Give some examples of qa+q)1e 2 sy g7*wpc ygy:vx*g-evx*keveryday vibrating objects. Which exhibit SHM, at least approp*se:v ygqxg2 + *71v k qgy)way-cxe*ximately?

Is the acceleration oe 2u9u,s:auq8gqhd se 2q8l) of a simple harmonic oscillator ever zero? If so, where?

Explain why the motion qulaa*(fo5o qt.+nebl (u p3s a*f7)o of a piston in an automobile engine is approximately simple ha(onq7(ff3oatae. 5 la*)us* uqpob l+ rmonic.

Real springs have mass. Will the true period and frequency be largp 8ziq+a6z cd7er or smaller than given by the equations for a mass oscillating on the end of an idealized massless sp6z dazic7pq+8ring? Explain.

How could you double the maximum speed of a simple harmonic oscillo,g+jiy hu*ds1xe1 h 1ator (SHO)?

A 5.0-kg trout is attached to the hook of armh e6 jslg2a*dp/.a- vertical spring scale, and then is released. Describe the e 62pa hmgjlr-.d/a*sscale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gainc p 6,rxlesy5- 4i-zle or lose time when takeyils,-e4 c5lrpe- x z6n to high altitude? Why?

A tire swing hanging from a branch reaches nearly to the grou3cm/hev;lr d:nd (Fig. 11–48). How le: r3;vh /mdccould you estimate the height of the branch using only a stopwatch?

Why can you make water slosh back anvy zd .u2g/ ( 030w3bainm6 mehgkcda-d forth in a pan only if you shake the pan at a certaigb0ay3.c2h ievd(gkzu0 wa3m/d- n6 mn frequency?

Give several everyday examples of reso d uxrh6ll8n,wxx1o, +nance.

Is a rattle in a car ever a resonance pheno 1o0.o d-free)uw/m ufmenon? Explain.

Is the frequency of a simple periodic wave equal to )lc66q.060 fopjv9ybk;mcc bla3yrnthe frequency of its source? Why or whkf0r0c y 3jm6l;q 9v.)on cb6pabcly 6y not?

Explain the difference between the speed of a transverse wavp4 m.m+ -vqyohe traveling down a cord and the speed of a tiny piece of the cord.mhvm 4q +y-po.

Why do the strings used for the lowest-fre eyx-+hzs )a(qquency notes on a piano normally have wire wrapped around th)sx +zh-qyea(em?

What kind of waves do you think will travel down 0f nua7mz9ci,a horizontal metal rod if you strike its end (a) vertically fromzi, anu f79c0m above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase inch 57ogzsol2l z9l a(.8 ;wqeq temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the s5z.clao7 q98(llzhwgq o2es; peed of sound waves in air to vary with temperature?

Give two reasons why circ1hm5z4v;8 xh9kvnmm ;j4 7hoj w6sg-rodl k.bular water waves decrease in amplitude as they travel away from the sourw9s4rd m o;nx;1 j.m m64kzl voh7vh5 8-hjgbkce.

Two linear waves have the same amplitude and speed, and otherwise are identical,8ybdkqmgevgo4c -ihw0m/4m6r 6lx3x4x qh * 3 mq36d3*qvx xom8 4gb4ew-c4x6ir 0hk myhgl/except one has half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the bounda-mm9g lrk29a2jjb g2x ry between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelengx-2j g2bj29k9r gmal mth and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places yiw kx7fj:k *3e 86uchwoez6 m2ou could touch it with a *z ckej63hwx8ku: ew2o6 fm7 iknife blade without disturbing the motion?

When a standing wave exists on a string, the w* ffq0xi 4w+yvibrations of incident and reflected f yfw qw*xi+04waves cancel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that enerj8a z3li+f7:affkcw- jw )f x7vr+ (dogy was being transmitted from one place to another, how might we determine whether the energy was being carried by f7z r -ova ffi8 xf+7:)(+awjld kcjw3particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, whadbosx)p( dz(cq6 /hbbz8nxa9s6) tw(t is the total distance it travels in (8q cbdxtx/sob6 w9 6n s()adzz(p)bhone period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs froh-gw/mrp07cqj1 0gm km it but is 85 cm long when a weight of 180 N hangs 0m-wkg0cr 7j gp 1qmh/from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver6h/ ymupmr+-l gets into the driver’s seat. If the car goes over a bump, what will be the frequency of vibryl /mhu+-6mrp ations?$\approx$    Hz

  A fisherman’s scale stretz)yllv 2 /s xpwvpf2-,ches 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the sprws2)v/zyl 2-pp fvx ,ling stiffness 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 ,d7: g(,kssm oywgx*wof 0.60 kg is hung from it. Wh7,gs*(kyww : mxd,s ogat is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x 4 xrma(y4 kp5 ai;fmpv :(opr2of the mass in Fig. 11–2 at times t = 0,t2mprkp5(xm ;4poaar vf(iy:4 = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 gv4 yk 8rcw-l krib m2y1z*ag7 r.:w;aweb vibrates predomina;k caw-g *4:8w2z ri1ml.7rav grybk ytely with 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 vi pppsa*-,dftytir tv4ro 9+ (6brates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hy+ot,*fvp ap6 itd -rtsr 9p4(z. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrateso4; nna4vcbm/ ;tzi0u 3.0 times per second with an amplitude of 0.13 m.zn mn4 o4;avc/iu;t b0 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 speedgaselrb(*eu+ yxa 9l*tryf,i j--z,8 of a SHO half the maximum valueyes+-rx z*rtjgi8l(a*-, u elba,f y9?$\approx$    A

A mass attached to the end of a spring is 2wnoo/qobeo/wqo * -* d75cygstretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. If the sprkr8 t g)):e 8frov)wzcing is stretched an additional 0.130 m and released, how long does it take to reach the (ne:c teror 8zfk)v)g8)ww) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffness consta q1gl,v0 o*:vmr;iciint k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium posimgo10:ii lvqic; v,r*tion, 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. :(j cvilnu0wlf/fe6.0 N to compress the spring of a toy popgun 0.200 m to “load” a 0.180-klu.c j0n/ l(f6wi :fveg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attaciwu sxm)cu;/ va +l/ ;pa3mu+shed to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the +u3/ v+ s ;/;uacuaipmsx w)mlmass 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 i59 x0dme xnr*vn meters and t is i*r m5xv ex09ndn 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 and half PE(j+d ebr.ld. neucv 23 c0l(un(en n3bvc .le 0(ludc2.jrud+ ? ±    A

  If one vibration has 7.0 timess vldh)z8m ,4i3jxn3 p the energy of a second, but their frequencies and masses are the same, what is the ratiz8lvsi3)j3 ph4, n xmdo of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light styn,air6eum ;/ cg9ec)fl0 u4 pring once every 0.65 s. c40f/ya6,u gn imlu ; 9eerct)
(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 partn9qxugg;0z 7 allel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequenu9 ;xn7gg0t zqcy of vibration?

  A 300-g mass vibrates according tdmll6 i n* c3v53bkr7ko the equation x = 0.38sin6.5t where x is in meters and t is inc6rld vm* 53ikkb7ln3 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 Szgi4p.a50mq d+:48nbsr vngq..tjm0ctcd/tHM, 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 horizontal spring (k = 124 N/mhzj v;( y(jwp*) is struck by a hammer, which gives the mas h(;j(y z*jwvps 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 constan*(trg2hwh4 hy t 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes thrhh h2r4w*tgy(ough the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring stiffness cons.beyu2d lg-u2g3itu, tants $k_1$ 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 bld n1k6-yh p 69m4vaqgsx79e.qu*nh;,d ktzzw ock attached to a fixed horizontal spring whose sprin nq 7t-6d ehzg6p.vu1am4xw*ksknd;z hy9q , 9g 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 w/5jh5 3l0 evpggd , djcz.o;m65.0 kg jumps from a high bridge. After reaching his lowest point, he oscillates mg p/ dj, hv55.ec;0zjg d3olwup and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 605gya*n+/xiiv94f d i2pj tsm: s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swing per secomo eq u weqt1 :ew1v-)m.1-ivknd? (That is, on- w:qm1v1 em1) veow.-ukqi tee complete vibration takes exactly 2.0 s.)    m

  A pendulum has a perpcci+ c6 qs9w3iod of 0.80 s on Earth. What is its period on Mars, where the acceleration of gravity is about 0.37 thc3cci s96p+q wat on Earth?    s

  What is the period of a simple pendulum 80 cm longe; )8vf-c:tj1q+-upip wlhe n
(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 hassdpreuyx 2 kdzx4- 4a-ua)-r0 a mass of 365 grams, and it is reludpr ae4)k a0 24us-d-xr-yz xeased at an 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 0.9+2abizmh l--ba;f) qv930 m. If the clock loses half a minha;+-)al- vf i2qbbzmute per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum za-j 7g 1:ryfanhrbq lyi*3,h :0htq,speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At it is re8q oyvy2 q)gj.t3l/m jleased from rest startingyy qj)ojl/. 2 q3vmg8t 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 wave1ia7.s/ irvk h(iyc1 p crests pass the bow of his anchored boat every 3.0 s. He measures the distance/vpc ik(1.s1 air hiy7 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 spee5nx;9 ehdn311 bp xogg+oey9 cd of 343 m/s How far apart are the wave crestpnge+n ;x11by35e 9cd g9hoxos (compressions)?    m

  (a) AM radio signals have i0 -rfs ox5xh* je-0yofrequencies between 550 kHz and 1600 kHz (kilohertz) and travel with a s5 xioxfoejh*0y--0s rpeed 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 wave*;a iting --6dpqn vg2 dz:/q82b hyurs in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but on;xs bxy49ei 5jw7 pcoj412w yhe is twice as dense as the other. In which yhy42o e4j5x bix9 7 s;jww1pcrod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretch8/-k;pyp7u ;g a gi3z6h 4wtu3lncacfed between two supports 28 m apart. If the tension in the cord is 150 N, how lo picfawlzku8 uh nga;p; g6y t/c7-343ng will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the tg ji) z+pz43jrop of a hill by a steel cable of length 620 m and diamete)zr j3zgpj+4 ir 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 cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the sug4 w(i3wf r1verface of the sea. He hears the echo of the wave reflected from the ocean flo3gv1 f(4wr ewior directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an eaf 98, zm/a6jjma ;,oxb 3pnqh9 ys3t4kuia/jrrthquake travel at different speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbance took place) /,m8fa3zkjr3x,ij otauys4a/jm nqp9 69;bh .
(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 transve- k ry7 ch:bfjd6f;9v3zfpsbyk09-b zrse 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 with the ground b- yv0 7 9-6zfrcp9;3s:j fdfhbkzbky? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of an ea .c6 ij*evoj8 6um3qjsawd7o/rthquake P wave passing through the Earth and detected at two points 10 km and 20 km from the source?(aj j e38mv6q76d*iu. j/owcos a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measuf)e /y7ele ekv3mdp/+red to be ye/ kped3f mle/+v)7e$ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency travel through the s 0j 5o7 z903whvitf z4y qm+(oimpd0veame portion of the Earth, but one is carrying twice the energy. y0 i ve(v3p0qfj 40h7imw 9 zo+z5dotmWhat is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequenco2 0f) umn/lc.s9jbhfy, but one transports three times the power of the other. What is the ratho0f).2c9bms nljf/ u io of the amplitudes of the two waves?   

  A bug on the surface of a pond is observetspw;+0jm) fy ul;f3s d to move up and down a total vertical distance of 6.0 cm,w)m+l;0 f 3ju;ytsf sp 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 moving toward each other. (a)6l cz 8 qy5qf/:mq *5snwb9sqh j z8z,2,yuogt Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at f5y yh2sq, 5cgz8q tuo,qjb* z6/z9ms: ql8wnthe 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. x*(bvb d0 zn/ebhd,m as its fundamental frequency, what are the freqb.n/zmbvd*d( ,h0e xbuencies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294w3d lgn+9c l+ 1-s*ak;nywwur Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only tw++ lga9c1wn-ury;wwl3 dk *sno-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loop9sp qal ,9xb gm*n;t9l4; m8sa 2vllqns at a frequency of 280 Hz. Name at least three other frequencies at which its *glqmbsx2ma;q9,nl8v 94lplnt a;9 will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a sti+ xp(: ( wd-e581nyxpmfhlq bej:p)hring is 92m/s If the frequency of standing waves is 475 Hz, h1n:b d mlx:y+-e( h8ew)(p5xjp phi fqow far apart are two adjacent nodes?   m

  If two successive overtones of a vibraa 1 wr/gemn-, po/p,u;,mljzfting string are 280 Hz and 350 Hz, what is the frequencuwf, gj;/ma ,por/nl1-z ,epmy of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. Thejgt jw :.5np4a1y9me ro;tjv.r6) o fo distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two ovrjn .j9a6: oje .4tm p;fo5g)1tvwyroertones?    Hz

  A particular guitar string is supposed to vibrate at bk cw0u: 9dwe,0sww)lho7h 2 m200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?S 29ebs:wwwmk, wh huol0dc7 0)o the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar cp46pq uqd ;m;string is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz.dqu;pqm;p 6 c4 By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attache:juxnpqr(e, ip140u+o i unx3d to a small-amplitude mechanical 60-Hz vibrator. The string’s mass pep ip+n,1ex in: r(joq4x0uu3u r 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 mkwr51 c)zpp e;ay be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L 15pe;wpk cr) zbetween 10 cm and 1.5 m?   

  When you slosh the wa d a+;wu.lg9uater back and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. Whaaua.;dgw9u +l t is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary within the Earth 6z5 qm4ccm/q (rpl /rabetween two kim/c(5r lpq 46zcmrq/ ands of material. If it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “sh)hjnthfzrw,bqe ;;t):3uy - j qs2g1a elf” where the velocity changes from 2.8 m/s to;tj ; -3etyhf,u br1)hq ) aj:2qwgzns 2.1 m/s If the incident 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 of co(yy v6y,a m8sg)nfno sqrpqq 569 9hb.ld, dense air. If the sound wavq nv hfq5bagry8(q m)n9 9o66 py,.ysse 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 strikes -5j5q.zkaf7 jzte (m rthrb 3/a boundary between two types of rock at a 3b .(j5tqmfrtj5 zhe7z ar/k3-8 $^{\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 abo;h1 7l kqfa4djs+(ngv ut 0.5 m in diameter. According to the user’s manual, the dish has to be pointed inj+k qhs; a(4d vg7lf1n the direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 km/h travels across the Paj(/bow4t 5tw x q12zyucific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died du 2wo/y (wbux1zj5tq t4ring tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a sprirf9gb(6srba/c-- c rung stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a s6( gur/fr ab--s crc9bpeed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a winddv;j;g j70htdr ;4psr ow to a fire net 18 m below, which stretches the net 1.1 m. Assume thathgs0;rd; tj4 j; v7dpr the net 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 l;5ae( s gj(3xgmx) l(ik9f/xn r ,jomon the end of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency / jxil((e)frjgkogx;m5(ma3 sn lx9 ,of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a spee 9;-quh9(gun qe 0y1qb7 -wg9swvrnqyd of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness consqre-u9 ; 9wy(-9s0qhy n7g uq1vngwbqtant 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 cup3hj,a5pwqw3f v .8pcwm/e ak. of coffee (diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until event85v a.h,fajwwk qmce3/w .p3pually 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 groov;o + 0n.pxt/,dbvrpe, o, silsa3:h qne 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency ofoo+/; v 0a,,x.pb :ns3q,l ietpshndr the sound emitted?    Hz

  A 2.00-kg mass vibra,+cz/xrrtfr 5 tes according to the equation x=0.650cos7.40t where x is in meters and t in seconds. Determine xfrczr , 5tr+/
(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 wiw.uh .dx/7lb- neu m3(ic -hbsth frequency f. What is its frequency if it accelumch 7id-.ul/n.x( s-h b3 ewberates at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft.rca ,xc,omc8 ce wb5/ floats on a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates x 5o,r,cc/ ebmccw 8.afor 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 /.begtyh c:tib h.l1 wh:;8zktuned to play at 392 Hz (G) and 440 Hz (A) /b ;.h:hc:l8k ygw1ei.bhztt.
(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 travel4 ;zq cf5oti7ving down the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of th;qf zti57o4cv e speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a fre)as9nqdc135v1 f gjcpquency of 264 Hz, and the tip of each prong moves 1.8 mm to either side fc s31p59cnva)g q jd1of 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 moj)f *rfiw2sph 2+i 2rgtion of 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 placed there (Fig. 11–56) will not losr rwsf*g+fi i2)jp2h2 e contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a ringtej86 zbgl+8o) 0ygfx that can slide without friction on a vertical pole (Fig. 11–57). Determine tyfg 6tbz+ol8 8 ex)jg0he wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-wayy u182p:lh3pag z -wuvopd00zx c3uf9 swing takes 1.00zdx1wzv0-893y ucu h0fpp2: ul 3o agp0 s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertical direction or bamsoa)nbk(c m3ip 8p:3:o5s can swing as a pendulum of small amplitude, but not both at the same time. Which one is l3 okabbp )::m 3i ss5(8mnpocaonger, 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 1--a6.sen hl mj8wgep under a tension of 255 N. A pulse is generated at one end, anlj1e-waps-g nemh 68. d 20.0 ms later 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 ceiling by a spring with spring5lb- d- bjdrmt)3slm 6;do;c g stiffness constant k. A pemj c;- 5)b 6dr- dobdmtg;l3lsnny 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 1200jr)/4 jgi7z-d 3zvh q1gmebd:-kg car at the junkyard. 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 is the period of the bouncing? [Hint: Refer todg -jqervdg4)/z 1hz mi73:bj Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 1s/2 xw/)fz6u-mi e ftn1–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 5wfsi 6mutzx/ e2f-/n )20 $N/m^2$ and its density is 1300 $kg/m^3$    Hz