavhegb5 sstance $x_0$ 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 spr )eb;2lez43eut4 xwcuing is stretched an additional 0xe eb e;zw)tcl4u34u 2.130 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring wi jwzrzdi) -.f:th spring stiffness constant k = 280 N/m and is executing simple harmz.ifz- j) r:dwonic 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 to8v8fsqj1 k,+s3b umv ny popgun 0.200 m to “load” a 0.180-kg ball. With what spe u+3ssnf,1jvv mk8b8qed will the ball leave the gun?    m/s

  A mass sitting on a horizonjy7ma2a37 k7m pv 6gvetal, frictionless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of m2 a6a3 7pvevymj7kg7work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates accol: af4a/bl qm,d 3dt4rrding to the equation x = 0.45cos6.4t where x is in meters and t is in seconds. Determine l4 tb3r/daqm : aldf4,
(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 t 8b1xkyuxlzfz(kad ).k4l:d.he energy of a SHO half KE and half PE?yf8d. kz:4u(zaxkdlk ) b1lx. ±    A

  If one vibration has k;: iavi4zivbo3br 047.0 times the energy of a second, but their frequencies and masses are the same, what is the ratio of thebov4 3 :ikiiav;z0b4 rir amplitudes?   

  A 2.00-kg pumpkin oscillates from. ( pc:wq/ helsvl03rt a vertically hanging light spring once every 0wl3 0ptel./ h(:vcsrq.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 suppoz yq2pi;7e7 rlrted by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibrp l2e 7i;7zqyration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x 7u0d .;pzpq w kq7e t9g4swt.zis in meters and t is in seconds. 0p.7s9ttqq . ;dwp7zk u4zewg 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, labe05jzbec. k+7mm 9oh czled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal spring (k = 124x(k+0 qqe ljk: N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Determinjq(k:0q kexl+e
(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 an amod)l,f:0apkw plitude of 28.0 cm when 0.260 kg hangs fro 0:p ,lw)kdoafm 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 spring stiffness co+2emw z+wj4v3w nif(l+nszo; nstants $k_1$ 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 fixerp s29yb* mp6i.i5j o7mi44yyl hms f8d horizontal spring whose 9l iimibppos 2hy7y4rfy5s48j m* .6m 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 frc) ;5 jrt(ud;q ekhd-on 1gqw9i 1xyn*om a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the le xd1wqi; ntk qoy9gu rjch;(n-51)de* vel 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 in018,k hms plhshyr3kud6i8 h5-v:yib exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulkba vi;da ep1o-0 ;-eeum be if it is to make exactly one swing per second? (Thavabed a10oe;k-i e- ;pt is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its pe 2yoq.1o1xe el7 tlwbj40p 21xfdpcr6riod on Mars, where the acceleration of gravity is about 0.37 that on Earo0bpt1.j r1ly ce4ef1x7odw x 622plq th?    s

  What is the period of a simple pendulume,/wxgpm r 7,l:oyj* y 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.76 tv4*fvk nw 3 ys+/j.x1lsavt.0 m, the pendulum bob has a mass of 365 grams, and it is released at/tnsj 3t1fy kvv+ *a4vs.l x.w 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 clocv.noi fv-* mqnls -a(xj4:0 np .bns1hk’s pendulum has a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of tx4-(an.jiss vpl 1vm*n b:f-h q. n0nohe pendulum? shortened by    mm.

Derive a formula for the maximya1 oe3( (hbe3ux ri9fum 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. Ata8o0(jwkzbs ;) b*wj7y0oqdg it is released from rest starting at an a obksjyd78 0*b)0j wq a;wzg(ongle 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 gr mn x5.4sv ,*;ogdb f1f0xoycrests pass the bow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. H4ybxx* 5 oomvsf;0 n,f1g. drgow fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 26u*cr1+h8b s uoxy1w 5h2 Hz and travels with a speed of 343 m/s How far apart are the wave crests (compressions)? c+y 5uo r1u1bh8wh*s x   m

  (a) AM radio signals hdrn pq ec53m06c6hp9f8d:wl aave frequencies between 550 kHz and 1600 kHz (kilohertz) andd938ma6cfqlh 5 cre0wpp n6:d travel with a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal waves iat evn7ixsua10a p*l *;0j0 rin
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but on:vep zi-rhk;6a,m+ v2w ctez/ e is twice as dense as the other. In which rod will the svm pz/kv,-e er ;cz6+2:waih tpeed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two suppxd as;ed:r bj5 lm*n:7orts 28 m apart. If the tension in thls*:band jx;re:5d7m e 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 top6 q 1iqbg*eq7u of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondolab1e6 qg7*qiuq 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 shippp1+xpbo5jjzv ;o*8:g6. k b) hnmilq just below the surface of the sea. He hears the echo of the boj:iklz n6 m )* oxjppv +1;qp8hgb.5wave reflected 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 differenco f1lqkym2ktn,qp -49 e helps io2 yk4nl qq9mpk,-1 ftn locating the 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 /246s,m rtxp y.spwup:f)n3ym3 fu whbe approximated 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 mfw6np 3. pr),2py/h3wsx 4mus:tyu fobjects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, ao77os*hq zm(f nd (b) the amplitudes, of an earthquake P wave m(z*ho fs q7o7passing through the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquakez:crtq:j (7vqo/ )px-gh uf(b wave passing through the Earth is measured to be v :/( qxhjuct( :)-zrqo7fpbg$ 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 frequencdi cuzun8r:4-sspl -- y travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the ampnu --lu csrs:dpi8z-4litudes of the two waves?   

  Two waves traveling along a stretched string ha)/i ce)n1a-0+t5v hgjati yx gve the same frequency, but one transports three times thnev) ta tc5) 1agj0i+/-x hyige 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 move up and downy6gk p n9xogs++o 5vkgn/*v:i a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum: k*/ p yvgs9+ovg5n+go xkin6 KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) Sketch z,bmr)68 +y0ye rkp9esgn xg1nxuwb.)b 8c8u the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has z80 cn g8sxu ,e b168npy r9x)gbrmk.+yw)e buhappened to the energy at this moment?

  If a violin string vibrates anwl;ot a)f)y4 py99tofpc: ur+s6jy / t 440 Hz as its fundamental frequency, what are the frequencies of the first four harmonif 9): unw;oyyoftspjyt) a4r c/p+69lcs?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency w--j rs 6, cxogb szd3y-1izf;4gsuc1kill it vibrate if it is fing3,1fybisg 1gu;r6cod s4jzc--z sx- kered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency 0hc7 3n-c zrobof 280 Hz. Name at least three other fr 3n0or-b zh7ccequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of wave) lcta-n b .(lf8m-rn-ihq. lnr) nf.os on a string is 92m/s If the frequency of standing waves is 475 Hz, how far apart are two adjaibahq..nf) -m(tnrno-lcf). n 8rll -cent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz d/(z-e jz+.*avc rkosand 350 Hz, what is the frequency of thezjakr -+. vo*/(ed czs fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distant (jwinq4./)n dmkwe (ce from the bridge to the ). ( e/w(m4dtnwnqkj isupport post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is suppo3.bgyk(-wc vq2gqlf,b o.s s/sed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By -.( q.g, f sgcy 2olv/bk3wbqswhat 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 supposeda w7u atca x4m+fv2a(uu r)3gt8el6.s to vibrate at 200 Hz, but it is measured toteu)8fuv( lr g7 a.aas3u+64 taxm2cw vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-q i*vqli-8c1samplitude mechanical 60-Hz vibrator. Th*i8l si1v -cqqe 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 t7/:zneucwhu 1t vm:6uhe string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many diffh uunew:v m76c 1uzt/:erent 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 tub at just the right frequencyxwxlebomb,: q 9 /fm*r7tat;), the water alternately rises and falls at each end, remaining relatively 9t l/ *e m,x tqobab:r)x;7fwmcalm 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 within the Earv65m.fh(o(,b 9w iiy+uxew tvth between two kinds of material. If it approaches the boundary at an incide.ti bv((ohw mu5,f6xyw i+ve 9nt 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 velocitv spe9r daac,j3m. 6t5y changes from 2.8 m/s to 2.1 m/s If the .rdva5esc ,3ap jm t69incident 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 hits a layer of coldf zdi8ng,w9 y hh0kj am-.cfh7x+s*6q, dense air. If the sound wave hits the cold air interface at an angs d-6hhq7 f,+8gzwk h*cnm.x0fj9i y ale 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 nf:mep .8b7 bztac6u 5wave strikes a boundary between two types of rock at a acf :p8 6nbzt.7emub5 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. yhsb ( xf)g7kk(yd+5j According to the user’s manual, the dish has to be pointed fd+b(yjxgk) hs(7ky5in 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 k+/o johtp:4olc4 r,7f xe8g2h4y iig lm and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harrx o4 l feoj+hpityo/4g8l7 hc:i24 ,gbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness lvwv38s)w;o ct1 lsbm.s y l8/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 conservation3.l tvlsw1cy b8v)ms 8l;sw/o of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 pxsqjx--uv 7uw81i9qp pw/e2m below, which stretches the net 1.1 m. Assume that the net behav9xwev xq wu7 pq s8ji-/p21up-es 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 fr y 5 q37alur1xsclo- hdh1.tz6eely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of the oscillationsll hdauz. 13yhq-7txo 56rc1 ?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s :ioq1r8 ad kfhe:s3r4 (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant or o4 8:1ir3dsa fe:qkhf the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just the right t es23p) skh+:yu2llsi himw i 7o--h;pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spil2 p hsow-2h; :ileis)- 7mils h3ky+tul over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33kj/gx )ie9 dhh3 x8gu--rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sound gjg-9ud3 x xh)hi/ek8 emitted?    Hz

  A 2.00-kg mass vibrates accordsjo/m xm4p9 fvog;;6 ling to the equation x=0.650cos7.40t where x is in meters and t in seconds. De;4 /fsgx9moo vj;pml6 termine
(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 oscillat3 1 a-sgiu8epies with frequency f. What is its frequency if it accelerates 38e s ig1up-iaat 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man i5qzlk*6g 2 ligg6a/9e4 yig cstands on the raft, it sinks 4.0 cm deeper ingc62ig 6e54lz i *liq/gg9ayk to the water. When 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 n ry7iy y4, de0,jdap8are tuned to play at 392 Hz (G) and 440 Hz (A)4,j ay80 , ryded7ypin.
(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 do) a vyhi,nfk77wn the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ,f 7ky)aihnv7 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, ando+p 8fe c(:neo the tip of each prong moves 1.8 m+ece fonp: o8(m to either side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmy /dur ,xtf(l2w5ug;c onic 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 pebble placed there (Fig. 11–56) will not lose contag wut; fcru2d(5lx/y,ct with the board during the oscillation?

A string can have a “free” end if that end is attache t 9ng(:97pphz)y n l1bwhtxb9d to a ring that can slide without frictiw(l 7: 1bzp9h9n)b tyxngpt h9on on a vertical pole (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 periox:tu2d lkh/o :d of exactly 2.000 s — each one-way swing takes 1.00/lh:: dtku x2o0 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 sprint 0 x; tfon:ctq 1lsqo7+jdx2xvmf+ -/g 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 djs/otof:tx ql-x01nqx;27+ fv+tcm amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched under a jx3ghmy7 (+cx tension of 255 N. A pulse is generated at ox 7 mhx+cjgy(3ne end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with 6gdzxf : sgjucw*3c7 *osda*0spring stiffness constant k. A penny of mass m is placed on topj*g7awdd*fc6x0 ussg :co *z3 of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg crv(fv+b jw: *n3 tqn2car 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 the bouncing? [Hint: Rf*r nq+jc vb(w2v3nt: efer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which also m-wzkh:sk1oze/*j6 n gives the dimensionsown*:sh-k6 z1 e/zkm j of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the 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