Give some examples of everyday vibrating objects. Which exhibit S+3hht*q-yi ckHM, at least approxq+3h-tk cihy*imately?

Is the acceleration of a simple harmonic os8z1wh3ac y+ yjrei4 :qcillator ever zero? If so, where?

Explain why the motion of a piston iqf:8idau4; 0 4rcq zquxi72u un an automobile engine is approximately simple harm8czqqu4; 2x:4darfii0quu 7uonic.

Real springs have mass. Wi (k0sosgovu0w+ 0dr:1:zrxy ill the true period and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized massless spr(i0rykg+00zdo rs ou1::x w vsing? Explain.

How could you double the m 13y ,em:/i*8ifzorbv)cdiafaximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook o eqt2l j)w6nsp.c8 ;vpqe a07 o59egerf a vertical spring scale, and then is released. v ojle a6 rew5.tsp qng08)q p792;ceeDescribe the scale reading as a function of time.

If a pendulum clock is acclu7nxusa5 k2 a *lvhlo ;3d76curate at sea level, will it gain or lose time when taken tnu d7ha2l7 *uc 6x ;kl35svlaoo high altitude? Why?

A tire swing hanging from a branch reaches nearly jg9:k, 6p n76bo;oong9bahavto the ground (Fig. 11–48). How could you estimate the onooa b;v6bpk g 9aj:7ngh ,69height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake the ech:;* z0rx ocf*cu (fpan at ;f *0czceor *:h( xcufa certain frequency?

Give several everyday examp7vd x-l28nrlv les of resonance.

Is a rattle in a car eve *e3;8mi (1jau).8x0ww ue cbdjaimgq r a resonance phenomenon? Explain.

Is the frequency of a siica3y04v m 7esmple periodic wave equal to the frequency of its source? Why or why4 3eyvs0c im7a not?

Explain the difference blqzw3 bpbg8 r); 20b4-qjob/ wrt2pbketween the speed of a transverse wave traveling down a cord and the speed of a twqgw qj0brb -pp)3b 2;8 k2rbz4 ob/ltiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a pian u bs h5dyeuvb7ti/,*6j/y d;ugqjs34o normally have wvj/tgbqs;53uyb6 du/ 4ijy se d ,7hu*ire wrapped around them?

What kind of waves do you think will travel down aucl-: pj+5v jg+m7zxx horizontal metal rod if you strike its end (a) vertically from above and mj xuzpv7cg+lj- :x5+(b) horizontally parallel to its length?

Since the density of air decreases with(1 ybks k0;tgrwb2fhv 1m 2)ip an increase in temperature, but the bulk modulu0bwb;f2s p1(ir1 y k2mkv )gths B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decvjycg o 5z0 brw5p-l5eizw:ge s 52+q(rease in amplitude as they travel away f -lwbcgp(zj 5 s5iv0+:e2qew g55 rzoyrom the source.

Two linear waves have the same amplitude and speed, and otherwise are i;.q).tsfiq gy7t m s/edentical, excs./;.gqmyeqt f st)i 7ept one has half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the bou+z2t h-9ao ili hhs,sl-.f:fundary between two sections of cord as in Fig. 11–33, the frequency does not change iffu2is- .,:zth9hh o+-llsa (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are thexkc /nmvp+:)*cwr+ zg fr-yx 5re any places you could touch it with a knife blad fp /c) +wz-x*nv+x5 ykrmr:cge without disturbing the motion?

When a standing wave existl-cmd 7htr7*tzl +nb++)h6pjaun.zbs on a string, the vibrations of incident and reflected waves cancel at the nodes. Does this r* bna+ n6lh)cd7hm+tuz.+z7l -bptjmean that energy was destroyed? Explain.

If we knew that energy was being transmittedr 3f.snzilpjo)q160u from one place to another, how might we determine whether the energy was being carried by particles (material bodies) or by wavesj ron3i6z)fq1 s.pl0 u?

  If a particle undergoes SHM with amplite( x; ad3v-dvy1fjl, iude 0.18 m, what is the total distance it travel1l 3vdvyj x,ieadf;-(s in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from . ltw/3bpn e klkcns*k:gi5*6 it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this ela*.6p/:sn enbctw53k kg l*ilkstic cord?    N/m

  The springs of a 1500-kg car compress v,7 z kb1jxef):l:en9ld: a tx5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what willna1kfxtel ,v: eb zd:x: j9)l7 be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretsx 229 fjl/wk dhmjb* 8oj.qn,ches 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the/2.k8q2 xj, j*ndolfbwjhm9 s spring 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 w5d -th*3qw,sdqsxq3;kzc2x /ble ,n3.0 Hz when a mass of 0.60 kg is hung from it.q d*2eqww xq, ,5-3ds;n hxz/sbl3kct What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 atx1wnrb ;-w4iu times t = 0,1nxw ir ;bu4w-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 wev, z5pe):0+auefjkec b. The web vibrates predominately with aee,u:p vaj0z k5efc+ ) 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 vibrates with a frq ,/ndg2zmc/kot3 92/ qsea frequency of 0.88 Hz. When an additional 680-g mas/9k sed an3qf rto/2zcgqm,2/s 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(h+hh rpnz7 o( vibrates 3.0 times per second with an amplitudopz(n h7hr +h(e 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 maximumx n3ln1(zk:iu value?ix:knl1z3 un($\approx$    A

A mass attached to the end of a spring is stretched a distbx7oljqmg *46imldr)t74 qt) ance $x_0$ 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 sprlxiy d)z;dy07v/0p pxykk5 7 ring is stretched an additi )y7kpy /kir7vdxd x0;p05 zlyonal 0.130 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffneco. 8;h baear/ss constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is mo8/ah.baorc e ;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 to compress the spring of a toy popgun 0.200 m to dj3w9,qbnh 9/zyw m1h “load” a 0.180-kg ball. Wit jny/zmb 3h9hw 9dwq1,h what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictix3uogar/ 3aj6 onless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. Ifro /3jua63 axg 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 equatio1dj74 h ov11euw3*2/h.zpakdieecy a n x = 0.45cos6.4t where x is in meters and t is in seconds. 7ke iye12e/cv1.uz1a* wjdo 3 4hhpadDetermine
(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 *zxgtvcl ux w8.v1) n-qhr9n2energy of a SHO half KE and half PE?)hv 8 2wxxu9rtl-ng* ncqzv1. ±    A

  If one vibration has 7.0 times the energy of a secondy f-t26ql(nzk, but their frequencies and masses are the same, what is the ratio of -fklyq zn26(t their amplitudes?   

  A 2.00-kg pumpkin oscillates from a verticallpkk, **bgcon;fcj-r 0y hanging light spring once every 0.65 s ;rkbf*- oc0*np ,jkcg.
(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 vez ; +e;od t3hkkta d82, tkt*lxh6)nrertical springs, each with spring stiffness consta);tkrhlo3keta ;+dz,x2t6 *kn8dht e nt k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = *crh ;ir9r g1d ksi(3k0.38sin6.5t where x is in meters and t is in seconds. Deterks rkrhrdi g1(3 9*i;cmine
(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 exampl oi 02o8y6)jawhy8elv es 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 horizontal spring (k = 124bf nbfa,+rg+hnez ;5- N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Determine hzgr+5nb-ea +;n b f,f
(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 f-hu o tmc35(nN/m vibrates with an amplituu 35ohfmc t-n(de of 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 to two spring;h)7*0x kpzcu kdpn p )boh86ws, 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 toyryn)2qh/l q +jka/) t a fixed horizontal spring whose spring stifflry) nqj /yqt) 2h/k+aness 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 i j3msw gi 4b*:1;zdfqfrom a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate tsqwi i;z :j4*3b d1mgfhe 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 60 s. Wh0fxfj,-d oc9jat is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if i4maj-t8bhh nje3y7r 0ju +r8bt is to make exactly one swing per second? (That is, one complet0bj38u4r8 + jbtnh 7rmeay hj-e vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s onkb ,jcsof 6q*jg)(o p) Earth. What is its period on Mars, where the acceleration of gravity is about 0.37 that on Earth? p) 6of*sqkjcg,j)b o(    s

  What is the period of a simple pendulum 80 cm lon; zpqfwn97ss9dl 61 oiq v 48u5oivhb2g
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m1wu , (eajuiu2/hh b(wcu6 g8s9z-ksm, the pendulum bob has a mass of 365 grams, and it is releagk/i(u w(-wzbhuj m1u 2hacs8e,s u96 sed 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 0.9930 m. If the ywdq;/repf;hw / x;nt4f4r-dclock loses half a minun d-y 4t re;pqww/h/xr4;fd; fte per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum speed ke.de8 e6kvas xn*. i4$v_{max}$ 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 releasedq 4.ml(v)ymvsjm q2;4dl -bjb from rest starting at an an.) ymdbq 4(4mj j;qvlsvlm-b2gle 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 pa i s kt;l*szlqn5g4x(b-9g y-gss the bow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fastxtgl4 qs5- z*9lygn;i(- sb kg are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed of 343 -v7sh ch6 ,4e4 wxy1ho i1jvbmm/s How farmexbi6j,s4wh14- hhv y1 vc7 o apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies betweenxun -2 yoscqncj m;7hr85-y/r 550 kHz and 1600 kHz (kilohertz) and travel with a speedsr-qy/8;hjyo ccxm27nr-5 n u 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 longp zzxo9w)2+vbo,0 /2 qv km.tonkw(r witudinal waves 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 dense as thee vrj3uh. :mek2aej7 2g 1nwt9 other. In which rod will the speed of longitudinal waves be grea3enh1vw2ge.jju: at kerm297 ter, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 mr7g;c7s6 l ,kelvpyxg5x.u;u apart. If the tensio lgxevr u ;gk7,;.l 75sypcux6n in the cord 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 hill by a k ,0x*. x+ -vsxgzav aksgk18csteel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of+, .zas 1vks k*gxxxa0k 8cvg- 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 surface of the sea. He hecy6jx,cv8jv r z gfgcn/13ozyva4) (1ars the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep isccv/a6v1,v1zryj8() z xfc go 3ygn4j the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and this 0zwf(l4: qt3se)apx xdifference helps in locating the earthqua3p )x0elw4xzaq f:t(s ke “epicenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced sc93d7 hgi+o 94syb8wc k3jg fpurface wave can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to lejihb+g4 yk39 c w739gdo8psfcave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, anmv(cv+pd 12twd (b) the amplitudes, of an earthquake P wave passing through the Earth and d mt (dv+1w2vcpetected 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 to beugbqxq 0,gja pij**7/3 v/k vo o bxi vq/*7jugg,k*3 aj/q0 pv$ 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 fre99i3b ;3b4 4 +u,jhv vbf9jgni coeyuuquency travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratihfb+c9u;o9y 9uiu3 i4 vegvjbb4,3njo of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same p9ypskg+se e)i r+ jil+5v,l ,v4:asyfrequency, but one transports three times the power of the other. What is the ratio of the amplitudes of the two sgle ,j+yv iys +4+sp pa:,5 lr9ei)vkwaves?   

  A bug on the surface of a pond is observed to move up and down a total vert5l2uc rt5k7, zabujtf.7-m d fical distance of 6.0 cm, from the lowest to the highest.577br f5cl,2ujkf zmut -atd 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.l v q ;qnrbg)yiye.104 11–52 are 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 moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. 1ev)lyq. qn40; gyrbiWhat has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequandm (e(je)tuueq,: fxw( h. 9ency, what are the freqq:ux()fmua((dte e ,n9j whe. uencies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency *rlpk:5i p7gk will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrat5iklk7*gp :pr es as a standing wave.)    Hz

  A particular string resonates in four loops at a dk*k 5qw:lgc, o8r: qlfrequency of 280 Hz. Name at least three other frequencies at 5rg lcqdow*,k:k:ql8 which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequ phy a fs i3nbn:-x.40xvy a)xbw e,(rk,oi2m8ency of standing waves is 475 Hz, how far apart are two adjacent nnxamy 0i r,.4fkbo8 ,-avw3i:(sxx2 byp )henodes?   m

  If two successive overtones of a vibrating string arp sx(56q(+:fs 1r p1x.evwhigiz2ri qe 280 Hz and 350 Hz, what is the frequency of srriv(g:1q izx6.x1(2ie qs+ph5pw f the fundamental?    Hz

  A guitar string is 90 cm long and viu i3o6jed uma4/l),okx -(ohas a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the-(xai3oloouu/ ,ev4mj d )k6i 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,8.py p52dlrk o1.bf mb but it is measured to vibrate at 205 Hz. By what percent should 8lopb. 1ry .k52pbmfd 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 supposed q t(6acr)m-u gto vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in th)rm t 6(ug-cqae string be changed to correct the frequency? decreased by    %

  One end of a horizontal strine/my1fr:*,4ebis i1zpuy 0cc g is attached to a small-amplitude mechanical 60-Hz vibrator. Thy, bic* r e1u: ys1m4pfc/z0iee string’s mass per 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 len9)/aefdke ru 2gth of the string may be adjusted by moving the pulley. If th9aku/ed2)e fr e hanging 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 just the right frequenc(c8 -l8lwcbrwt xat 57jp ;wh(y, the water alternately rises and ftlcpxwt(7hja rw;5w(8b lc8- alls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundaek)d-6 bg+rd.q/h.8rjvqrl ery within the Earth between two kinds of material. If it /)h 6v8drjdb rk.+.qql-eregapproaches 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 “shelf” whxjqo4x, 4(i h(0+wcvh)gykpaere the velocity changes from 2.8 m/s to 2.1 m/s 0xgy(ioc 4vp,)h j aq4whx+ k(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 cold, dense a j3p1 jer.)vbkir. If the sound wave hits the cold air interf3r bepk.j )v1jace at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary m5/-dawse d7 gbetween two types of rock at a s7 eg-/ddwma538 $^{\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 diamktzaye9 s.9)deter. According to the user’s manual, the dish has to z.kta)e s99ydbe pointed in 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 (e(b) t f(cmvlfl5q4 ltravels across the Pacific Ocean. As it approaches Hawaii, people observe an unusua(5 bem( v)lq(cfll4ftl 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 sp9v3 lbu6qk;d y kl (3s7bxhwh+ring 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 speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use col3b ;6 7sbwhlxh(3k+qy vu9k dnservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, whichkd3s )cz-p k3w stretches the net 1.1 3kpsw-dkzc3 )m. Assume that 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 on the end of a freely hanging s+84j nc *tmalypring. The mass then falls 33 cm before it stops and begins to rise. +y tam8* jcl4nWhat is the frequency of the oscillation?    Hz

  A 950-kg car strikes a hug+gr)gnl6 qo 7y.eeo b;e spring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (;rg+ 7eqeo )y g.o6blna) What is the spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just the righr+l2 1ylf w9 bkzrvq;v5jes- ,nh4 i7rt pace of about 1 step per second, the coffee sloshes more and moyrbf,n v5 jl7hr -kzs1i4vre 9wl2+;qre until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-rpm phonograp2;w1vw uwprfga g6gf h8)4x -sh record have a wavelength of 1.70 mm. What will be th4hg;1)awpvw8 gf6r-sx fwu2 ge frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x fbo8o,zns1.4pv )ips is in mefoo . )1vzs ip,b4psn8ters and t in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. What is its frequency if it ac0h zfawq.iie+ufq25 /celerates at 0.50g (a) upward, ii 0f+ezfq.aqu2h/5w   f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raft, id d63.9uu)q5*:uzd tenndkwe t sinks 4.0 cm deeper into the water. When he steps off, the 5*dzu6 dd9uene:ud3.tkn )q wraft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play at 392 Hz (G) i bt5wt3m1,5vh5acvs and 440 Hz (A). w 1t5t3vmia c,s5hv5b
(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 traveline0.y w vwqnei9) 8,v khqhp.zhu. z;3yg down the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the s9h qwh;e3 np kh.vv8yqu.z.)iye ,w0zpeeds 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 frequency of 264 q(rn2cl bx-w97w; ttvHz, and the tip of each prong moves 1.8 mm to either s; cvb(t2t7 l w9-nrwqxide 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 si5 p6sknq9 avhk 5+wzp,mple harmonic motion of frequency 1.5 cycles per second. What is the maximum a,qapk skz9w v+ hpn556mplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end iukqg :3)wei *jug z:6ys attached to a ring that can slide without friction on a vertical pole (Fgziu q):6e:wy*kgju 3 ig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s —g fxbe1l;85bga-b pn j 1-;ch y.foq-v each one-way swing takes 1.00obavhn ;jyfpg-- ;.18bx 51e fl-bgcq0 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 dir8+srlod(axw gt/s:hj 9+1pvdection or can swing as a pendulum of small amplitude, but not both at thesow rg/8p:vs+ ddj (+xtal19h 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 25bqgfb3eqqk/):i lx 3(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 the tw(k3f3qglx qq/e)i b:bo pulses first meet?    m

A block of mass M is suspended from a ceilint 8ix )mn lu*ijt2/f(tg by a spring with spring stiffness constant k. A penny of mass m is placed on top of the bloil uxjit/t( 2*tn8f)m ck. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cable is 22 m8 h7chofsq3-g+5 agh y 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 to Tablea357 q- h8ggsfh+c hyo 9–1.]    s

  A block of jello rests on av/czy: b 8r ksxp: nyv+/a4si9 plate as shown in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, gip4 s9 c+a:/y:yxb kiv/snz rv8ven that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz