Give some examples of everyday vibra-k 62ctg* qxfa;f* ieds4xv 1eting objects. Which exhibit SHM, at least appaeq vs4 e-tgic16f xf*;2kx* droximately?

Is the acceleration ofwxqgv)0t, vf8q7u fm)ko j tjx e5s ;4q1+9dai a simple harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an ay*ry etkuld 7+t ;d9-butomobile engine is approximately simple ha br*te9+7dltyd; y-ku rmonic.

Real springs have mass. Will the true period and frequency be largenk3u7 )zirpjx;1b 7k7; (b lne/uiqder or smaller than given by the equations for a mass oscillating on the end of b/nu(;p)7 deq3rnjk7iebi ;u kx1 l7zan idealized massless spring? Explain.

How could you double lo /dx;fzqi *,z2/abafkx l;n,5n/zr the maximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the g o/t;3 f327 tqiia-m;yudw ighook of a vertical spring scale, and then is released. Describe the scale reading as at / -imd7wgutaoi2i33f; qgy; function of time.

If a pendulum clock is accurate ;(l avp r+/0vqyqz3stat sea level, will it gain or lose time when taken to high al+ vv/rqlps 0ayzt;q3(titude? Why?

A tire swing hanging from a branch reach;6g ajlob v/(ees nearly to the ground (Fig. 11–48). How could you estimate th(g6; j/v aleobe height of the branch using only a stopwatch?

Why can you make water slosh backm,l h( j ha k)+bw+4guz6 j:( mgtcle*mjs9+mb and forth in a pan only if you shake the pan at a certail (tmmj+j(bgu4hj+a:h 9e+mm w)s6zg*kbc l , n frequency?

Give several everyday examples of resonanc; ml7g4zjr a8;biv 1cte.

Is a rattle in a car ever a resonance phenomecvccf89 i3 ijlz+/x- rnon? Explain.

Is the frequency of a simple periodic wave .mn82c0x w9i bize d.z),ipl requal to the frequency of its source? 2rmc9lzwzii8 0ebd .p n.),ix Why or why not?

Explain the difference qxh3ik 1.tv06, vcmuy between the speed of a transverse wave traveling down a cord and the speed of t6y 3.0c k1imv vhxq,ua tiny piece of the cord.

Why do the strings used for the lo4 l,vulvqnu19 u .w-mcwest-frequency notes on a piano normally have wire wra qv,v-l1 nu.9uwcml u4pped around them?

What kind of waves do you think w*z9tcgy7k4) ofc)d5dooyh v m3)2pmt ill travel down a horizontal metal rod if you strike its end (a) ym)od7m9 yd 5ckvgp ) fh)*tzt3 2o4covertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperatu8 o oqgaxzqfzckm./9b i18f9w(a i6e/ re, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound w 69fo 1zko//aiw8zxmc(.gib8feaqq 9 aves in air to vary with temperature?

Give two reasons why circular w j hvl1raf*o8+3m4mnaater waves decrease in amplitude as they travel away from the sourcen8*43hlva 1mmrajf o+.

Two linear waves have the same amplitude and ,n up/0siq hr,speed, and otherwise are identical, except one has half the wavq/ ,nhrup0,sielength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of cord at, nyh9rk 1 ssp 5bb1pr2ik7w9s in Fig. 11–33, the frequency does not change (although the wavelength and velocity do c strbs 7,wik95 2 nprb1y9kp1hhange). Explain why.

If a string is vibrating in three segmea aii ;x1 irnkx6;d v18csuz+-nts, are there any places you could touch it with a knife blade without disturbing thx6n11i+d8ic;s-;vrxa iak zue motion?

When a standing wave exio,v qnm z/r9))fm;u mosts on a string, the vibrations of incident and reflected waves cancel at the nodes. Dmv/mqf ;mu )zon9,)oroes this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted fro3 snl(h+(afhz-k0 zx td.j u2hm one place to another, how might we determine whether the energy was being carried bj 3ndtk sf(a+-.z0x(h h2zlu hy particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the t91ju qtn1;jvayaw 5 j2,3 tafqotal distance it travels in one period59jyt waajq1vn ; 1a23qu jtf,?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but is gdqo+nu0rp9ip 7hed 4) ik h(685 cm long when a weiph( )nupi7 g od0i49dr+kh6qe ght 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*n roamfip(h6,r3sp*hkl 7 de r 4yz*6 its 68-kg driver gets into the driver’s seat. If the car goes over pkr(o*46l7rezsnpfrha y*m*3 h6id ,a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from iti)ibx./7w(i3+i yces toxya 9. (a) What is the spring stiffness +it/siiaix7 w) o(yexy3b c.9constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mass of 0.6qkhwuxm5(f gf) 34klq)fg0+nxc s; f20 kg is hung from q3 )k0f )x f;+ncxsm4hqwkfl 5fgu2(git. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the positvvs77-s ,4n(9gs rmw5j brbmsion x of the mass in Fig. 11–2 at times t = 0sbvrm4- (vgsbsr5 s,7 wnmj9 7,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 vibratejz17dtbur 0oprb02 2a b8w)dvs predominately with b072bpobda j81 2wrvtzur d0)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 spe. hf:qc mt ;o;n m:.s-x2ulfzring vibrates with a frequency of 0.88 Hz. When an additional 680-g masss:umhmtqoe.x;2 -;l .nzff: c 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 vipyjd5gk19t ml7re33zbrates 3.0 times per second with an amplitude of 0.13 m. Determi 5y epgltz7r1339kjdm ne
(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 equilibnfk ,f9 d4+teifoyd( *rera ,8rium is the speed of a SHO half the maximum valun de+a, do,ff*(yeri9k rt 4f8e?$\approx$    A

A mass attached to the end of a spring is strd px)/vc5t0tm * t7tlq3vq(yh 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 b*9w59sbum 3l (yfdgzspring 0.315 m. If the spring is stretched andg 9yl b3b9sfumw*5z( additional 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 uomg. v /vi;s9a 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,vmu.g v/o 9;si it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a toy pokxjk)t+m2 dk7kqd1r7. h 1lg.nnf 6lmpgun 0.200 m to “load” a 0.180 n77 2d.h1rmjnl6 kkd.)t1lxgkq +fmk-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surfe0thu, *i4s;z6x b. g gj0kkewace is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work ibgu te.g6k i;,j04eskzhw0x *s 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 equation x = 0.45j s( gm d.j17t+ggcfq);inx:tcos6.4t where x is in meters and t is in seconds.:.;c + t 7 gt)mjjfs(qgndgi1x 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 e 7lw/omgxh-3cquilibrium is the energy of a SHO half KE and half PE? g 3hl7o-mcxw/±    A

  If one vibration has 7.0 times the ew xvuhb(30w*re 4/pdz nergy of a second, but their frequencies and masses are the same, what is the ratio of their am z0wvpd3x*4rhwu/ (ebplitudes?   

  A 2.00-kg pumpkin oscillates from a ver7 ,g-,imzek i lng3.-kb rj)mutically hanging light spring once every 0.lbigk, kn.7-rm-3i m, e )uzjg65 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 verti iqcoqd(j*.8vtb r5w- 06jgfrcal springs, each with spring stiffness constant k (Fig. 11–49). What wio6g(0*wt 8 rc5qfriv . -dbqjjll be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x is ina3 -r3w 1ykuzsvgb9+n meters and t is in seconds. De u-sn9yv3zka+b3wr 1 gtermine
(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 is 9-48xtsi twwx
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal spring (k = 124 N/m) isrh-i - rh:t qe+txb4t+ struck by a hammer, which gives the mass an initial speed of 2.96m/s Determine bqr ti--h e:htt++ r4x
(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 ti7zt ealy2: 0stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrez7l ai:t 2ty0ium 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 constzufx1u3 xi ;t9ants $k_1$ 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 h8jjvs wjm5mhbr:z0 i-1 **nggorizontal spring whose sprini v:mg0r*m*ng1j5 zh-wb8 jsjg 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 massnx2i u42k mw)j7wk+fsl *zr; x 65.0 kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finak*zw +mn)si 2ufw;k7rl4 x2jxlly 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 m6d-0lrcbl qkg c :7t360 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to mao6j yei+50:uc*d oirdpoh,m 1ke exactly one swing per second? (That 1j6e*oiid upo0h:do yc,m5+ris, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.8*+/o()tpsqa,b7ukabm c ey:1w5epil 0 s on Earth. What is its period on Mars, where the acceleratione oq7 5b1/,cuep*)a: k(iywt pmsa+l b of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendul;sn ey1 gab9)hum 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 i3 -ul wjvs1u2r+hb-mvr9 )gkof 365 grams, and it is released at an angle of 12.h1- b)-rw 2+virvl 93suuk jgm0 $^{\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;tc:-j r1v5vb augt6 g’s pendulum has a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pendulum? shortene6 gjtrg;vctbv :-1a5ud by    mm.

Derive a formula for the mhwc ol0g-w8nhiuvej r/+5t, t+t qp65 aximum 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 oscillyu w 1u1)a f/gf/sc;wzates at a frequency of 2.5 Hz. At it is released from rest starting at an angle of 1a c)g/;/z yffw u1suw15 $^{\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 anc7 ,tl bwkc8xhl+xs*g 3hored boat every 3.0 s. He measures the di8tg3*h + bx wk,llxc7sstance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speg z2u 2,t5tmqxed of 343 m/s How far ax2, u5zgtmt2qpart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 k ct2zc*vltg/5 Hz and 1600 kHz (kilohertz) and travel witht/gc5*z 2c vtl a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal wav0ikzfl 6r3kun:.)copo-56eiw,tv nk es in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one i jk;kvipgn, um9)-xxap:.rp *(k f o9ys twice as dense as the other. In which rod will the speed of longitudinal waves be greater, and by what fac,);p9pif x pamgvkn r-o :*jykxk u(.9tor?   

  A cord of mass 0.65 kg is stretched between tw8c-h7qicx5 r: pw7*kcmr 3 ovgo supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulsp:-cw7k3qv r5m8c*c ir hgo7 xe to travel from one support to the other?    s

  A ski gondola is connected to the tt)oe6h+ qk9akxl. 6wwop of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the k wk+wtxa6oeh.6l9)qterminal 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 j1l,fmnhp7y9 s6 i2t puf. p-3uevp rw6ust below the surface of the sea. He hears the echo of the wave reflected from thup9e,tps mvn.3ir- wy pplh6fu7261f e ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and this diff sb9,newb:d d5ie5q a1erence helps in locating the earthquaeib1w q95n5e ,sddb a:ke “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( o ,sol(7.jx9nq8imip1 f 2sb 7smorv wave can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequo pifixj( r bs 8(79mlo7v2m ,.osq1nsencies), 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 intensities, andl*zh4ozd +f r 9dcy6219zkswk (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points zs2 6h *k9 y zkdlf4+9wozr1cd10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquak-ks -, xpijss.*oc.qre wave passing through the Earth is measured to be ks,cs-x q*jip or-..s $ 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 frequm/*fy2ln6 fwsj ut*.n ency travel through the same portion of the Eart*yfmsj. *un6flw/ n2th, but one is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string hr/1gm g7lnj v)ave the same frequency, but one transports three times the power of the other. What ismg nj71lrv g/) the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond ikp2lw.)e 2q:whtt au 5s 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 faclqt)eh upt52: wawk2 .tor does the bug’s maximum KE change?   

The two pulses shown in Fig.)s +s o2 g97u ,ctzr-:batliqe 11–52 are moving toward each other. (a) Sketch the shape of the string at the momea l o+79-t,rist)uszc qe 2:bgnt 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 fundamental frequency4 8 (tny*c-gv4xaxwwph * h+ss uw0pe4, what are the frequenccyps48 gwhew xu 0 -pn+ s*4a*xtwh4v(ies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At fq6 q9w+c ouq5what frequency will it vibrate if it is fingered one-third of the way down from the end? (That io u5+q6q fwcq9s, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequen- ys /mkvf17occy of 280 Hz. Name at least three other frequencies at which it will - /fs7mcv1yo kresonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of sekj0*sdd+;rp+p (i votanding waves is 475 Hz, how far apart arerjp+espok;d *0 (+div two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, what ihqrn jl5o/+l5s +qlhjn/5o 5rl the frequency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance fromt0elgsq - lj;- 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 first0- -tgl jlsqe; two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 gsaxm+ z0k, *k7 i/blnHz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the f*7mzs n akgibl+k, 0/xrequency?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 measurab2,bsv y q*nn-*evb8ed to vibrate at 205 Hz. By what percen s- 2*,bb eqnvbanvy8*t should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal d/pvyuht 0n 9vmd ;g77string is attached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass per unit length is7dt0;ngym9vpuv/h7 d $3.9 \times10^{ -4}$ 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 the;t+cr;sak/b p pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing s;;abkc+ rtp/wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the watco8yz:h* + yh (4hjgbaer back and forth in a tub at just the right frequency, the water alternately 4o 8hy jz+a:hy(cgh *brises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary with6jy v395ioypa 1 +ik*s jv3hhxjg2q6k in the Earth between two kinds of material. If it approaches the boundary at ank5*3 aiko h6vy3 j1+6jj hy qvx9g2psi 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” whvo5qb5u9qey4 l9 o jc2ere the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave cre 9oe5q5l4y29 ouvq jbcsts make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer of cold, dense ai ftac+o 7yg+/wr. If the sound wave hits the cold air interface at an angle of go+/ty+f7ca w 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 types of rockiwh* y0,p v9hf at a 38 h* i0wfp vy,9h$^{\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. .b9 sgc obh -x;,(fxstx1sz t-According to the user’s manual, the dish has to be pointed in the direction of the satellite, but an ersg(b tt-sz cf;so9h,1-x x.bxror 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 velocity 750 km/h travels across tl wuajibeg+ zaf 0: fv282/y1khe Pacific Ocean. As it approaches Hawaii, people observe an unusuavu e/fy j2ia+gz2fb18 kwl0a:l decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring sti7h;tavot w*li7 f9uan/e.hr7ffness 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 (approxiwa9th7r7 i .n;uo7tahv lf* e/mately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a 6ju8 xwpd4 j :h1(arpdwindow to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a simpr a18pd(d6 j4 p:wjhuxle 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. Them *xyl0xs 5ad2 mass then falls 33 cm before it stops anayd5 x* 2slxm0d begins 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 (Fik3z+ yunduw sqp-52yn8ou-5 og. 11–54), compressing the spring 5.0 m. (a) What is thuk8- un+ p2zsu yy5woo-5dqn3e 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 9npgx.rxh-- m5iv 4 vlpccq :98 cm) at just the right pace of about 1 step per second, the coffee sloshes morec:p.4q nml -ri xg9 xp95v-cvh and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the ceolvo3w (7 ;mcznter of a 33-rpm phonograph record have a wavelength of 1.70 ;owlzo7v( cm3 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates apu./3 / h.mlbrd6vubqccording to the equation x=0.650cos7.40t where x is in meters and t in secondsub3.rh/ ./pbqd m6v ul. 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 z51i01is8 q ypwrtc /jif it accelerates at 0q/pz0r y 5sicj8 1tiw1.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on th3e w)i kvvkir);z- k,vvr:4sae raft, it sinks 4.0 cm deepei 4z,svr kv-ive )v)k:wrka3; r into the water. When he steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play at 392 Hz5+ ) f(kx mt.wr9of iyngj+tk4 (G) and 440 Hz (Ai.jrx g+wf f5k+(4yo)tmt k9n).
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stretched (6 wbdlb ,udz c;hi/s7two-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 rd/w(bib; lu 6hcd7, szatio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency 2c6y0 ns2w ;l xaxt gn+inzr: ie,t4r0;5fzozof 264 Hz, and the tip of each prong moves 1.82 r0z2 i60erlczw+5nf tx 4 n;n:gxao;yt,szi mm to either side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of frequencnmrpk+;j*lp(n6r ak7-/a:b*v i oc mj y 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the bnak+iom-nrj7/ pv6(a;j k:* clbr m*p oard during the oscillation?

A string can have a “free” end if that end is acgi6jjqovi5b )7v av8++h qf6ttached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the g7fvca b6i j+qqvo hj 6i8v)5+resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a perio9sdb..dt wje+1 gbqn a8jj z6+d of exactly 2.000 s — each one-way swing takes 1.000 stje jda1.bsd6+ n w+q9j .bgz8.
(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 3 nkgvcv(d 84tin the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of gk83 dvn4tc( vthe 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 ij5id u,d:ous e4w sel.5fz mz-w7 eq):s stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms late45.izu:e,zo swuj7 - 5ldms fqw:) deer a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceil ,r57 oxqm8e,nrtn/uv ing by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations t5e7 mt,v/xn q8 rroun,hat 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 cran -3ko;rynvm7a e cable is 22 m long and has a diameter of 6.4 mm. A breeze vk -7omr3;naystarts 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 (which also y(( gzv0fdmq7gives 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, (gq0(f 7vmyzdgiven that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz