Give some examples of everyday vibrating objects. Which exhihs6ii mmvh wp/h.:55 gbit SHM, at least appro/hmi wms 5 56igv:.hphximately?

Is the acceleration of a sima apqk).j(7hsple harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approbdva.)a sugh8p2 )zs5ximately simple harmonic.z asbs58)u. gh2vad )p

Real springs have mass. Will the true period and fr9/e+i7n l, wajgj6gnc equency be larger or smaller than given by the equations for a mass oscillating on the end of g+ nl9nji/, 76w jcaegan idealized massless spring? Explain.

How could you double the maximum speed of a simsc 9nc z.9dua byuq)3,ple harmonic oscillator (SHO)?

A 5.0-kg trout is attached m:u )y5,7t;f elhu7o *pplkpito the hook of a vertical spring scale, and then is released. Describe the scale reyk mi)lo*plu h7epuf;5t,7: p ading as a function of time.

If a pendulum clock is accurate at sea level, will it gain o4u: ( +oi7fifwjp;au qaqzd4 /r lose time when taken to high altitude7jqi dfao: /w;u4i+ p(a uf4qz? Why?

A tire swing hanging from5:(.7t1iumuk8r aj5 a+yui7 ci ym5v-ufrb ys a branch reaches nearly to the ground (Fig. 11–48). How could y8 m c um: sj-iu5uuby5f+ 1t77vry(r. 5kaayiiou estimate the height of the branch using only a stopwatch?

Why can you make water slosh backd s8x/(jab4si um7i1 fcf4jk8 and forth in a pan only if you shake the pan at a certa sd(k87 bixms/1u8 ff aji44jcin frequency?

Give several everyday exampd8zrk.3 r1f7+xapka2ysp ul:les of resonance.

Is a rattle in a car ever 61ex8 jxk 1a*:qk2liqog gmo3a resonance phenomenon? Explain.

Is the frequency of a simple periodic waa u.3aeq(de s;ve equal to the frequency of its source? Why or why not?sad3e u(eq a;.

Explain the difference between the smae5/k84b+rm1hz/ giq fr9rz0h q1gl5iy: u dpeed of a transverse wave traveling down a cord and the speed of a tirbzi1u g/ g dilhz:q 0ekq5rf4a+1h8mr9 my5 /ny piece of the cord.

Why do the strings used for the lowest-frequ;/ yv4s yc+5 uucw f4l;ib1dzeency notes on a piano normally have wire wrappedbdyzu4+si vl 5e yw41;fu;cc / around them?

What kind of waves dotp 9c2awi8h q1 you think will travel down a horizontal metal rod if you strike its end (itc9w2h81pq a a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decrg2umxp;pmkfi.cz8 7/ vy vw3- eases with an increase in temperature, but the bulk modulus B is nearly independent of temperatzx-i32/f uc;mv7 k8vyg wpmp. ure, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves deetw n5b36 nm0gpx. d/screase in amplitude as they travel away from gb 6wtxn/ 3.s0enm5 pdthe source.

Two linear waves have the same am .ogqot n76v3xplitude and speed, and otherwise are identical, except one has half the wa 3v6onx7g. tqovelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crl gwfka4r:nq ;u-at-, mjw2.zy 2lb3x osses the boundary between two sections of cord as in Fig. 11–33, the frequency does not change (althouukzfl,: ban jxl-;.3gyw42mqr aw -t 2gh the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are ther4id2 rst m+cx27jgo xvxd 337ue any places you could touch it with a knife blade without distur7tdgj 4xsmx o2xdr c32+7u3vibing the motion?

When a standing wave exists onra:i6 v1va mv41v19iqqyjlb- a string, the vibrations of incident and reflected waves cancel at the nodes. Does this mean t b4qvqajrviy v1mv16l :i9-a1hat energy was destroyed? Explain.

If we knew that energ mr:3ea*lk/ / (1fudw v:hyvycy was being transmitted from one place to another, how might we determine whether tfh:vlv: d3/m(r */1aekwyuyche energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total distancew.* ols 9fvg(b it travels in 9fwb(gl .vso*one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from x3 kib)i-5wt8e*o5oczaz/+q x.iou fit but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of *3q 5ao i+xw .ftzioxok8c 5i/zube)-this elastic cord?    N/m

  The springs of a 1500-kg carfy)nr+:ks; wam;4xlp compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car gor:n;y; f+awpsl) km x4es over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cx 1 geozva:vow6i(f3,m when a 2.7-kg fish hangs from it. (a) What if w vz63 ei:vx(1o,agos the 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 frequenc8 xx(jwry j8okmw(i*bc e8 lw8zl6.8i y of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs fx8. 8xjicw( (w ez*lylibo86r8 8kjwm rom it?    Hz

Construct a Table indicating the position x of the mass in F2eed(lq s- d2 bpab6 :g80k djf-t9ienig. 11–2 at times t = 0,k(f ld6-de2j89b2b teeidps - 0aqng :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 werqb) ** 5v7vha jhzy1gb vibrates predominately with a frequency ovz*71 r)havyg5j* qbhf 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 wit y;8kzj5 m1g q wnats,x4/1oxu3.3eroed3 qh ph a frequency of 0.88 Hz. When an additional 6x1zeeo/tr,; u4a 8j mw d33nqop5s.3yhk1qxg80-g mass is added to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 timi(ev yaw ebi8y k)d.07es per second with an amplitude of 0.13 m. Detiiawveb)yd .yek8(7 0ermine
(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 maximumr qo14z tmhrcxe.( 33s value?3h c4qsr1t 3oxz(.erm$\approx$    A

A mass attached to txulol adb22,e6;m m jq 7cus z:8b9.nnhe end of a spring is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a verticw1v d0o9k af:,iri0l6vsple +al spring 0.315 m. If the spring is stretched an additional 0.130 m and released,wveoi9dl+i a k0 1r0fpls 6,v: how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a springg10kaw2gtr+u+ec6 5 es /w kntd pqy72 with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving dqk/tk+ n7 c gyrw1u 5ep +g2t2easw60with 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 m)i bwzpd4l. l1. zfj( 5xo8ppmb:s 6o0.200 m to “load” a 0.180-kg ball. With whatpx)4bip85m 1 bzm:dozjls 6. w.lpf(o speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionl (cxbt9ee+n x)rnd61hr8yi(b ess surface is attached to one end of a spring; the other end is fixed to a wall. c8ie6 (br1x yn e(x+dn tb9h)r3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equatqyxvhc2nc) 50c-.ga2e ws l1xion x = 0.45cos6.4t where x is in meters and t is in seconds. Determinc aelg21yqc 2 v-5.h)0xwxcsne
(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 enerm*qm,4nci;. 7nos paygy of a SHO half KE and half PE? .,q7y;c oian*mn sp4m ±    A

  If one vibration has 7.0 times the energy of a second, but their freque.x/3l.i+tzm mdz)xmr ncies and masses are the same, what is the ratio of their amplitudes?lzr+.t/) ix3m .mmzxd   

  A 2.00-kg pumpkin oscillates from a verticjd2 z(;ksezk, ally hanging light spring once every 0.j( k;z k,ed2sz65 s.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is sup1wnwi/ v.mm9 e /cgsqrl(f;o/ ported by two identical parallel vertical springs, each with spring stif9w .i gmen/qwlfov(r/1/mcs; fness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x is in gpw: iyjh8)y sc49y7h meters and t is pc:h4 ) s7igjy9y8yhwin 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 e4 rwrmg): rm h34/cyqdnz/w/,(plm x, 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 oakin5(+w2j o/ u+ ll8ishdv)m f a horizontal spring (k = 124 N/m) is struck by a hammer, which gives t +j/)a+s28dhul wlm in5ik(v ohe 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 stiffnemb (3d1 i1xcdess constant 305 N/m vibrates with an amplitude of 28.0 cm dd(1ci me1bx3 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 springs,j(gubh 0rpq-or e-c6--g.ky.ep / xoj with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed horiz)v j9*w9ql0aslsu xp:ontal spring whose spring stiffness c*aj wslq9s ul09) p:vxonstant 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. After reaching hie7y) fhjre0z22 t+etfs lowest point, he oscillates up and down, hitting a low point eight more t j e20ey+t)fr27 ftehzimes 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 60 s. What is its 4syeue k-83/,n9c/r +6 e-oy lwjyfz.utftsf
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swing per seconejx,d scb.,1pyvg4t 7 d? (That is, one complete vibrayt,g1x. 7s, v cebjpd4tion takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is ivhd/*ds9an gr*fih 2jfk 9,10 fzh pkvh8;q5 bts period on Mars, where the acceler1h2 fp,nia hbf ;rk dg9 *0hqf vhj/kzs95*8dvation of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm longle /;z;h z zssoa6cd1yr7 9t:j
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, jguxwzr (d5u 0t;o,d 0the pendulum bob has a mass of 365 grams, and it is rextj 0u,w zd5d0g uro;(leased 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 pendulum4omq5zwrcd tr:uul,q uc9 5+- has a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pendulum? shorten4:o5l+ 9q,udw cr5 tmrucuq- zed by    mm.

Derive a formula for the zzbkvjdy0k;bnpj* 0 sw-p :; xe+87ovmaximum 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 oscillgcn,h; 99lr tq ks07jbates at a frequency of 2.5 Hz. At it is released from rest starting at a9;r, q 9njlcgk htsb70n angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his au/s om-bxv2pu ct;; 3fnchored boat every 3.0 s. He measures the distance between tf/-3xm; cpo ubsu ;tv2wo 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 ds d. ,.c p,i/stivfcr 6ey5)na speed of 343 m/s How far apart are the wave nr 5fyts)cic .ps e6v. d/i,d,crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilo 2vp8qyo,lhcvrx 6 (fk.i0ak:hertz) and travel withkr v., xhv8a0( iy fok6p2qcl: a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitud *5vphfw8hd c8inal 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 the o6bvc:8qn do3t ther. In which rod will the speed of longitudinal wave 3:o8n6t bqvcds be greater, and by what factor?   

  A cord of mass 0.65 kg is stretch1hk, * 6xxqfeaax 5ad,vag,9 eed between two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse tvxaaf 9,ahd* e, g1q5,xexk6ao travel from one support to the other?    s

  A ski gondola is connected to thek7 x wzchsa1a u,,*bz. top of a hill by a steel cable of length 620 m and diameter 1.5 cm. As th,x zabczu ,.*17hkwa se 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 s0k bmsx 2:w4*ah avs)vide of his ship just below the surface of the sea. He hears the echo of the wa m: 2vxkb*shaaw4) s0vve reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an eartcp r-3pk4p)r6 u6zkv+o bbn0 rfsc 2*jhquake travel at different speeds, and this difference helps in lc*o 4z2b 0f6s rcpk3) jkp+rubp-v6rnocating 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 canh-cu .48c0qs0*kj rdjvpl a0q be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actc0 qula-s d04*jqjp vr80.h ckually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitu /t7+;l9:xudnx r;hc c1qdjjides, of an earthquake P wave passing through the Earth and detected idjnx:1r +h9;7 /c;dcu ljtqxat two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth 42mqm+rs l4 ow()bupzis measured to be q mw4b)lrm4+zp 2 (ous$ 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 ttg.p, w 6cm(ttb(3z9 ibx5r nx,pcuy6he same frequency travel through the same portion of the Earth, but one is carryin6tcrun5xiym 9 ,p6z3tx wct(gb(,pb.g twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along avkuz,kw9fh 60/ 9m:w fn z2i g3l;mihh stretched string have the same frequency, but one transports three times the power of thew3nhihfzh6k9 l 2m wk gfu0/ivm9,z: ; other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surfacea y29d7 pst5pj of a pond is observed to move up and down a total vertical distance of 62pdt 59spj7ya.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving towc.i0ydbtbxfv 3: cw3/ard 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. What has happened to the e tbx yic3bvdf .0/3:wcnergy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, wha+e.m.wie p* pvt are the frequencies of the first fourwp*i.vep m e.+ harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibr4zehq- qu2(a ya2 6 +unsd5wnqates at 294 Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (Tha-+qsazuhq(nw e2yqn 6u 5ad42t is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string reskt3l:ju1 +gbdonates in four loops at a frequency of 280 Hz. Name at least three other frequencies at which it will utgdkbl :j 13+resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string +)52l;xjjo)4s qh d( vw rxgluis 92m/s If the frequency of standing waves is 475 Hz, how far apart ars2x )wlgx j5dq)(o 4v+j;lh rue two adjacent nodes?   m

  If two successive overtones of a vibrating strp1bh;,hu p 30 s 3mdps 5sb0ca5q7ynehing are 280 Hz and 350 Hz, what is the frequency1 hhbsp , 3as0m;ey7u 3sp55n0chp qdb of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass .2 (j.)5vwkfeumdh,a a gm/ dyof 3.6 g. The distance from the bridge to the support post d.j,m y.()a gu5m vdha/fwk2eis L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar strintomyrn z(yts1u.+4; jg is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension ino.s4 ym+ (;yjtru1nzt the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar strmg9:(f8.o)y -q, a ie+m:hwwleu fvx ling is supposed to vibrate at 200 Hz, but it is measured to vibrate at wlafelu- yw,8q :v.g x9) i(m:feo+hm205 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a sm.nsp7zvcz; f* xq;hk wug-/-xy)t sp 6all-amplitude mechanical 60-Hz vibrators*ug ;cyhx. v f)/k7q6;zzpp-w-txsn . The 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 lengt 5/q rnce0u7ngd6ug*ph of the string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how m7ug/g 0 du5*6qnnc perany different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water backyscl: )xek r7: 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. Suppo r7lk:xe)c:ysse 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 travelin6an,zb,vbqmbdq ; 6/jg at k.0 km/s strikes a boundary within the Earth between two kinds of materq/najdb z ,6bm qb;,6vial. 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 “shelf” where the velocityujor b*qk(uuq b: :a+5x+ hao- changes from 2.8 m/s to 2.1 m/s If theu a5-rb: uaq:(xujh kqboo*++ 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 m) i0m:6b+t , aifnthbair. If the sound wave hits the cold air interface at an:6bfht i,mbm ti)0an + 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 strikb7vzki znk3+3 es a boundary between two types of rock at a 38 kib+v 3z3nkz7$^{\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 0v(-:5x :rec iwiefsf8.5 m in diameter. According to the user’s manual, the dish has to be pointixifc ver5:sw8 (ef: -ed 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 travels acro7 l*)dkub1lj/u 3kgrx9ij 5rcss the Pacific 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 during tsunamis, some of them attracted to the shore to see stranded fishes and j*r)ur7i1 x 9klku 5b/j gcdl3boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of/hg0r*qvzzd)r* n224asx oivg. med; 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 conservvsg 4z gdzrv.m*nqah02) ei/* xd ro;2ation of energy.]    m

  A 65-kg person jumps from a window to a firehp1vfgg-l v;k p645ufmgkzni7+ 9 i/q net 18 m below, which stretches the net;uifkgppgiz fn-47+ 19gv/q h5lkm6v 1.1 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 pla16 zuwrpt/p*bm y:fn/ced on the end of a freely hanging spring. The mass then falls 33 cm before *wnry6f /1p:zm putb/ it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a , pm evsh 36oqt(:zo c.lwmi5,y2ses6speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of the spring? s6eo6:5( z,h ipetssyq.ol3mw,c2 mv   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 r bqec7w2bymk1- qp99 jight pace of about 1 step per second, the coffee sloshes more and more until eventually it starts 2199k7y-je bwcqp qbm 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 phonograph r/x k y6*c-ohjgecord have a wavelength of 1.70 mm. What will be the frequency of the sound emio-h /cgxk6*yjtted?    Hz

  A 2.00-kg mass vibrates accordinpwrs4jce w1t+;. r ninz5no+(g to the equation x=0.650cos7.40t where x is in ;(.5r n1ozwtw+r i nscpn4+ejmeters 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 frequen7qh 7 y yj jd,gecg.;yv:+qn,dcy f. What is its frequency if it accelerates ah e7:yvdgd;gqj .n y 7+,c,jyqt 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stbaj pfc0 o/9nop;ypjr ,d(uro.jx:via 50 :+bands on the raft, it sinks 4.0 cm deeper into the water. Wh.oj5n yr(j0ap , 9vf:dx0babo ; j: cuo+iprp/en he steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play at 392 Hz (G) and 440in u)mod+-zlh*k,trfzi 46n - Hz (A)l,tkr i4n* -dmo6 znh+z i-uf).
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stretched two-part cor jrlhyahg, :ni9yy8vqk87+x j n90x) jd of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or th8y)r7l0 g:hjixh9xn aknj+9 8y,yq v je lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of each ) k;o2uq9shpj prong moves 1.8 mm to either side o)9p2suh q jk;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 simz8w5 i 928tm,-zbmwj z:cxiojple harmonic motion of frequency 1.5 cycles per second. What ij:x z-c95jwwomim2b 8 8z tz,is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a ri0ozb y 8jd-p7ing that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed an7ido8zjy bp0-d the other free.

  A “seconds” pendulum has a period of exactlym8i+w4zc o;r o i1dla. 2.000 s — each one-way swing takes 1.000 omil 1o rawz.c+ ;id84s.
(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 cab v3)(z38 r*k uw-ugs;mxq 6q,eaxsp pn swing as a pendulum of small amplitude, but not both at the same time. q) mpb-s3ursvwek ;(a g, u*zpxq836xWhich 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 of5thpg 1c6ye(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 is generated at the opposite end. Where will the two pulses first meet fe56ph1gyc t(?    m

A block of mass M is sp tb qeyjfl, sb (l0/xk5fk206uspended from a ceiling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum kbbl q/0yxp, t20f6f5 ej(lksamplitude 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 cat 2wa4 yz,na6/o -12rhducpsh ble 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: Re r6/uwyhz ht2d4n-aosc a,p12fer to Table 9–1.]    s

  A block of jello rests on a plate as shown in7: vz9 k ea,tf32kmgu 8fyxti8 gcr k,1,dk2jy 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, given that the shear modulus (Section 9–5) yi8afdtzge31j tcx7rym :g 8v,22,9,kkkkuf of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz