Give some examples of everyday vibrating objed8ld is l1t1: 9a 37t/wzv,vullxxsi 8cts. Which exhibit SHM, at least appli7ul 3vx/9 tiws8 1d,dl1x 8a t:zslvroximately?

Is the acceleration p1xo 0 zw *;xdt)qnn),wgyn2oof a simple harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine rycaqyx01 ;**owa+ mvis approximately simple h*aaw yyc *+ vq;ox01rmarmonic.

Real springs have mass. Will the : 5guze0 v;wkftrue period and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized massless spring? Explaieu v;kg0f:z5w n.

How could you double the maximuo. p htf24vu2t,vgszz5gn 86jm speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of0na+p);l;q7w wpk/ ojv/vkw z a vertical spring scale, and then is released. Describe the scale reading as a functivk0jq+oapvn7z/ pl)w/;w w; kon of time.

If a pendulum clock is accurc;rslwg) +oxd6 3b eij ;nc03iate at sea level, will it gain or lose time when taken to high altitude?js;x 3nd63 l)+cr;cibeow gi0 Why?

A tire swing hanging from a branch reacheszc6r. v6vfv:an2 xrzi(0xu6w nearly to the ground (Fig. 11–48). How could you estimate the za6uvnzrxfr 0vcw6(6i : .v x2height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only:n9w sju u0wubb4v aul x3g9;1 if you shake the pan al0u 1;4:3usvubn9 a9wxg wubjt a certain frequency?

Give several everyday examples ofa)l /w+0 .t: rxvzxfxw2vlx4n resonance.

Is a rattle in a car ever a reszi 06q 7ite+i1nikc5ponance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequtlaivb:4q n4:)r+i zzq :/iquency of its source? Why or why n utl+bv 4/zar::in qiiz:q4)qot?

Explain the difference between the speed of a transverse wave travelint.8g y(9y x jyzy/zp2fg down a cord and the speed of a tiny piece ofz tyjf8y9z /.( 2pygxy the cord.

Why do the strings used for the lowest-frequency notes on a piano normally have hhl; (xf7k-axt 1cl6pwire w;cak(lth7xh x f6 -1plrapped around them?

What kind of waves do you think will travel down a hs .n6xpcj( su,orizontal metal rod if you strike its end (a) vertically from above and (bs ns ,cu.6p(xj) horizontally parallel to its length?

Since the density of ai*nz:-3 cgvbu kr decreases with 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 temperat n3zkugc-v*b :ure?

Give two reasons why circular watq(6tdjsaljj 41*vg8 ;.vxjcf tl1m/per waves decrease in amplitude as they travel awf 6jltjg;pvx8mq 4/sltjd(*c1j a .v1ay from the source.

Two linear waves have thhwhe6 7ph;l r(e same amplitude and speed, and otherwise are identical, except one has hal6rh hhle(w;p 7f the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of co 25w/x c ur csqembf7;;*kw,f,ti7yzm rd as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do cbfer/7xkq ws ;cm z ,,cm*;7ufy5i 2twhange). Explain why.

If a string is vibrating in three segments, are tfzu2m 1 ad0xbtrj d:5;here any places you could touch duxf:2zt5; a jbrm10 dit with a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incident a7 3cxcq1d2cs pnd reflected waves cancel at the 31 dxc2qsc7cp nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to anoths*x )8f13ezji ma ,yxivnb xh21xkj7di l7;g*er, how might;xd ,mvliz xh)j1x ksi 877*yag2xin1j e3*fb we determine 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 distance ie*-gxz4qmf4 i,j9r szt travejqrgmx4 9f- ezi 4,sz*ls in one period?    m

  An elastic cord is 65 cm long when a weight of 75-olgre7qc 17hk cc 3u: N hangs from it but is 85 cm long when a weight of 180 N hangs freo 7 ukcq7c:1c3g lh-rom it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500*.;nkd4tk ,3y pd.unfp davk7jul5j 8 -kg car compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequeldk tka 57 p*f8u.jpd du3,yk4vnjn; .ncy of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hann ii1 sa,yl y3s7dst;vx* j1:oi4+npfgs from it. (a) What is the spring 1 jysx4f7 :opd1s,vsn+3ni ly *;itaistiffness 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 vibrat hamm/o8p tx c335jg(n;-fqgq 1 n;spxes with a frequency of 3.0 Hz when a mass of 0.60 kg is hun;8ngm;t1h3f5/gq-xxap s np ( moqcj 3g from it. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass iy05k7s 9o /epogr(u1rds a 2tjn Fig. 11–2 at times t =do592(g rsjtoasr 0y / 1eu7kp 0,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web. The web v. cr a9+xhms qb wuheb,n926:sibrates predominately with a frequency of 4.0 Hurb+ sx9,c 9h2sn.me6b :ahq wz.
(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. W -f2rsw1v1m1px3,wz3v vj xj5cqf n,bhen an additional 680-g maj nf ,crjmp v,-v s1wz1xqwbf 523vx31ss 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 springh ,ku78ohbs+e9rjw r 6 vibrates 3.0 times per second with an amplitkoj r +br8uwhse769,h 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 spyko, 6 9k45 vfkc9nmtseed of a SHO half the maximum value?6snko4tkky 9 59,mcvf $\approx$    A

A mass attached to the end of52 yf w( 22:gs+-sg l5olwntcnx7o nxe 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. lwd+ o6oq.+a;19 z ip4b/keo wuh6mxfhw;p-g315 m. If the spring is stretched an additionalxaue 9do+ wl4z iw- f;.o6/oqb + mhk;1hwgp6p 0.130 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring wijm bl2g9. fus2th 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 with a sjf.lgb92 ums 2peed 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 o p22ymynp d+jgf3v 19pf a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed g3nmjdp f ypy 1v+92p2will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is atta7jk3 )quomb bj 41jc(by++s cbched 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 wy +ujqc) 4 (c3 k1b+jmo7sbbbjith 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 aci3 bg)n ryj3+ccording to the equation x = 0.45cos6.4t where x is in meters and ny+3 brj3c)ig t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of a SHO/0tcre0f-) m3a2rjfc ,sldsu half KE and half PE? ± )au0e/j,t-drc3c 02fms s rfl    A

  If one vibration has 7.0 tiab ihc)i.f; 9c 4u+ivqmes the energy of a second, but their frequencies and masses .4 c b)uvq9c;fii ah+iare the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring once every 0cgej0;k2 nv9a+sja u6 .65 s. vk 6a90gea2n;ujc+j s
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallel vertical x8qgmd )/*hv gsprings, each with spring stig qg/x8dhm*)vffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrateen6m8) jj(to al b+zv4s according to the equation x = 0.38sin6.5t where x is in meters and t is in seconds. Determinen mje()a b+6jtz l84vo
(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 exampb m0 fvy+u07oqles of SHM, labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on uma m34 kwz .yx)l4dt:the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an inia) km.ml:tw d3y4x 4uztial 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 stiffnes2c*l*funli8v4 wfx )gs constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velo l xu*n wcg2fv4f)l8*icity 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 t5:0vjrr, q.pt hbty: spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed h1 xvf p(o5pt-vorizontal spring whose sprinvvp(t5 xof 1p-g 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 qtp8 da j1j+rq h/ 9jg)6/zynbfrom a high bridge. After reaching his lowest poinjjqaqg rdh+ 6 1tn9b/zp8 jy/)t, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 60 s. What iji 6od8o 6z bk3/ pte+9slc+phs its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if i7(nw n+x;o + 8ixyyqoxk)+fn it is to make exactly one swing per second? (That is, one complete vibrnqyki+7x n(y)ino+x8xwfo ;+ ation takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. Wha9as973jt iqlvy) q5oqt is its period on Mars, where the accelerqjv39) q7 tslo aqi59yation of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum0rof/: ,zbrrp 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 pendulum bob has a mass of 3 cn6guzs,+ 4jk65 grams, and it ig scn uj,k4+z6s 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 0.9 fgoluy 0dzz5iy9 4shf:9* jcqztb)-f9+ n+l g930 m. If the clock loses half a minute per day, how should you adjust the lenbj94 *t9l5z +yzo sgznu+ -ci9fyhl)ff0q : dggth of the pendulum? shortened by    mm.

Derive a formula for the maximuxel:v 32/vm qni5*md tm 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 ofy/.ls(r) 2l xv* wgkbc/ tgji9 2.5 Hz. At it is released from rv *b/cl2y.kjtsg/9iwl rg ()xest starting at 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 th:btc ihh,. 9oze bow of his anchored boat every 3.0 s. He measures the distance between two o:i.9z t,ch hbcrests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air h 1w0goo8z( dpx d;v7lvas a frequency of 262 Hz and travels with a speed of 343 m/s How far apart are the wave crests (cx d0o8(p 1ovdlvg7z;wompressions)?    m

  (a) AM radio signals have frequexy 81c; z, qpn2xg5ysxncies between 550 kHz and 1600 kHz (kilohertz) and travx, yn2;xs85x1pcgy zq el 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 long z mn 45gmh.qs6w0,p) lsdfv-jitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, nno pgm 7 g za,/+f2x0/jkr1ecbut one is twice as dense as the other. In which rod will the speed of longitudinal waves be, aer2g/mpo7j0f g /xk+cnnz1 greater, and by what factor?   

  A cord of mass 0.65 kg is stretched betwey gofa kdnk:)mj.e//oep8-5tqr ,g , 6z4twzpen two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel f q8p. -et/jgakyo,mwzf5d4)/zp,ek ro t n:6grom one support to the other?    s

  A ski gondola is connec0 t yhks5en8maa((p 7ated to the top of a hill by a steel cable of length 620 m and diaeamk07h p t(5n(y asa8meter 1.5 cm. As the gondola 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 ship just below the surface of the sea.u xrkc+gh3r5ib2o el-93mg f( He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. c u5 omgxhrr(b-ie33+l2kg 9fHow deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and this 4f3;x9gy,e2 hubkqd zdifference helps in gfdeu ,k2qb9y3xh; 4z 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 be approximated by a sinusoidal transtk1 .q5xq )-idzmd.zm /wmj5di0f2 xgverse wave. Assuming a frequency of 0.50 Hz (typical of earthqu 5 z/k.dmwqxi5d0 j it2xzqg-d)1mf m.akes, 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)* 4 dkr/ xuwmz9v5(he9a al4wm the intensities, and (b) the amplitudes, of an earthquake P wave passing through th *e av w9mxzu4lwrkmd /(5a94he Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthqu3hp+b(w1h.r k d 5*oz)m nslymake wave passing through the Earth is measured to be 1hp r(ybo mz+nm.d*s 5khl3) w$ 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 frequenw4 xam(,kdr;ixx 65+pnkc z: 9ms0c nacy 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 wavessmp0zkm:x 5ia( 4,na 6c9k+ x; ncrdwx?   

  Two waves traveling along a stretched string have the same frequency, but one tr:bsjq fm(twe3lx8 *d6jdmu ; wx*8l l6ansports three times the power of the other. What is the ratio of the amp jjl*:;6we b*dd6um8 t3s(xfxq l8mwllitudes of the two waves?   

  A bug on the surface opd+b/4hds 1 ogf a 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 wave passes. If the ripples decrease to 4.5 cm, by what factor does po1 h4d+b/dgs the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) Sketch q)th8v rv b10ethe 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 straigh8vqetr)b10hv t. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental fp9 bib,pi3+k yh:ce- srequency, what are the frequencies of the first four harmonicpb3-ybksc h :9pie+ i,s?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency will iaozxb0+p49 kg d5s)3twfv9fft 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 standi9 z0bkw39 5fv)t xd asofg4+pfng wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz. N57gbsb 3 0a0chg x0vivame at least three other frequencies at whi5vicxa gh b70s0v 0g3bch 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 svd s xl4xrvqz-:gixghp)i1 z+ 8k3(i-;( j ckitanding waves is 475 Hz,;8-ihdp i -lz(j i)ixgs vg3kcrxz( q 4+x:kv1 how far apart are two adjacent nodes?   m

  If two successive overtones oe/oy j* mti+ct.snf0vy89v 3 ef a vibrating string are 280 Hz and 350 Hz, what is the fv9n y.yf *3ti jsoe /0emtc+8vrequency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance fx3:uzc y )o*)grh *qri*vrsv4 rom the bridge to the support post is L = 62cm and the string is under a tension ov3 *si o*)gqux* 4hr rz:vyc)rf 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed *o0r)gf;bnk *gx4t t7m w lqv,to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the t)o740r*mkv qg* xlf;bwn,tt gension 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 is measuma 6rhxc(g;b)ao2xs ae0yh 57red to vibrate at 205 Hz6e( hb5ac7mx20yrxah o a;)sg . 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-amplitude mechanical 60q,uh5lib0 e9- ya.xxa -Hz vibrator. The string’s mass per unit lengthx5 lbaqhxue-.90i ,y a 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 ofsd q6moa13 ;yold9kh,q0d 8ij the string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how maoq,okaid3 8 yqmd1h9 sjd0 6;lny different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and f*i8d qtyivcwhm.c186 orth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relativelcyhwc.iqdtv86 8im *1y 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 wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundaryn5g-aw;ab4x -8fklc yflx. n 4 within the Earth between two kinds of material. If it approaches th;k-faln-5g f .axb4lnycw4x8e 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” p i2 ,8u1n sbh4c4 ;dwzya)7mbnfjd3jwhere the velocity changes from 2.8 m/ djjz3fb2;4n7 4ahicb pwnmyd1us , 8)s to 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 aiyupchm8 3lmi( y.w s,gys ea+wzc;-7.r when it hits a layer of cold, dense air. If the sound wz.7m hu ci-lgp;c ws y,y +w3.y8(smaeave hits the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary between t0*l l0bd kw o7ldcz t)ozxc 269khpr)4wo types of rock at a 340xlck)l drz*op9bdoch wz)lkt 2067 8 $^{\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 d; mh uo r( ;1:pxaizl-f5fprc*mo;kt3 iameter. According to the user’s manual, the dish has to be pointed in the direction of the satellite, but an error out-pf p5o 3oi;1k(rmaz;fc:m r;x h *lf 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 wh- :r)0 emtlc250 km and 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 doc 0-lew: rm)th 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 con2rl c 0;sk/xevnktptm7 v07-cstant 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 energvxt n; k-p2mc0 7k/7erctls0 vy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which stretchslaw;vl(ex6nf9ik+3 es the net 1.1 m. Assume th (3+; nfk 9ivlea6xwlsat 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 zi.4e4:b cp/d2mcujlfreely hanging spring. The mass then falls 33 cm 2p zdlubcmjce 4.:/4 ibefore it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge. 9k2 ymgfx2zo+3epxi spring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of thex+ 23. gzmif pkyxoe29 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 cou +l.apy ihi*1ffee (diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top pyha*i. li1+u(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 f*y5im9x4 n -h3 ltbqwof a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequencb 5tnfy4h 3- *qi9lxwmy of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=f ;oui w;, ,ebooqud08c:rr+jy1 0 ehx0.650cos7.40t where x is in meters and t in seci0 :,o fw ; 1y+b8r0,xhu;rodqceojueonds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscil xg b)tue.2.julates with frequency f. What is its frequency if it accelerates at 0.5ux. b.)gje2tu 0g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kgv2/j umcmu.ss97qd j: man stands on the raft, it sinks 4.0 cm deeper into the water./m. 2ud umq9s:7jjc vs 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 are tuned to play at 392 H .p1ewsa8usy p*:c dq4z (G) and 440 Hz (Auys14csw8d p*p .q:ea).
(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 dudts zmqxf.(*74h (yxy n8c 5 w6tp/ddown the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the 5m t/z6 d(* 4s dcw udy.(yhp8xx7fnqtwavelengths 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, and the tip of e+l6gep,gzr z3 /nzx z0ach prong moves 1.8 mm to either side of6gp,xlze nr/0zg z+ 3z 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 frequency 1.5 cycles b 4fct4* i*.h lnikzu.z27skx per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed th4. z bu7.hkxti4czs f**2inl kere (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” ejo-rh*ow1 w ,imh:c- hj-t-ogd-dj;jnd if that end is attached to a ring that can slide without friction 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 fre,;w-wjc-hjid :g oo1dj--mho h r-tj* e.

  A “seconds” pendulum has a pap9npt:. bt q-v,e 0deeriod of exactly 2.000 s — each one-way swing takes 1.000 de:ppe0nbt ,tvqa 9 .-s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertical direction or ca27 afe,,vo en)igq6wln swing as a pendulum of sia 2,on,w)vlg q7f6eemall 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: 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(q6y* vlx 6 b;u7sosff stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generx uf*s lq6;y7sv6f(ob ated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spri7c 5zdrt:: piing with spring stiffness constant k. A penny of mass m is placed on top of the block. What is thez5ti d:c7r pi: maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cabqi(dk 7a4a- c4r rezu9lgou 80le is 22 m long and ha e(9qrza 07-c4a4 iru8dul ogks a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (m d pog h5fyi4-5o+owh :gq;7k.*wb tkwhich also gives 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 amb *owqggo i5tkdf7hy-4:k w; 5o+h.pnalogy 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