Give some examples of everyday vibrating objects. Wh3tepqm8 w pz+ / zm(,dz6:hwfzich exhibit SHM, at least approximate:mzp +3zz e(fd8mzt,p hw6wq/ly?

Is the acceleration of a simple harmonic oscillator ever zero? If so, w.pvu c2s:-xat here?

Explain why the motion of a piston in an automo;8cs6rrim *l pbile engine is approximately simple h6sl8pc *; irmrarmonic.

Real springs have mass. Will thh:k.a j3.khkbe true period and frequency be larger or smaller than givk a.hbkj h.k3:en by the equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oe,iqm l- 0bxe 4+) kazrw:;avgi;kw(lscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vermw h6jd vu0 .fls)*ee1tical spring scale, and then is released. Describe the scale rea1*0j.wvuf l6eme h)dsding as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose t v c)ya9uzel *vd ,z 8o733pebw1oz(ycime when taken to high altit*ao v3o)dwu7z 8y1 yclpbcez3, (ez v9ude? Why?

A tire swing hanging from a m e8 tuc3 2p,w r+qlhpcygfm++r4,d.a6a y;h wbranch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch usin cg,8a+yha h;w+tm 42rf.6 yppqerlw3 dc+,mug only a stopwatch?

Why can you make water slosh back and forth in a5( yo 49px18,wzmuf gxaim5xk pan only if you shake the pan a 585mu fgy91x4pi wmz ok,axx(t a certain frequency?

Give several everyday examples of resd98/oq 7 f5z;3ixg m skexx/waonance.

Is a rattle in a car ever a resonancewzygd7r *ctjj,2a5p , phenomenon? Explain.

Is the frequency of a simple periodic wave equ ):fj0ey:w dzqal to the frequency of its source? Why or why not :j0:d qy)ezwf?

Explain the differen41)rb6yma tos ce between the speed of a transverse wave traveling down a cord and the speed of a tiny piys1 )4o6btma rece of the cord.

Why do the strings used for the lowest-frequency notes on a piano normallyaxgv-p4m)ya +r);*j r kav e8q have wire wr;gm8r4q - )* y)erpvja kaxa+vapped around them?

What kind of waves do you think will travel down a horizontal metal ro ,n1nkwy 4aids 7q-)yim0u0pdd if you strike its end (a) vertically from above and (b) horizontally parallel tos a7k-w 0)ypy ud,0ni4dni1mq its length?

Since the density of air def5o,w p-nc: zbxm*g- wg)kbm+creases 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 w- mbw5z +)cg kpfgm*:o,b nw-xith temperature?

Give two reasons why circular water waves decrease tbd2)x8 n8s:9bv 2tcla+pe qbin amplitude as they travel away from the sourcct+: 9b2stdl88npb q 2vexa )be.

Two linear waves have the same ahirh 6 m;/cy3j/zgxu /mplitude and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits more enyx/ mgz/hr;hic 63uj/ergy? By what factor?

When a sinusoidal wave crosses v*0jh5, ; sccrv wkn.gthe boundary between two sections of cord as in Fig. 11–33, the frequency does no5.j*k,gsncv w hr0;c vt change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segzwi;zt/d,v7 b ments, are there any places you could touch it with a knife blade without disturbing the moi/zvb,zd; wt 7tion?

When a standing wave exists on a string, the vibrations of incident and reflec cr) gipua5 dmuz1.t:;ted waves cancel at the nodes. Does this meanu agr5;:tpd) i1uzm.c that energy was destroyed? Explain.

If we knew that energy was being transmitted from one p6shzc /j,yi, l5bt r*qlace to another, how might we determine whether the energy was bi/h *r5,zsj qtl6y ,cbeing carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.1 zlhs564h sy( y1kkw( eexqjs0v-1fpb )y;o:d8 m, what is the total distance it thhe4 yxyw(d(-)z k ;1lv:sjk1fssy60p5 boqe ravels in one period?    m

  An elastic cord is 65 cm long when a 2pvg)h8)jfqa weight of 75 N hangs from it but is 85 cm long w8) vajqg fhp2)hen a weight of 180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kjd*5,/ cxfoftz3l+2bvki *: ffhr n:r g driver gets into the driver’s seat. If the or*5r fnht3/*f+k:ixj l f2: bv, cfzdcar goes 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 hay6dqhpt 6 a3m7ngs from it. (a) What is the spring stiff6a7 6qhd3ypm tness 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 whll/-fc eek 2a6en a mass of 0.60 kg is huae/lle26f c k-ng 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 in Fig. 11–2 at timepvov80; nq,ln s t = 0,t = ;l 8nvvpn0,oq$\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 predomudekcu gevwe2,,.a sq8 qs5rw da5- ,.inately ws grwq,wusue ,.8ced5 5 qa,2e-dkv.a ith a frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with 9; h( a qflhx5z)cl5qea frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the value ohq e;a c9hf5x) lzql(5f m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per seci ;swt8pa:5*1 zzfo vkond with an amplitude waz5 :tf8 *zp;iok vs1of 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 ofd olk- ), ,qea+ca il6hw.;-qe ykhrmq*:;qot a SHO half the maximum valykqmh;aa*q,d t :q., 6;l-qwehl ie+)k r-ocoue?$\approx$    A

A mass attached to the end oc1gbd f,wv.iuz*:c z-f 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 str-ylgkf4+fl vfi,t./mf/k 3oqetches a vertical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium position again?v/itkl/ f 4, kl3fm.+o-qgfyf    s

  An object with mass 3.0 kg is attached to a spring with spring stiffnt+4u ie 0 de6n/h1yyjw3pz*exess constant k = 280 N/m ann063 p /dyweeue+ 4j t1*zhixyd is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress t4d6 uo;wck k)v;rv8-ya)b aukz b rz 0do7,/tdhe spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the b)azkow78;vcy/4k)r 0 dkbz 6do,u bud-v;tarall leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one endxdu .:3xqkx *b of a spring; the other end is fixqkbx:3x*ux . ded 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 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equ )z+,+tm,c oom ioyi:oation x = 0.45cos6.4t where x is in meters iy+iot,,o z: ocmmo)+ and 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:67uxsvj a*dx is the energy of a SHO half KE and half PE? dxv:as 7 j*x6u±    A

  If one vibration has 7.0 times the energy of a second, but their freqqf;f.c) smbsk.eqt * g7w i*:4f02xwj :ckviiuencies and masses are tv*wifs.m ijbcx2wg*.)t:70e;s 4 kfq:ciqfk he same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanpj dl/;( smre/a: z)j rqg+ib2ging light spring once every 0.65 s/ z:2r+jep/ a )jq; (igrbmlsd.
(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 paralty:q gf8sq y2;23 ,vs6s cvadilel vertical springs, each with spring stiffness constant k (Fig:d82vq2y;a,3 vtqsyigc s6sf. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates u),y7 6rl/n*8piabe ga zo:vz according to the equation x = 0.38sin6.5t where x is in meters:,)* v68 gpzauoie b 7nalyr/z 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 each, what izuu72l auq ki:cfq6 +m/(.8kb bm 3pres
(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 vybt 0 bc84 l5(o4r0 ezgv.rtvrest on the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/tvz yr8evblcr4 o04t(vbg.5 0 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 stiffness constant 305 i7tanyt/l9o-xp 7 c1 i:+egcpN/m vibrates with an amplitude of 28.o t:a7p-71pxeci+ /i 9ynclgt0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring stiffness consta1 i8t -;bhodgqnts $k_1$ 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 blockreh9e 7e6ulu05i 47r lmxzs7r on)2cp attached to a fixed horizontal spring whose spring stiffness constant me4clsxren i hr 20r7 o lu9)pz675ue7is $ 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 bri3wjm*n +l5bl wdge. After reaching his lowest point, he oscillates u lnwwb*+m 3l5jp 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 lqbwbj8 6i/u(. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swing per se.fg xb06crgwip/b 051iwz0 uc cond? (That is, one complete vibration takes exap0 1f 5ruwcig.60gz0wbc b x/ictly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period w 7p hasj11z-gon Mars, where the acceleration of gravity is about 0.37 th7asp wz11j gh-at on Earth?    s

  What is the period of a simple pendulum 80 c* 4qj, mxk(yry yaf-: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 pendum ty7ay1vcq+,l: d*yg(2p af hlum bob has a mass of 365 grams, and it is released at an angle of 12,ya pf 2t 7qv+*gml(aycy:hd1.0 $^{\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 mf0ztn5cf. c1k 60hhxa y 0ay0q. If the clock loses half a minute per day, how should you adjust the length of the pendulum? shortenenaq0chaff1 yh00yz 65c xkt0.d by    mm.

Derive a formula for the maximum/.)rkqio duz8a4xz 5 c1gjd0. 3ynrt p speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At it is released from r; sz( m zmwsvhezw2/aa79 ;4pkest starting at an ang;m akv7;2zhw4s9/z(wam sezple of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchorebwgr7 fq7 e49ad boat every 3.0 s. He measures the distance between two crests to be 6.5 m. Howa 77f geq4rwb9 fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a spelpa)1k; aspue0zkx7 4ed of 343 m/s 4up7kz e;sxk1l )a0a pHow far apart are the wave crests (compressions)?    m

  (a) AM radio signals - ;pjcukps 3-,jbt ikrhif4f+ iq5p-; have frequencies between 550 kHz and 1600 kHz (kilohertz) and travel with a speei+i k-k;j q sp4 3 t;ruifpfj-p,5b-chd 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 jbeq6+sui1q08ddibg; 3im. byh f7l5of longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic mod6xmdf( d4d:vnulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, vfm(:6d dd4x nand by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart6 pt *5 r(0*)su,rqs6if wvqw:vaw g2fsy)ppu. If the tension in the cord isg6fqv652sfrqw pvy)w *(0tu,app ur* w ):iss 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a0o n8/cah b*ra steel cable of length 620 m and diameter 1.5 cm. As the gondola comes * rhbcano/0 8ato 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 thx ezx46 4lj st*g:n9mxe sea. He hears the echo of the wave re 6n44zst:g9xm xjx*leflected 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 differented(s u25)pkzgl7f ff) speeds, and this difference helps in locating the earthquake “epicenter” (whfpkg uze)52(7df) lsfere 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 jslw 4uy9unkc 49g s3,can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of f 4skgw, lu34u9cnys 9jrequencies), 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 isis:*a * vwq.mntensities, and (b) the amplitudes, of an earthquake Psq:v*.sa i w*m wave passing through the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an eart8 m,k9eyh6 km j4up*rohquake wave passing through the Earth is measured to be mkmk4eh 8ur6p9,* j yo$ 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 ;*mrpx *w1z f5vjin/.fgjr j5 frequency travel through the same portion of the Earth, but one is carrying twice the energy. What is ; f/ 15jr.*jwfg*n rj5vzpximthe ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the sameya:ybcg cwk7bt+ seyrc4 524 7 frequency, but one transports t4 :7rsa gcc5tw+7y 2yekb4cby hree 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 move uhdyi)kv e ss(t-uq0mgw:5w1: p 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 facth-gmuq)(wei:sd v0yks:1 w5t or does the bug’s maximum KE change?   

The two pulses shown i 5mu xk- (-l aolp.ltz8pfom66n Fig. 11–52 are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the str m.ok llp6(-fza8plu-5t6m x oing is straight. What has happened to the energy at this moment?

  If a violin string vibratec kmi.f5k7tjge j0 exsj51-7ws at 440 Hz as its fundamental frequency, what are the frequencies of the fir5jxefk .gjm1jtkc57 7wi0 -es st four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. A9t-3 fpx+c 9wbgtfbz,( s l0gst what frequency will it vibrate if it is fingered one-third 9 +gbpbstg9l(tw,sx- cz03 f fof 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 of 28 .+ip6p+z imru0 Hz. Name at least three other frequencies at which it will resonatp r.ui6 +imzp+e. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequen7l *y b7.ghvigcy of standing waves is 475 Hz, how far apart are tw gig7*blyh v7.o adjacent nodes?   m

  If two successive overtones of a viync yftm 6w;;:+djm)i /5pcymoj4 /i.ldj 8cabrating string are 280 Hz and 350 Hz, what is then5jja;: 4/dycdomm)j;6 y +cflt. ic/y8mpwi frequency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance from thm9+k8y4d3 thz3ekkpt e bridge to the support post is L = 62cm and the string is under a tension of 520 N. What ar9e tm ytkh8d3p43kk+ze the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it iski2*b6: ph8+;ss jv/gip kbsrko6h x/ measured to vibrate at 205 Hz. By what percent should the tension in the stringo6s+: sskx*vb/82k rjghi/kh pp ;bi6 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 vibratm)17dsrl t q1b,mv7hoe at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed ,7d11qm trm7)h vlsboto correct the frequency? decreased by    %

  One end of a horizontal q1j v1wvlax(c q.4e9 2rmvl blmt04h 4string is attached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass per unit length i l01lja91wle 4hq(vvc.qt2m vxm 44r bs $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be adjusted by moving thqm13crxdno: x6 sz+8 ee pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be acqdzxmn 6so exc18r+3 :hieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at.0bfmk.yfv: rsmzn; a2 1:q dyh7in v2 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 afif hbrs2yz:: mn 1k 2vqy;dm0v. n7.the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary wit7ba n0kbp c/;mhin the Earth between two kin b0;mcn7 kpba/ds of material. If it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the sj q),w+p.ltwvelocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests makejs,p. qww+tl ) 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 cold, dif3pug vo; w/8ense air. If the sound wavfv/8gu 3poi; we 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 *xy aq j+mokwz:x1i 28strikes a boundary between two types of rock at a qxy2xi: oaz 1wk+*m 8j38 $^{\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. Accordinvk e).b e(:msbbji1 z1g to the user’s manual, the dish has to be pointed in the directie1b( zs:bkbj m1e)v.ion of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and veloci*x hfaelqea*7 lp3m *.v1(o tfty 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 warni*pl e.7oa* 31*mq l (avfxetfhng, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper h z71xogm -hb2i5y0k0)aq g m bday:*dfas a spring 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 mimaz :y0xqd7b*if omy gg)0h-a2 1bdk5/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which sv z-)07l9aztpqe (kss tretches the net 1.1 m. Assume that the net behaves like a sz0v s9) za7kelt (q-psimple 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.idaopg bgz9:cs yd :/qg1.+eeely hanging spring. The mass then fal9e.zoi1d./ qgcag :s:b d pyg+ls 33 cm before it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge sprg 2esr 8c-l8bdt 4od*sfy34e+ui,s e xing at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the s- 8i*,d dxssl2ergo3s u ec48y4feb+tpring 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 8 cm) at jusq0 m33(cy nvkpt 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 ynmkp3v0(3 c qspeed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-rpi:bl j3spa( 0wk.(kh cm phonograph record have a waveib j(p:0 a(sk. ckw3hllength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to tcd):xn a/t c5i2i7vsb he equation x=0.650cos7.40t where x is in meters avbi n)t :2s/c7 cx5iadnd t in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. What is its frequency/z vhl1gdnm 9p4p .w*h if it accelerates at 0.50g (a) upward, ph nmd*lh4wpz./ 1gv 9    f
(b) downward?    f

  A 220-kg wooden raft float+fl+3r yv xoco4iu7;cl 0i34pmwxk, ss on a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for s7;ci4 ,w+03 oyxlluf vko c4p3 mrix+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 ays) hs6r;; gpt(k7bbp:ka f gqvd4-5qt 392 Hz (G) and 440 Hz (pkqvhqb gs-7s g6r :;4 ;dbptky 5(af)A).
(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 theuoo8 +nuvvx d)9.s +co 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 wavelengths in the two sections.us +9vx+ouo 8c.dn)ov (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 eay4kpt,9z6jn vv;a5x -ctqfh ( ch prong moves 1.8 mm to either side of centey(cvht,qx zfv6a-k9n tp45 ;jr. 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 hrif+ i wfnme-,hnz-( ,armonic motion of frequency 1.5 cycles per second. What is the m,rei- ihfn -n z,mfw+(aximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a ring that can slide4htau i65wqed 3dkhx c)/a-u: without friction on a vertical poleu)tcd3 4- auakd iqehw/hx5: 6 (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 period of exactly 2.000 s — each one-way swing takes2tuh2,u 9 jupd 1.000 ,2 2uu h9pudtjs.
(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 direc. /wlx y6p1zc hq;x3qvtion or can swing v 3xc16.hl/pz;xq qywas 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: 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 tension of 255 N. A puls i0si d ce+sxv2/c5)cie is generated at one end, and 20.0 ms later a second pulse isv c 0/x2 i+c)is5eicds 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 wg,;vycg 6.xtx ith spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on topxx,;6y .vt gcg of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cable is 22 m ,t7;n7a(a)on deh yasx7gt4 e long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the ca7, tdn7nt) oea;ahx4 y a(e7sgble. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a p ) d*sbg dt6pb/ept.s9late as shown in Fig. 11–58 (which also gives the dimensions of the block). You push it sitg/b.6p9be) p ts* ddsdeways 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