Give some examples of everyday vibrating objects. e jg f(aaq5au4su6o)- Which exhibit SHM, at least approxima-a 4 ajsa6(qegf u5uo)tely?

Is the acceleration of a simple harmonic osc-npgt31dzp w 36lemg2 illator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approxima fz7k)b, mgqb6)ja ,hwtely simpfhb)b76g a ,,)zjm qkwle harmonic.

Real springs have mass. Will t9iplyaub8**i 7amih 9he true period and frequency be larger or smaller than given by the equations foahii*ui*ly79p a9 8mbr a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of m)-gn8itl +k yw)bmzl wu2r6;dj/hl 8 a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale,:-b.i0tppbo .yl 2ouh p ab2p, and then is released. Describe the scale reading as 2pho:..y,bpo b 2 p-ilb0atpua function of time.

If a pendulum clock is accurated.t 5c.9ks +banradu) at sea level, will it gain or lose time when taken to hik9cbrud dnsa)5 a .t.+gh altitude? Why?

A tire swing hanging from a branc 7 h zgag(y8oy2i-tx,qq;ag,eh reaches nearly to the ground (Fig. 11–48). How coulga t,gaeio q h(7-y8gx2;zy, qd you estimate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake thq tknxakc 11;7e pan at a certain f1k7 q1ktcanx; requency?

Give several everyday examplesnr2 d9.k(xwut1f6 w4 n vrp,xz of resonance.

Is a rattle in a car ever a resojk,e.gj * fr;cck /,honance phenomenon? Explain.

Is the frequency of a simpl,qjz edq/ -b 5zzm9r4oe periodic wave equal to the frequency of its source? Wh94mz-e jdqbo,zzrq5/ y or why not?

Explain the difference between the speed of a transverse wave z*pbb :r .a,fq moj 39aykti9.traveling down a cord anro 3, m j.z:f9a 9qitkp*bbay.d the speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano norma 62jgl h.ewr)t wkpp82lly have wiltj28pe6)hgw2w kr .p re wrapped around them?

What kind of waves do you think will traveljc /g.,ot1fyo down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizonf/ygc t.1o o,jtally parallel to its length?

Since the density of air decreases with an increase in temperature, but the bui-8)t4j tturholxc ykts4 8,c3j(h,rlk modulus B is nearly independent of temperature, how would you expect the speed of sound waves i, tujs x- 8(3tckto,8il)yh4thc rj4r n air to vary with temperature?

Give two reasons why circular water waves decre,xbo lfhr/;s 8 p*ca*a no9n0a8yrp2q ase in amplitude as they travel away from the sopno 8/ ,0*nshbx*qy al 29rrcap8;afource.

Two linear waves have the same adsxn3f,qbm mp7:p - +umplitude and speed, and otherwise are identical, except one hmf- qxm:p7,3 +dsnbpuas half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave cr la,yqt;* n3, sxxn)zkosses the boundary between two sections of cord as in Fig. 11–33, the frequency dosz*ky),nt,lnxq 3a; xes not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any p6;6lw6ic b awty7 bkz7dgu(v8laces you could touch it with a knife blca u6b w 76(blk;ytiv8 zg6dw7ade without disturbing the motion?

When a standing wave exe2 6faa-r2yzqists on a string, the vibrations of incident and reflected waves cancel at the nodes. Does this mean that ener-raa2yz fqe 26gy was destroyed? Explain.

If we knew that energy was being transmitted from one plai1c zv.f7 d7jjb+z l9ace to another, how might we deteifj7v+jc. ldb z91a7zrmine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m,,l 9x:m13y,akjhdu xb what is the total distance it travels in one period? 9k1b, my xd,u:hl3xja    m

  An elastic cord is 65 cm long when a weight of 75 N h f.i;v5 yh0inhangs from it but is 85 cm long when a weight of 180 N hangs fr nh;iy05hiv. fom it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-k m7 z,bsriwb:d9mh.2a g driver gets into the driver’s s azdb :2ws,7m r9mhib.eat. If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it.vfqp o6,c1 ep 3c i2q frau:,skoqg244 (a) What is the spring stiffne c:4oo1gu,k4eqf23q pfi6sv,q 2a cr pss 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 0.60 kg t)v l22wuj4rqd.5kni is hung from it. What is its frequency if only 0.38 kg hangk qitd vjlr2wn2.)u54 s from it?    Hz

Construct a Table indicating the position x of the mass i(da1i4eh;he( odo8 tjn Fig. 11–2 at times t = 0; d18eh ioo4e(ta(d jh,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 vibrates pr,i )a/cqsi0jr edominately witcrj)qs/ ii0a ,h a frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring tz65 9gy. k ck2pkp:tkvibrates with a frequency of 0.88 Hz. When an additional 680-g mass6:kky p.k5k zt2p 9tgc 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 times per secon l)bkliq6 b2 d09d 4p+bzc1dnqd with an ampli k2 ld bdzq6cpb)94iq ndb01+ltude of 0.13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed of a SHO half the madxtl 90id ,t5lximum value?ltdi9t5lx0,d $\approx$    A

A mass attached to the end of a spr l5ql z b3x: awd 6p-c(p30xzl.ysfym*ing 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 stretches5*g tqq4g m9 xos)(-sk(d4d a6zxipub a vertical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to4oqb65q*zimsxax-() pg 9(tgsk d4 d u reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with j1ys zyt o0:)qg-g.a bspring 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 moj)-y:b s t1qy0gzgao.ving 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 towb4y qqg6op8/xl 0+dcuz4h:h compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg8q/dx460oh:uwlcby+ 4pgh zq ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one end jv lm 9;dpp(0,oqmg ok69-kkwm ks/u+ of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0,vk+okj;kg6s9m9- q0( mw pumold pk/.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 = 0.45cos6.4t where x is h 9b,/(e qath13amp9cvtz8jlin me9 q a mt zvh(p,c1a3etl/89jbhters 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 a SHO half KE ,rc29hf2;/ffks yer;ivh3etb y :oh*and half PE? ± /;t3; :fyfh,b o9ery hchvr*e2f si2 k   A

  If one vibration has 7.0 tw)1l8uck/m:u jb l-th imes the energy of a second, but their frequencies and masses are tjc: 8 t1b/hlu-ukl)w mhe same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring o-6nhh ijc r5mp/5x6ponce every 0.65 / monp6r-5ichx56 jp hs.
(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 d xy+22 )txd9r lk.s fnj8e8luidentical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequen)2 +x lr9f28stkd.n yx8eldujcy of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x is rirpq+--:npt)s a b unt.*mb7in meters and t is in s7tunbmpa. -r):pqib -+tnr* seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and B. For each, w5s qxc7nb5j nwcqo5)t. cj.i9 hat 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 dkl 0vuztm-u94 m2r j7on the end of a horizontal spring (k = 124 N/m) is struck by a ha -7 0tm2dlru9kvzjmu 4mmer, which gives the mass an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305 N/60:1;p c wi2vatvne m+yyk3a um vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocityvt;w23 kci:un map6yev0+ay 1 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, witg i o;4u +fyevbb8jz48h 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 horizoefyi18, f pc 5k87lmlxntal spring whose spring pfkce7f58m 8l,1lxyi stiffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high bridge. Afteralwt.u 8:c.v)s5 nj.luwnj;r6 e dt-v 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 n.vnjr 8d6ta. jw5eu; :ts vu.cw l)l-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 vib zhx,fv9x 0.alcxw r;0rations 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 mo llosucdiz (tkh3339 9i6o*t ake exactly one swing per second? (That is, one complete vibration l9sht*out3o o3iz6k(ldi3 c 9 takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, w 3vimegx-v6 pv jpo45:d vh,jepn6; 9vhere the accelerp6p m9 d: vvxvn5;p v3vh6 4jjo,eei-gation of gravity is about 0.37 that on Earth?    s

  What is the period of a simple *+0 s3ovsmi9gyyle;x pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simplegh*v0rp0 ; cjgd5x g/ cdg24le pendulum is 0.760 m, the pendulum bob has a mass of 365 grams, and it is released at an angg0d/*depx r4 cg0cgh5;jlv2 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 pfc*c.hqw pw;3dh-z0c endulum has a length of 0.9930 m. If the clock loses half a minute per day, how should youhp3z w.fc h qw0c-c;*d adjust the length of the pendulum? shortened by    mm.

Derive a formula for thuq9g- u x)2o c; 2kkd,bp;hlete 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 frequen 7vy x*-nrnge;cy of 2.5 Hz. At it is released from rest g ;v-ey *x7nrnstarting at an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests passafr9j.-yqd;ywv + r(g n k)x-n the bow of his anchored boat every 3.0 s. He measures the distance bet(- k9jvqyd f+g ary;-)rnnwx .ween 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,f4 lf es/bif2 a speed of 343 m/s How far apart are the wave crests (com/4,2fsiefb lfpressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilohertz) ad3z+uboh k m8(3.yj/ ten(i8) v bnenfnd travel with a speed of (n3 buye h.8ei/ oz(3d)mb tn+k8vjfn$ 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 w9 m55l g60fqunjbu d-paves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as tb7y xjn) ,,11aouolr92j itvdense as the other. In which rod will the s 29,j)l1nu t,ir7yxo1vt joabpeed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched bet,y lqovd nj ;,( ,azl(fs;tp4*hud0dvween two supports 28 m apart. If the tension in the cord is 150 N, how long will ,sdfj ,dv doula0(lv(;z hn 4qt;p*,y it take a pulse to travel from one support to the other?    s

  A ski gondola is connectedoxo z(vq-s/;h50fc dx to the top 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 terminal and sends a wave pulse(zsv/h d fxx5-oq o0;c 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 t7*juv0* j2vn,b fcw sjust below 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 ocean0fws7*c , tv2*bjn vju at this point?    m

  P and S waves from an earthquake travel ng )oeamf6-2g at different speeds, and this difference helps i)-nme gfa g2o6n locating the earthquake “epicenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated by a sinusoidal t:8t ;wwuc0twnv nw u4-ransverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with4cnuw;w8wt 0vnwut-: the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitzq j7. p2*ba(mijn5ie-ak hx*l 2+ekyudes, of an earthquake P wave passing through the Earth ki2- 5x* h2az+ajji7epqlmn(*kyb .e 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 measure.8p/ f r4zy xoak3,khwd to be 34pk8rfh/y oz.k,a wx$ 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 throuwhy9odjm r19 x.m ;om/gh the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the a91;ox mr/ oj9y.wmmd hmplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, but o9ixm/;1b2jmknb x tk;ne transports three times the power of the other. Whatxm;m/kk ;b9b tx1n2i j is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a f.k8p j)khr/hpond is observed to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples8 /hpfj kr)hk. decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 a a9b9 ,szdrpx07 5tkfzre moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few momentsk70r99d fasbp zx5zt, 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 Hz6szt2eurr r;9 as its fundamental frequency, what are the frequencies of the first four harmonic euzrt rsr26;9s?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At/ ,:fm q/jtdgnzqzq/ /6 (yjlz what frequency will it vibrate if it is fingered one-third of the way down from the j zf/dq6tn qg :j//,yz (lm/zqend? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a 2it(0 ta1 dnjcfrequency of 280 Hz. Name at least three other frequencies at which it will res(1jd anctt0i2onate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string i xao/j, qvf5a0s 92m/s If the frequency of standing waves is 475 Hz, hv5j0ofa/q , axow far apart are two adjacent nodes?   m

  If two successive overtones of a vibrrfu 65rw d8w/l f9d.e;l gh9rcating string are 280 Hz and 350 Hz, what is the frequency of the w fewu5d9cd ; lhl r/9rg86.frfundamental?    Hz

  A guitar string is 90 cm long and has a ln1y5j7r 49b ze 8 of)qts-kvzmass 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 anolt1rb y) kznjv qf54987s ez-d first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, jf u /p: f w.xn6c235hau4hx,rzztyu0but it is measured to vibrate at 205 Hz. By what percent should the ten ,w.2 ynhp a:uchxf564r uu/ztzjf30 xsion in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it is meas3nsueby ,lt3etgx 8vhaj62+s q4 7qi -ured to vibrate at 205 Hz. By what perc - +gsetehxjt6 u7ba3sq,43 nvl 28iqyent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal stridii ;mhp -z6/eng is attached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass p/im6z-d; hepier 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 of the string may be adjusted by movin:qz/nq8 jbboke)n 1g0g 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 between 10 qgbzo)ekbn/n1 0j: 8q cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the r2,rhz- 0d rdvbqre7z.9v9k xoight frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of thrv2.r z09 9o-q dkr hzbde7,vxe water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundarypz0ru7kg79hq4 hwuo yj m1n+8 within the Earth between two kinds of material. If it approaches the+m hw41 nkqugpz 7j0hoyur9 87 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 “shelfz ;yne6 mf2)9n din-dp bpuf95” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests make a nze2; p 9iff9ypb)56-uddmn n 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 co:qpgh g 5rt-t0ld, dense air. If the soun0 qtgtr: h-gp5d wave hits the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave str 2h6ov0 dji+txnq*f c7m gt+chuj;2o;ikes a boundary between two types of rock at a 3qcdo+g fjci 6 m70*n;j+h2v xu;hot2 t8 $^{\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 ukm,vbojlp-b8:j-u , a ser’s manual, the dish has to be pointed in the direction of the satellite, but an vja8 jko,,p l:- ubb-merror 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 vevz9/ij ,vvrmy8u (*p zlocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, pvuz( ympz/98j,ir* vveople 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 during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring ssi 3v7l;g am sc,qn7j*tiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides wit7l j ;ais q7sc3mn*,gvh 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 fire net 18 m below, which stretches t 1/0hgfh)b hknhe net 1.1 m. Assume that the ne0)bfh/hk n1h gt behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed o.g gpl;dkvw0tw7v4d8 7sjf ;zn the end of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise p7g fg; z7wt.wdk j084dvl;sv. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huvtbp*)rsa. * yge spring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness con .vab* tpsry*)stant 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 cly6gr+ .sq.btc 0 aphv s:/9ekm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it sta .kp.vchgltqyse s09br +/:6 arts 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 frq vsarx99kc./z pvt,+om the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of thevt9csp/,ravq 9kxz .+ sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t whvl l9yr4m**u:mc pj f-ere x is in meters and t in seconds*lv yrm9u 4:l- jpmfc*. 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 oscillate e6mg m1 bl-fkllh 1+)y+eg,tbs with frequency f. What is its frequency if it accelerates at 0.50g (a) l+fth1 ml- eb,g+l61kbm)egy upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg .*9iqc fhml)b/k2:b8 bzedr12xx gv nubiy .(man stands on the raft, it sinks by h ). bbiue9f.r 21gz2kq(/xvb *c8:lnidxm4.0 cm deeper 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 tune;co94 qr zfzw+d to play at 392 Hz (G) and 440 Hz (A). q+9wzc4o rzf;
(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 st)ln30xbensn k w, /ck,retched 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 kcxn3b) k,/0nlw, senlighter 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 the heavier section of cord or the lighter?

  A tuning fork vibrates : e9w;ws9gig mat a frequency of 264 Hz, and the tip of each prong moves 1.8 mm to either sidmi9gwseg w;:9e 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 b(wqhl tswq/3l glf0x3e.l1/ frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placedxh 30qq/3f1wb (ltwlsl.e/lg there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a ring that ogvepm/knz,. l3.mf) can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant viongm z l kf,3.ep)m.v/brations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way sdd1;nvfe/7 l prowl9-wing takes 1.000 s. d f vlw1pr9n;lo7e /-d
(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 vermpou gn)oz l1yc (.s,s,x92vy-bp(by tical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period,sxnzpc-gbl 2()o vmbyo(u .ysy ,19p 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 o,ai h,5cx5 gh.zpsgi) f mass 123 g is stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse ig 55s,z ihah.g),c pxis 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 sprine4g(r, vfd4knfd 0f7ais +x3og with spring stiffness constant k. A penny of mass m is p 4id r (3f+offx0 4vs7ndg,ekalaced 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 jun+y5qd zdq j)u+n13 xij2abzf bf*+.wh kyard. The steel crane 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 iwn*xjqq ab2u 1 ifz y5)d bhfd+3++.zjs the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in p z5muqo 1p8z2fl *.ym5u wuv(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. In8 vzufq.1 m *upo55z2um(l wyp 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