Give some examples of everyday vibrating objects. Which exhibit SHM, at least d:xg6; emi7p ;uu7jmwappr wgme;7xpju:u ;7md6i oximately?

Is the acceleration of a simple harmonic oscillator ever zero? If so, where?tr,nuqw (. wl;

Explain why the motion of a piston in an automobile engino (f k.hkbxs,t*f8- abe is approximately simple habt (f.*ox, f-s8khb karmonic.

Real springs have mass. Will the tokmb bh;3y:bwpdn;mse 0:2 b7sw :l*a rue period and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized massless spring? Explyobm7w k0spbm l3 :bhe; an ;w2b*:s:dain.

How could you double the maximumc;oly s ssvp;p0u (,vf fe6.-k speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached tz6cyz*+/ran0x * s qryo the hook of a vertical spring scale, and then is released. Describe the scale reading as a function / szry*0q+c6yznr* x aof time.

If a pendulum clock is accurate at sea level, will it gain or l fq +xbe,9zho,fgga 5)ose time when taken to high altitude?ga9go,zf,e)+ x qh5fb Why?

A tire swing hanging fromrag4 ;f ;:hw4zsi oj5el1 y;zk a branch reaches nearly to the ground (Fig. 11–48). How could you estimate the height ofl royzhzf;ek1a5;j4:4gw;i s the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake j-j.adb dt7(4v**d efe1uh jgthe pan at a certain frequevtdu-b7.h*j f(j1 da*4jeed gncy?

Give several everyday examples of resonancex4n2s ph0e-g mvq (5b6k n;eng.

Is a rattle in a car ever a reso h1jd sa fti-0gg:6b+knance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of itpy4:y 4u2+n+b5:cca:r vaa b8s fw/tfe 9wf yks source? Why or+:8cy4a p se: b2wyrb/yff+5w ntv cuak4f:9a why not?

Explain the difference between the speed o(lx;ry ic7ys ;c78eso87ukdi f a transverse wave traveling down a cord and the speed of a tiny piece of the cord7 s ix7clds8y;eki7y ;c rou8(.

Why do the strings used for the lowest-frequency notes on a piano normally h(e8hy zh5;5pq0y1w maufj s1iave wire wrpuw5h1 e ;a zm1(h5fi yqy8s0japped around them?

What kind of waves do you think will travel down a horizv4zj.sj pzb h( +. m(sen2qy2vontal metal rod if you strike its end (a) vertically from above and (b) horizontally parallel to its lengthznp. vzj2yb2.hjq s+mv (4 e(s?

Since the density of air decreases with 0os7 rpti-.lsq c523u) oinh fan increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air tsf7 .ps)05ro2h coqtn 3-iliuo vary with temperature?

Give two reasons why circular water waves decrease in a 4xwwwgl/d.e qhh4x*h); n 1xfmplitude as they travel away fromx 4;wlwgxe nhq4wxh1d/ *hf) . the source.

Two linear waves have the same amplitude and speevr/sdni 8c--0o vp yh0d, and otherwise are identical, except one has half the wavelength of the other. Which transps0yn/-d-c8vov h0irmits more energy? By what factor?

When a sinusoidal wave crosses the boundary uuhh- se10cn( between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and ve-0n1uh (heu sclocity do change). Explain why.

If a string is vibrating in three segments, are there g-rpsl :i p4ls22pt65 giu5waany places you could touch it with a knife 5s pasri:4 -ptg2w5g lpi26lublade without disturbing the motion?

When a standing wave exists on a string, the vibrat*: awi .7 kqd4g*n smbv;zz9xvions of incident and reflected waves cancelk wia*7nm:v;z q4vb.s* 9xgdz at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was bei6g,dv2wzc9kevu)-)zq u 7ksw vz d/;i ng transmitted from one place to another, how might we determine wh6k2d)uzw-eczw,;d k)z 97vvqg u s/ ivether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with aecq- o0st)zg *mplitude 0.18 m, what is the total distance it travels goc-s 0e)qz*tin one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hat-c 5 zbo0,cx *d33sg/ mryz2pbvxhs/ngs from it but is 85 cm l/ocb/ -ydm btsp3032xsr hv c,z5 zgx*ong when 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 its6.r gi h14rwsm 68-kg driver gets into the driver’s seat. Ir4. sgwr m1ih6f the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale streralv2ksolr+:q z .x,*z 6/rm etches 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring str6xk+z:* ,sl .aqrm2zlor ve/iffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mass of 0. :(ghs-n .p );ofod:h-z xei7b1kngza60 kg is hung from it. What is its fr:sh:)z.p i- 1;bo ngfa-hgkezod7x ( nequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the positi7 bzbe8(taegg3md/ sf14jxa) on x of the mass in Fig. 11–2 at times t = 0,t = f)e4at(3ed g 8/1sg xjbza 7bm$\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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’smnp1il kp5aic9zcv*42t 9)xf web. The web vibrates predominately with a frequency of 4.0 Hz.cv it9fm* 4p2inxc5a 1)p zkl9
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequenyeh,2qfpsyh j/)ed : ,cy of 0.88 Hz. When an additional 680-gy,:)hde /jyqp , hsef2 mass 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 vibrates 3.0 timelsa, ln 5p/e9, ad6l.y xkr:bes per second with an amplitude of 0.13xbk5 aal pdl6ly,n s9,/re.e : 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 f+d a uwa)p49:r/ nvdqfrom equilibrium is the speed of a SHO half the maximum value?9wdpd:v4f+/)nqaa r u$\approx$    A

A mass attached to the enjn .tki9fu z ,hjd5(.p82d ixh2yg+imd of a spring is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a verticalwn 8+ a 8hwv besl4dalh e80m:2k,dkg6 spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to dwk8e 8m8e6,hn a :+sld2bvg4khl wa0 reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attagtjel2 /1,fpyupox1o8ms5n:vg m +5ached 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 a,s8jt1: 5ym1eg /lofvm px n+o25upg 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 st0uv5fu (n.q compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave t n0t uvus.5q(fhe gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one ea9 bu- :veh2qcc5q 0upnd of a spring; av2hp0queb95q - ucc:the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest 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 = 0.45cmi d9;;)o obj:+jy /6aic8-podtw akhos6.4t where x is in meters db: pwdyhkaca9 86it-)o;o/jm o;ij+ 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 is the energy of :wlb ds*k:u e,*1 fiuia SHO half KE and half PE? ±l*ds*:u1ifk e, bw:ui    A

  If one vibration has 7.0 times the energy of a srl6;thifx z;x d.6fp3econd, but their frequencies and mass. ;3 6ztdpxrhf xfi;l6es are the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring once everxah c2jq7py9 8y 0.65 s. 92 qcx8h7jypa
(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 springaly*m, 3n r 4a)*a8v;b if8pvlxzlqj7s, each with spring stiffn v vaq8malyl8 ,x;ibf rl a7p4j3*)z*ness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates m7fa9.w cxj:;roow) j8l n3fa according to the equation x = 0.38sin6.5t where x is in meters and t isa: xc7ojn 9a.fr;f8jml)ww3o 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 twvsx g,d5 ;xv/ro examples of SHM, labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horrlbb -dht *d,2cyj, 6yizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Deterlht*2ddj 6 yybcr- ,,bmine
(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 Nbc6ye bc;;edc+wo0i58xp q1f/m vibrates with an amplitude ofcw;6 yfi0+8qpc1e5;b eoxd bc 28.0 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/c6iraq8xo gz /( *rrd to two springs, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed horizontal spring2ke) fn oo(ftbhmn-5(oo* x5 g whose spring stiffness constant inoemox(-b o *(kh 5ff)ton5g 2s $ 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 bridge. Aft6mstab -i .c0jer reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstret .ijm6ca-t 0bsched 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 ,p r3:d0xf-vw6sbcpu in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make,6ntnly:;0pud7p0f cwy 6gje exactly one swing per second? (That is, one complete vibrat60npnt:lwj 7;uyd pfyg , 06ceion takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth mh;/c-sewl6l. What is its period on Mars, where the acceleration of gravity is aboutl e;-/6lwms ch 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm long dr97ks+jy:vfcr0d av7p ,;hbi p or28
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 ,n0f/ia vo b8jm, the pendulum bob has a mass of 365 grams, and it is released at aovn8 0a ibjf,/n angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 sc8g+ q0:2dih /k/:,fri 4zjpal twjpa-g6ca m. If the clock loses half a minute p0 h:6,jt +2awg /jck c:z4gs8la /pidpaqif-rer day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximh l711 upgm3cb ghhh*m)rg. m(um 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 Hzs w4;;m doy y/c-u1 tib,9trbb. At it is released from rest starting atu i b;1y ocs;bmwytd-/,tr94 b an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchored boat eec71efckt5q4m z-/-0 gqdlz tvery 3.0 s. He measures the distance between two crests to bez/c e7 05c1zqtgml qt-d-e4kf 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequx-m gz/s,dq7 jkp4.aui din4 -*rd,d bency of 262 Hz and travels with a speed of 343 m/s How far apa zs *u4g.dr,b,4/iad7 -i k npjx-mddqrt are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilohertz) a (1tz fk;fgktsg3s l0n)x ;qs;nd travel with a speed 1; kq ;sg (gtf ft;z3sk0nslx)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 f7:bqu) )q ozpwaves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the se3h a9k)uvm1l gh(0mts5s, hgame elastic modulus, but one is twice as dense as the other. In which rod will the spehm(9, kthsags 05 eu)13g lhmved of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stm h9orj+n0jq12r)y vygu y-k8retched between two supports 28 m apart. If the tension in the cord9 ry2o kum8+r0y1jgyn q-) jhv is 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a axwxs c39/4tjx. 0hwk 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 terminal and sends a wave pulse along the cablh.cxx 4s 3wxwka0t /9je. 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 ofjmspr u3zjr4 529cwcq b24 hc: the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s laq5 2m2j4uchc sb43p9:cwzrr j ter. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at diflvm5 ;2w,((z: dshl:qitk c wsferent speeds, and this difference helps in locating the earthquake “epicenter2(i,kswtvc h5 q l:;(dmls wz:” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approxi u;49vvp68uf4:disd hq nlgs: mated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually includd8spv;6hq 4u:gln4 f9 :vdiuse a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, an1r d) c6b)e7hm li.-uc 0hxxf7vgofb. d (b) the amplitudes, of an earthquake P wave passing through the E6co)g)0xec f vx.f1m d 7b7lu- bh.ihrarth 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 measured toefb5i g3 qj vv+w.tx,p:xdth :h5hc8, be 5h:3 :gtd8 ,xbphje vt,ixwqh5c. fv+$ 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 th , a6wfh81yukbxsz7 1ztix+y ;e same portion of the Earth, but one is carrying twice the energy. What is the ratio of 6tafxiy;y +b17wszk,8x z 1huthe amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same fb hw4: qq spig n8-zfn2*;irdlk73 x(krequency, but one transports three times the power of the other. What is the ratio of the amplitudes of the two waves? k7l;(k2 sng:4 w* p8rdfbniizqqx 3-h  

  A bug on the surface of a pond is observed to move up az2a8nopq uzj*6t p3om 4. te-5 eg7dkqnd down a total vertical distance of 6jnqdo pe67z8o5t 3t.2mu k-gze 4ap*q.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are movingze *1 f:df; sc :cajgg:b3hny3 toward each other. (a) Sketch the shape of the string at the moment they directly overlap. *:3d:gsc3jy :efgnfca zb;1h (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 gh fx;f(/u.za 51rsrg 9t.pl hfundamental frequency, what are the frequencies of the first four harmonz(.;s5 f /h.utpgh1fxalgr r 9ics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency will /nf nzwp8sx pdr8e jcpsj+13v2; hw;9 it vibrate if it is fingered one-third of the way down from the end? (That is, only p9c ;p jdj+ pz838x;sn efv sw/hw1nr2two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates ie(vdjhb)g x y2wv7(x/ geld:12+ eizw n four loops at a frequency of 280 Hz. Name at least three other frequencies at which it will vld j:(vx( e+2)gy h/wxidewg1z2 7ebresonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the ,zq bhaqv.i .8frequency of standing waves is 475 Hz, how far apart are t iq h.,a8vq.bzwo adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, what is obublb w;q4l.,-m bz3 the frequency lmo, lbqzb3bu-b;.4w of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance fr5ky(9 vua9xku v kd.neowgy4m- ou08/om the bridge to the support post is L = 62c9 o mkuykex 0nkgyau/(v5.8du4vow 9- m and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it iet cs9pl40m3rfqtac*- kh)( ys measured to vibrate at 205 Hz. By w) qr-(40l fthackc*e 9ptmys3hat percent should the tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is sups ,ey:c 5nnn0,v2h: (g ku1tilupad3 pposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tensp:p ie uku(yvndt:5cs1 3l h,2n,a0ngion in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal stra8+1o7l2vv 8j 5,wph/d dxx doego;-uzzzpp)ing is attached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass pvpxlvgz+z/ha;w j od8o1p2d 8d 5,-x) zuo7 peer unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length h/o64 lobi(.eahuu*vkg bt8m+ iu+ n4of the string may be adjusted by moving the pulley. If the hangino*vu+. i+m/ghh o( bknb4lu eau4t6 i8g mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at jucaf8)y+l/e tfzg z 7)rst the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the centerct8f /7+ eaylz)fr)zg. 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.0/7dedf2fpyg9b 0al j * km/s strikes a boundary within the Earth between two kinds of material. If it approaches the boundary at an incid 9g/2e jdf dap7y0bf*lent 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” wix :u5vnyayvd*h-s l,6. ym2 mee*p5fhere the velocity changes from 2.8 m/s to 2.1 m/s If the il: faxy 2ei-uvn5hmd6* vs py.mye*5,ncident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer q7i:h;zfr,e4)n/b*ew m djd gof cold, dense air. If the sound wave *w/zgr qbf4 nde7,d;je h):imhits 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 earthq2r0k vd cpo+l(uake wave strikes a boundary between two types of rock at ap o(rc0k d+vl2 38 $^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m in diameter. According to the user’j*sw i9o/ yk07 xjt57 og8szy- lpxdwq/c2t p6s manual, the dish has to be pointed in the direction of the satellite, bxo6cdpp 8sysq/5/ 9*yio wk02wxtgl j-j7z7tut 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 wavelen*:fmbzk c9kvc8 jbf67mm:w :mgth 250 km and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual d9 fb8bmmc*m::fkmzjv 7k 6c:wecrease 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 stiffness constant of 550 k ife ywkf0*a5j. 7ubi; jc,ab; f3fq,mN/m Find the maximum compression of the bumper if the car, with ma b 7ayjb* wfi0,. 5fcuq;i;,ekm ja3ffss 1500 kg, 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 fv1qup. t--g +g8qg t3wnqwx9otwnh3- ire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves likeq9wn-gxw8tt qtwqpu n.o3hg+- - 3v1 g 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 x0 -smp /enfq5yckjj 1*2ggs8mass then falls 33 cm before it stops and begins to rise. What is the frequency of the encq0s1jym- 8/2xgs f *gjpk5 oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), c+5pwt saw8j,8zokc 3jompressing the spring 5.0 m. (a) What is the spring stiffness cotsjk j,zwoc+ pw85a83nstant 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 pp pg+kal9 ta.bj01zw 1ace of about 1 step per second, the coffee sloshes more and more until evabl +tj91 pgz.a kp0w1entually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certai+brj 3zlq8s pf ;4x6bmn groove 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of 8pqbj; x +sfr4mz36b lthe sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t wher fvi 3e./l1 gug9z;tule x is in meters and t in seconds. Determine 93uu/g zi1f;elgtl .v
(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. Whatp2+aqp( )osh;i xndx* is its frequency if it accelerates at 0.50op*dxx; 2s q i(n)p+hag (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg maoc i )1ro082gs-qthsln stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the c)l 8roqths2io- 1g0sraft 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 pla*t4ml u5dbicgi1: x :by at 392 Hz (G) and 440 Hz (A).ctdig5:b b:*4ui xl1m
(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 trw9j 7 gky-;py:+i*pgire 6f bg-h0zmjw u8/ ngaveling down the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (cgeu*jhfi g680 rwbjzmk-;9g ygi n-yp:w/ 7+p) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequen6gfr05pa wq+ vw l5vv0cy of 264 Hz, and the tip of each prong moves 1.8 mm to either side of cg6a5qv5 +vfl 0vrww 0penter. 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.ti*g. o( 2+ewhtg vfy-0v6q ik5 cycles per second. What is the maximum amplitude with which the end of t*2h ftqkg.gi vvi( -w0y+t6 eohe 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 attach,aymzvr7*yym+x 52h4c k3rh qed to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and thrmh 7 yhmvxr2,q*4c3y5 yakz+e other free.

  A “seconds” pendulum has a period of exactly 2.000 s — mgh4 02wr3 c rfbeycq4ki2.pij z1b5*); uxlueach one-way swing takes 1.000 s. ;0uq bjprw3 g 2m4rli ) ui*c2z5 cy41kfbh.xe
(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 c mrunh:3q; . 5iij8dt+ z-ej z2l5icpgan swing as a pendulum of small amplitude, bu;iiejz+ rc:-u5. niqjd3gth 28mlz5 pt 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 25-1tcj jejdhfy) yj)6 )5 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will thed1j6f ))y yjhjetc-j) two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring withuz6p- 840i9;tgmev k- bsglpn spring stiffness constant k. A penn4bv -ipgl s9u8kmne-60gz;pty 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 top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crf9o0t / / skeibp(ros*ane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the periodb9osi/e o f(/tps*0rk of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as s87g 6b0 , xj*qqgygy*1fx- dymezqqt1hown in Fig. 11–58 (which also gives the dimensions of the block). You push it 6g,dyq0 f8q1bg qx7y-* ze1 gjxqmty* sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz