Give some examples of everyday vibrating obfwf im*s)(/((xwqa r rjects. Which exhibit SHM, at least ap)r(i fa qrxw*m(s( f/wproximately?

Is the acceleration of a simple harmonici*.h;fs((v0 r(l9k ysl5bf6yk bjqt v oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile k(ps k 90m6kyp -ho9owengine is approximately simple hakw -y kpm6s9ko9p(0oh rmonic.

Real springs have mass.i;p rjui kl,1o35 v7vw Will the true period and frequency be larger or smaller than given by jv5 k7;u,row iv3p1lithe equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speek:k/ ugpdpc+;d of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of axgps fcp8q813uj8wc 4) r/vjf vertical spring scale, and then is rg 8svcppc 18/uj j )rwxf3qf48eleased. Describe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose time when takiaq1f- +f4yzo0 phd6jen to high +zhdf-4i1oj0aq f 6py altitude? Why?

A tire swing hanging from a br bbz4da 7h ktt6png8ex-m d2 4ug8c/t/anch reaches nearly to the ground (Fig. 11–48). Hoadg//x t24 zh 74k8bcdn6ut-mbegpt8w could you estimate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth ize8 lh9ft8kd; n a pan only if you shake the pan at a certain fd8lef98khzt; requency?

Give several everyday examples of re8 d t:+p thd1n.fqxcf-sonance.

Is a rattle in a car ever a resonance phenomenon? Ex m 3tmld+kr56xplain.

Is the frequency of a simpnk o p7f*)uw)igxple.kg+)yv* +bsr 70w/alvle periodic wave equal to the frequency of its source? Whyi+glv)ke og/ pval7uw0bx*r)*wnf. k +) ysp7 or why not?

Explain the difference be+tl f0p;: kpka( ylj-gtween the speed of a transverse wave traveling down a cord and the y lkj0(f:pl-a kpgt+ ;speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano normally have wg3-dr pcbb1 13.25rwac)yf x 0cnj smwa).j1dx nc 53r3yw12m fc p0w-sb brcgire wrapped around them?

What kind of waves do you think will travel down a horizoz8e3rw rjrq p zq.b5+lcmwuw4o6 o)43ntal metal rod if you strike its end (a) vertically from above and (b) horizontally parallel to its le8)w34 mq ozu6rre5 jwq4.lb3c pwz+o rngth?

Since the density of air decreases with gmk v;sd6+rurbg..3 b an increase in temperature, but the bulk modulus B is +k6grg .r3smdvu.bb;nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as they travelwl y;h mg-0fei2pdrhx/:f,2m awayl/he-;w0hm,f r2y2d :pfxmig from the source.

Two linear waves hav k ,e.s;esg)ctr; q9: eyffxl*e the same amplitude and speed, and otherwise are identical, except one* q) es 9tegcf;yrx;:es.fk,l has half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave1 v*i gi3*ffan crosses the boundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Explain whi3fni vg1f* *ay.

If a string is vibrating in three 5md+ 5rnc2se u.ak0zk segments, are there any places you could touch it with a knife blade without disturbing t .+5nr5k0 ascudkzm2 ehe motion?

When a standing wave exists on a string, the vibrations of incident and rnz9x 6(byxr tl: yk4l c5i)v:ieflected waves cancel at the nodes. Does thisv t :6nlx94)l 5yryb:xkc (iiz mean that energy was destroyed? Explain.

If we knew that energy was being tre.7ert8i*2-xjj3 ( imofsra nansmitted from one place to another, how might we determine whether the energy was being carried by particles (material bodies) or n(* o r3i2jejt 7a8sm efrix-.by waves?

  If a particle undergoes SHM w ps 8gt9)eh.ntjz+ *rpith amplitude 0.18 m, what is the total distance it travels insnh) p9z*g j+p.8 tter one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs fr(:7h(x t ghv9j px*wfrom it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constxw(( *tv9hh:j7 gxfrpant k of this elastic cord?    N/m

  The springs of a 1500-kg c45mgj6y*;x d xn,8h:krksbt mar compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over hsb8 n*,ryx;g4dxm :j mkt5k6a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hae 9fc(a6+y9:abkn b -6 efefotngs from it. (a) What is the spring stiff 9o kb+t(69yn : eaff6cee-bafness 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 z;l6 hhdjy ;;aois..rg46u ai a mass of 0.60 kg is hung from it. What is its uih zyg .4dh6lar6.o; s;j; aifrequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at times ,d.1pp pmxi (6ibua cw+ vbp91t = 06b.1bpvi pwppax(+9 u,cm di1 ,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 ;rl1c5l sfcn8 c7xwa-g is caught in a spider’s web. The web vibrates predominately with a f1cl8 c7fwn xascr-5; lrequency 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 sprinru1 5 -lf-ufuxg vibrates with a frequency of 0.88 Hz. When an additional 680-g ma r xfuf5lu-u1-ss 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 spring vibrate w.oqzi0 q(c;fcqw-i9s 3.0 times per second with an amplitude ofqo- c.zfw(qw0i9 c i;q 0.13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed of a,)5puzf gicaz 91 4 kf6mwrkg: SHO half the maximum val1gfa5fkz u94 gc:,r6mwk )zpiue?$\approx$    A

A mass attached to the end of a spring is str)9m5h jnc;il,mr; + k.urk4okftr dj+etched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. If the spring is stretchepye9.d )sx: wnd an additionas pw )e:9dnxy.l 0.130 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 ap qz9q 4ajc 1ah,jx/5kg is attached to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a qapj5q z 1/xjacha 49,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 toy popgun9l/ 8v-dcvkgoe;srgjd7 yp*. 0.200 m to “load” a 0.180-kg ball. With what speed will the ball ke9rcy.op *g /dvd lg 8vjs7-;leave the gun?    m/s

  A mass sitting on a horizontal, frictionless suru5 t:5s kecl)l4omzb0sw6zd: face is attached 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 o dclte 465 wbu:m :)k05lzzssfrom 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 acx 5bnpeyx3(9*jb vga 6cording to the equation x = 0.45cos6.4t where x is in meters and t is in seconds. Det nx9b6g(ep*yx3abjv5 ermine
(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 half KE and gb +c9 r4ekh:l 5 df.l zhs:y(*ugn*bkhalf PE?ebr5:h.y49kh bf* l gcnl(+*ds:zug k ±    A

  If one vibration has 7.0 times the energy of a second, but714ert** 2ir xo)n9 kgmcqbh l their frequencies and masses are the same, what is the ra*r 7o)t4blc2em g1kh9n xri*qtio of their amplitudes?   

  A 2.00-kg pumpkin oscillates fror4j1br )kn -uhm a vertically hanging light spring once every 0.6n ) ukjrhr14-b5 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 s- bs3ntp qyvzmr,, g+9prings, each with spring stiffness constant k (Fig. 11–49). What will be tp-3rvtg ,,ysq z 9m+bnhe frequency of vibration?

  A 300-g mass vibrates according udl*jpjd 4f(b+n(r e *to the equation x = 0.38sin6.5t where x is in meters and t is in seconds. Determij*4( *d dfp+rejbnlu(ne
(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 kw 0x3sd5cyk;h wxw.8 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 horizonobw /ycz-0(+c t+m qd f26nlqjtal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Detercdof+tzbqwqcjn+/y 2 06-lm ( mine
(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/1t5 dpikh6z,ts on-a .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.,t shn5 6ak- 1zodipt) 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 spri+) *uru873yfiuwf pzing 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 bs s)qujk80z9q6te1 3t4ltz hclock attached to a fixed horizontal spring whose spring stit8 cq6 0qz9k43sez shjtlu) t1ffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high bril ud2 iopeg2nbee-xq91w8y 1 1dge. After reaching his lowest point, he oscillates by eenwg 1upq- 21e1xl298dio 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 i xo-,uu aa j6.wmd:3vgn exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simpl57cw8 v( z j0dlvqzmx/e pendulum be if it is to make exactly one swing per second? (That is, one complete vibration takes 0dwm/lvz(87czq 5vxjexactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on 5b)kuxl0*2kv gcxl,o Mars, where the acceleration of gravity is about 0.37 that on Eako *xbcl ,)0 gkl2v5uxrth?    s

  What is the period of a simple pendulum 80 lg f12oi 0 y8gs.7( fpvgjyr0cmx.. qccm 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 xj3d 0ro(tzs.pendulum bob has a mass of 365 grams, and it is released at an an rj(sd 0toz3x.gle 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 lengtefhj 1.2v si)oh of 0.9930 m. If the clock loses half a minute per day, how should you adjehfvosi2j 1).ust the length of the pendulum? shortened by    mm.

Derive a formula for thmke x7v8 m567u*y/i.tzf ) nsf ymy-tue maximum 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 h(i g-8mj b,q)p;q vzfh.4hri from rest starting at an ah; ,iv8zh(bq rhip. 4-jmgfq)ngle 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 anchored b m/xlpql - ez9x9o(f,riae+4v00tq rx oat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast ax9lai(r/,0v+ oe0 xpz ql4xm-tfeqr9re the waves traveling?    m/s

  A sound wave in air has a frequency of 262 a310 jku8agsiq/ lsn3nxpma u7lg1d-dm5g33 Hz and travels with a speed of 343 m/s p-aid0 u au3kaj1gm3g5ms 8d nl1qg7/sxl 3n3How far apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (k(yq8lmovcsqi15 b dl 64ds*u y*1i1gfilohertz) and travel with a speed oso dlu81c (y1ilbdi6*s qgyqf1vm*5 4f $ 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 longitudiv 9jiwd y/3de;fd ,ak2nal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same9h ,(fmtz)cd7u kdd )o elastic modulus, but one is twice as dense as the other. In which rod will t(zddu9)m,o7h ck d) tfhe speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched begh. xt)lvjoi7: y; o:pn,) ckztween two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse t: o yx ck,7vt;j)hn)opi:z.lgo travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel 1.+d 3 fnjqbtc k)2id*,c2ca 3embawucable of length 620 m and diameter 1.5 cm. A1i*3we) +3tdbcacm,kb2u fcn2.jdqa s 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 belocrn)ududf(b,1xv2: l9w1 f7h* 52l tjzycl ppw the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean atcyvwd1 1txc 7l,29fph:bp2d zl ru l( j*5)fnu this point?    m

  P and S waves from an earthquake travel at differen-ac nt 4udiw- 2o*zfdf :w/t(yt speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbaw 4tw:z*cy/2in( -fof du-tdance 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 wazm rd0fekp0dq8;k7 s91 hcz h0ve can be 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 tha;8 q ekhh00rdzm7z9c sdp1f0 kt objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of an earthqoq9ut,: g7;l+v1 fw ca.joykn uake P wave passing through the Eart o.+y1uk ; jcflo9gw,7 anvq:th and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measur(: 2fpsfqn :(c:cy.wm ( qfbxhed to be w(: xfn: 2:q(qfpy(sfmcchb .$ 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 frequency travel through the same portion oxh*adamv9j)py8 *drz ;,tp1 k ix zz50jpl;)sf the Earth, but one is carrying twice the energy. What is the ratrp8,*zd9) p dx)ziah y vj;50j ls*k1ztm;xpa io of the amplitudes of the two waves?   

  Two waves traveling along a stretched string havhys99sk6 c4k ie the same frequency, but one transports three times the power of the other. What is the ratio of the amplitudes of the twocskk496 hi9 ys waves?   

  A bug on the surface of a pond is observed to move up and down a total verticandoz/ , 6n9*0)3upc qoxbg trhl 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 o/) ugh0n,dx p3n6qz*rb c9tomaximum KE change?   

The two pulses shown in Fig. 11–52 aregis +cn2-bl/l moving toward each other. (a) Sketch the shaplg-/+ bsi n2cle 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 happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundaov 5ob lvq8vx(q3(g8fmental frequency, what are the frequencies of the first fourf8bv3( q (vovlg5qox8 harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibranq a6fytq+j4smw2o; ;y)y ih 6p2lcf2tes at 294 Hz when unfingered. At what frequency will it vibrate if it is fi)6 2c2y woh+q;;4a y2ljm nfyq pf6tsingered 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 of:y )i/w )esvjz 280 Hz. Name at least three other frequencies ajwi/: ezy)sv)t which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a s6/u6vt ooi pzj443b eo1iebs .tring is 92m/s If the frequency of standing waves is 475 Hz, how far a bsvo 3e toi1o e46ujp46/biz.part are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and p5 .yjh3xw (*c5qcno r350 Hz, what is the frequj*crn35x 5 (.yqpow hcency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mas *-jewjxf) ed2s of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and firsjeej w)2*xf-dt two overtones?    Hz

  A particular guitar string is supposed to vibrate n.k:gp6 .o pz*amg 5qvat 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be chan6o. anz: p5gqv kgpm.*ged 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, wwg t5sufd7tr ):y-.hpt+r 7t but it is measured to vibrate at 205 Hz. By wh)f t +.-rg w:th7d75pwusyrt tat 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 mechanicq:s8.1n /d+be3s vhds 8lip jdal 60-Hz vibrator. The string’s mass per unit lengthd .8 /:n8d+jh qlde3vbp s1sis is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be adjustedd u4 fy8 1nmr3n(4; l13xsjmaehcs3p e by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L e3n4c3m(jr sn1 1fa 3p4mxh d8yes ;lubetween 10 cm and 1.5 m?   

  When you slosh the water back and forth in ac0u hil b:d0tr/g 3paj9ul5h30qnv* b tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide q/jh0ul 0btcvgu3a 5d 0*nhpb:l3 i9rtub 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 with6l7y phxn(phz )zi9w9zajw(judw7 ( 0 in the Earth between two9)wa7zzpi pzyj7(wxul ( (nhw6h dj90 kinds of material. If it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shcpt5graou 2 1. ws9ix9zyf2f /elf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests make a 34i2/9wx5tuzro9 y 2ac1ffs.gp$^{\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, dense axlk p/gxh75j) ir. If the sound wave hits the cold air ij g/)kp5hxlx 7nterface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary between two rwxn6is v7zx32xws;a44x758mwfbsl types of rock at a 38 s v ;32w4 sr wx67wx la85s7mfzxbinx4$^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m in diameter. According to the usehaa qrn59)gg5b,c, ps r’s manual, the dish has to be pointed in the directgbpn 5hra q9s, ,)acg5ion 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 wavelengt5q xxn,vz 7r;wh 250 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 do they have to run to safety? (In the absence of knowledge and warning, people have died durwvq;5znx7x , ring tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffn u.-bm75zzdzh ess constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kghmu.z-d z57 zb, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a sm,ac.nx5 aw:fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a .a5sn w:xcm,a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hanging spring. The gm6zpz6.0 kdi mass then falls 33 cm before it stops and 60.zi gmkdz 6pbegins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s ecxds f 6u*w qb5h0e6 zam,8/d(Fig. 11–54), compressing the spri8 xe mas*u e5q0w,h 6/b6zdcfdng 5.0 m. (a) What is the spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just the right pace of a u+giazv;z28o(0(j -wlq9cjhljv) k fbout 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed hij o(k 8v(+flwjqg- auzz )v;09j2clof waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-rpm phono 9sl3ky0xiu5egraph record have a wavelength of 1.70 mm. What will besuy0i3 x el5k9 the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrate:d(q gcb:(ung6k8 nfis according to the equation x=0.650cos7.40t where x is in meters and t in secondf6gd(cnknq8(uig :b :s. 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 if4v:t7 joocr c1 it accelerates at 0.50g (av torc41o7c: j) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raft, it 07uedm.v kbb9z jr7f; sinks 4.0 cm deeper int7ku9j b. ;0ze7rbdf vmo 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 instrx5qxgxp(/ n9afm 6og1ct *kf 1ument are tuned to play at 392 Hz (G) and 440 Hz (A). (g1qxf9c1 tonp mx/*g5 ax6fk
(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 bxls: 5(u9p i8te(k sathe 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. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in :b85p9skt( xse lua(ithe heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tievyd-qwc9 lih3. z37b9v+mx e4 zar (lp of each prong moves 1.8 mm to xibqd7e9- ewmv3ah ryzc3 l+lz49(.v 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 harmonic motion of frequency 1..n7/grurrusr p.ciu2 3) 4 azu5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board dur )rnc izu3uap7.u/u.g42rs rr ing the oscillation?

A string can have a “free” en ((rugxlmd/0uv, bb,b:pv k n,d if that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11 g(u b(v xdr:npu0, b,m/lkbv,–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 e t v5j70stuei+xactly 2.000 s — each one-way swing takes 1.e5i vu7j+0 tst000 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 can0mecnoir0p54 /mptl 2 swing as a pendulum of small amplitude, but not both at the same time. Which one cmtnrm5 04ioe2/p pl0is 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 t6s-8bi:h+ejk gn)n6dttv q: g is stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pul6iq8sn vtbgjk)d :e-h nt+6 t:se 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 spring stiffn3gbmnnbee 3yp: u3h77b 4q s/xess constant k. A penny of mass m in spbhx n3:ge73bmy equ34/ b7s placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cacvrlublj.6+ ;,x xv3.w0zoz4bb md)dble is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. zmz cvx6 d; rldlv0xu.w,+3 bb o4).bjWhat is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as she.r 6zytbhq .v1g3c. iown in Fig. 11–58 (which 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 analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jq.6bzihc.1y r3v eg .tello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz