Give some examples of everyday vibratingq2 .+(f eadr 2d*vm-yhsll)f d objects. Which exhibit SHM, at least approximateld ff(s*2ld.)+ rq-mae hd yv2ly?

Is the acceleration of a simple harmonic oscf,/ ic, ya:uecillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approximately nw3rer 5n)pq -k6r1fwsimpr f3 rek1w-qr) p56wnnle harmonic.

Real springs have mass. Will the tru+*l;dh1ryp a2wyj2p pe period and frequency be larger or smaller than given l2p r dyj1w;2*p+ahypby the equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillator (SHO,1o vuc: jgv*: gc7zydi,oea;)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and then a*6y,7fj// *ijks 7gm xjuchq is released. Describe the scale reading as a fiu/h*qk ycm/f7jag*,j7xs 6j unction of time.

If a pendulum clock is accurate at sea level, will it gain or lose time when tabn h2;/,v j)jlakam;dken to high am)v jlb;da;,kaj2 h n/ltitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–485 ,obs vs8nal8). How could you estimate the height 5ns, lao sv88bof the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake,b(t.g3j9 ae/nj trnb the pan at a certainr( e 9nb3jnjgb.tta/, frequency?

Give several everyday examples odmg:;kmf mj8 -f resonance.

Is a rattle in a car ever a reso1 6 yb(g*zneccnance phenomenon? Explain.

Is the frequency of a simple periodic wl9;2zt7 )qgimvfi.ip ave equal to the frequency of its source? Why or wvm 9) ii2 lg7t.ipq;fzhy not?

Explain the difference between the speed of a transverse wave traveling doo)x 9avm r +p1bn3e1qi)k7wen wn a cord and the speed of rq me x1n bwp)+veoiank 931)7a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano norm1 sxnulne03by p( 6jh8ally have wire wrap8ns3yebhl n 1ju 6x0(pped around them?

What kind of waves do you think tr1t 26h(zd ce8.pmriwill travel down a horizontal metal rod if you strike its end (a) vertically from abov erm pt2i1.(6ztd8r hce and (b) horizontally parallel to its length?

Since the density of air decrea *mcfy.1y(n mq7e )nfe lqi,6qses with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speednqfnyqle e 6(7 q*,)ci1mfym. of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrewwi.smyoi 3t uoo( /ny1, .ji1w m01wease in amplitude as they travel away fr1w/o(ity ms uo j.1oi 3wnwm10.wy,eiom the source.

Two linear waves have the same amplitn1 f f70ue(:vsujb.wjvod36ja 7 t w+gude and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits more energy? By whatju6dg1v wa 7 +fus0(jofvt3 :bjwen .7 factor?

When a sinusoidal wave crosses the boundary between two sers+l 5izv(d) 1sie ,w-fbd6anctions of cord as in Fig. 11–33, the frequency does not ceslrd w fi-6 d+n5z(1as vi,)bhange (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are4; c zad-xgrn*9te e(z there any places you could touch it;a4 c *z-xdgn (ete9zr with a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incid7rwv zfn4apia 1 c :,ezl5.0usent and reflected wavez , e.s0c:r4wfi5v7lp1aa nuz s cancel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from vd4x 2, t;sfabz,pt+x/ j2p rpone place to another, how might we determine whether the energy was being cap/,rfxtt 2+,sdzp v a4x2b;pj rried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, whar66 xe2- vvkalt is the total distance it travels in one perler2-x vk av66iod?    m

  An elastic cord is 65 cm long when a weia:n0,ts (bhpmght of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this elastic cordhmbat:0n,s ( p?    N/m

  The springs of a 1500-kg car compress 5.0 mm when itvdst/). vkz6 2(mkwxxj-web(s 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will.wt(dk 2bxm6vs -v (kxez )wj/ be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (a)s jmbfh90l1 fa0byqc)s9(e5o What is the spring stsbqs c9ya1f0lfh50() 9eo jbmiffness 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 frequenc5xcdy -u-h cayju5*qx s)8-g6jnbrb3y of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frebhsyucu85q)x --d 6yabc *j-r53 ngjxquency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position xajhhe+z k4n2 ; of the mass in Fig. 11–2 at times t = 0a4z e hhjn;k2+,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 inod 8qoo* o)t mwxt sxj7h7cl7hxm31i0yv ,a:9 a spider’s web. The web vibrates predomino,lmxi 1covmht3jxt0 9 osy7ow)dh778x :q *aately 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 vibr;(pjuy5lq d:c ates with a frequency of 0.88 Hz. When an additional;y:5p(ucl j qd 680-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 times per seconom1 ,1mb jlvf1:;erxxt*r ge36 6rr lpd with an amplitudex1m1r1;lxv epb* lg 6rrotrmfe,6j:3 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 equ 6u xv,sk2 ;loa xnot;.ynfa32ilibrium is the speed of a SHO half the maximum valuextunxok; ,ynf .sv 2;32a6loa ?$\approx$    A

A mass attached to the end of a spring is stretxt,ksd78/ y fl ;-zdgkched 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 spring 1pgx5q4 z /pe)od y5q, h:wd1q2twqoxis stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrtog) 2q5p,qwey:xxpdz qw 114 qh/d5o ium position again?    s

  An object with mass nd* ytj2hc9a2xdj0 (q3.0 kg is attached to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the obj* 9nqjxjd( y0t2ad2 hcect is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N tt e/mfvprv km h52;vh,qcm u)*,x8 dc+o compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave the gunmhf+*m uvrd 8qht), c25,epcx/mkvv; ?    m/s

  A mass sitting on a horizonbjcyfk4e ()1vtal, frictionless 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. If the 14jfc y )(vbkemass 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 ah :v.-e ac*tts5qa-u according to the equation x = 0.45cos6.4t where x is in meters andt*qvua-:a.h ea5sc t- t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibri piv cw( zpmhko8k yfv3hp2u(d2q6 2v;yw/.5zum is the energy of a SHO half KE and half PE?p(vq(z83cvypmhkh2ofv u6 wi py 2k/w.;dz2 5 ±    A

  If one vibration has 7.0 times the energy of a second, but theirh3+*.bgxel7ejk t0 hu2kh4 t q frequencies and masses are the same, what is the ratio of theik.b 40* ex3qeh+ 2jt ghutlhk7r amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light sprin 5u sk,o cebz),/krg/dg once every 0.65 s. g uz//b,dk5sc)k, oer
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallel vertical springs, -* l hc11g)m;tvymndp each with spring stiffnm*)nt 1g;pcv1mhdl- y ess constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according t84vsrjr sj) 1ko the equation x = 0.38sin6.5t where x is in meters and t is in seconds. Detks j18v r)4sjrermine
(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 eac*d;cxfx z7+x zh, 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/xn0i7:xor : kdyj5ov/m) is struck by a hammer, which gives the mass an initial speed ofx jxkoi7d0o/::v5y n r 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 g 4j6ykerr;(*tqkb, hi )vmx.stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The(jex,)6riqmk;t 4rkb*h g y.v 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, with 31 25 ;,a+t txqq9v1umo o espqd6epbqspring 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 4 05-dnz qak9rq xrxa )tro52lto a fixed horizontal spring whose d-q qark0l9xr4rn5 )z tax 25ospring stiffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a htqis9 vfj/dc tq9s*;4er3 /wmigh 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 the spring stiffness constant and the unstretched length of the bungee cord.; 3*r/tf cqq/wvjsm9i s 4t9de
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 v./ s,xbyd(ro 6jn 5uevibrations in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple penw sslx)qp:c h .r:b(;ksg71zidulum be if it is to make exactly one swing per second? (That is, kw1i)s s7::sqch zbg (rxl .p;one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a pergi,b9k /bsm*z; es+q piod of 0.80 s on Earth. What is its period on Mars, where the acceleration of gravity is about 0 e;sib*9qg,/ z +ksbmp.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm long :k1o,u ebll: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 has a mass o km2vod(qdar apv1f/o3i 0z6+f 365 grams, and it is released( f1rd3zpov +/qakod ma6v2i0 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 clock loses h21 wd 7ssld*c qly1fs3alls7s32sqcd y1*ldwf 1f a minute per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the max7678trjdsqiwa8:ffqt8 p1 e c-1pvxlimum 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 releazg*p, up j1t:a6xe idc 8(cdsn,-t .kased from rest starting at an angl pn e.8tsj 1*igzc6(xta c,pad u:d,-ke of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchored boatgxv +q *i;pdq +)w4icswwnq20 every 3.0 s. He measures the distance between two crestqq;+ x 0vcq+) iwsi4w2wgp* nds 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 speed ofdtx5 glvp )3v4 343 m/s How far apart are the wave crests (compressi4ltd5x3vgv) pons)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilohertz)nlo1.fi35+qd vy tf jj;qz-j . and travel with a speed1j.+ q5dfnjz3ov;.l-fqjt y i 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 sdj8*rm9xo41nkht f)longitudinal 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)wjiizp2j p-1 f s/*bv as dense as the other. In which rod will the speed of longitudinal waves be greater, and by what factor1 jvf/i-ipw sz)pj 2*b?   

  A cord of mass 0.65 kg is. uko 8jmnp),1:ystv f stretched between two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one suk 1 j.msynt:vu,8 ofp)pport to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable .qhwwhq/y i1i 8pabu0/ ir*+eof length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.*hqi1pwi0i+ea8/b qu./y rwh
(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 bvnc.hx03s i sk*gg-6felow the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at t-x0v .36scgsg ih kf*nhis point?    m

  P and S waves from an earthquake travel at different speeds, abcim,3q+yjp 6:hagp7 j7 0 qgmnd this difference helps in locating the eartcgy7:qhq 03pap6m+7igmb , jj hquake “epicenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximatem13j x :-,n:yhgymg;d)o- ll qjru,zg d by a sinusoidal transverse wave. Assuming a frequency l-qgx-, :gry jdj gohu1:l)znmy,3; mof 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? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, +me8f sc: qefv. xdt)4m y1wm2of an earthquake P wave passing through the Earth and de8)ex1 dq :fyw2vem 4 mcmf.s+ttected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave ppe 86g ks8coto+ j2sq;yj3l+jassing through the Earth is measured to be g23 ++qs oepjkl j8j s8yc;6to$ 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 frequjs *upb:g9.m xa2d y u5do48 y)mmr7iyency travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the ampli :9d).yum8jm mra5go dxiu*4yypb72studes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, but one trq+jb30 /lmyabla3: rjo- ;m jzaq7e(a ansports lqj+3/ j3q-b o 0maje(z7m:rlaa ;yabthree times the power of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond:zbn2izm bk.7 is observed to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wi7b.k2mz:z bnave 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 g-fvp,9y 5j0z whrwgl2h: -wa 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. What has happened to the energy at this momen:,ygp20 zvhjr f lg5-w9awwh -t?

  If a violin string vibrates at 440 Hz as its fundamentavp;t1 w0dkk p.l frequency, what are the frequencies of the f;.dp v10wkkt pirst four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingerekt.;rl79c s(kt*yi:gxxki 4rd. At what frequency will it vibrate if it is fingered or9*xtkl .ix7rc 4s :( ygkt;kine-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops.j/b *0 0 5w1regw1i /u:wajuhpshgwx at a frequency of 280 Hz. Name at least three other frequencies at which it will resona u1gh0sa:0p./e *rj1wuw j/g 5 wxwbihte. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a 8qkxn8m tl*9d string is 92m/s If the frequency of standing waves is 475 Hz, how f* 88nlxmdkqt 9ar apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, whld t;9o, c:)lb6su(tp8lnx q bat is the frequency of tu6cs(bll ;qpx8 9nbtt,):l dohe fundamental?    Hz

  A guitar string is 90 cm long and has a mass r65on8hb 7i/3 vtt )8h:as wzmv+gaf sof 3.6 g. The distance from the bridge to the support post is L = 62cm and the string5 zobgt3 8fa7 in8w+v/: s)hsthmvra6 is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it arl du-1049m lomt- .bp d6mxais measured to vibrate at 205 Hz. By whar ad41o- -.utlx 6ad0pmlmmb9t percent should the tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 20g1rflxi m+ 22 -bath7o0 Hz, but it is measured to vibrate at 205 Hz. By what percent shou lo1m2+7bx2gih f rt-ald the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to :r9 :wyblxr)s a small-amplitude mechanical 60-Hz vibrator. The string’s mass per unit lengs 9wryr:bxl): th is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be adjusted by moving the pulikk 4xhaj/ vc 43g;r4hley. If the hanging mass m is fixed at 0.080 kg, how many differechvk4 h/i;axj4 k3gr4nt standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forthdtyv6 3i5;as- lnw7q t 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. What is the speed of the water wave? y 6dq5nw i- tts7v;la3   m/s

  An earthquake P wave traveling at k.0 km/s stnv*4ehe;(;4 :*iz4hwiaczg/ h s pamorikes a boundary within the Earth between two kinds of material. If it a 4zeo/4i*hms:avge;zhc4 ah;n*(i w ppproaches 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 velocity bv ub:5bsw wn:kh +ge76/dz;gchanges from 2.8 m/s to 2.1 m/s If the incident waugn:bb5 whz;7s6vg e /b+d:w kve crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveli-gkn,j s m sbuelmw;4 maa3cie9s3/00ng in warm air when it hits a layer of cold, dense air. If the sound wave hnbj/asg wmmi l0 cueks3,3 0eam4-s;9its 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 a boundary b)e0iw+h jtz4;ifw7 icetween two types of rock at a i0t ;)+4ih iczej7 wwf38 $^{\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 /4ew cdz (x0jfabout 0.5 m in diameter. According to the user’s manual, the dish has to w(j4fex 0zd c/be 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 travels acvf z.uob9 b9:iross 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 attract. 99bifo:vub zed to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 5k nyb:ec(:de 750 kN/m Find the maximum com:ye en:cbd7( kpression 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 conservation of energy.]    m

  A 65-kg person jumps from a window to a fireq;8dbeo2vz 7h5,l0zp xdu r9 q net 18 m below, which stretches the net 1.1 m. Assume that the net behave,hbd8z0 59pq xzevrloud;q 2 7s 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 6 rmr5xar e//9wt6xh rfreely hanging spring. The mass then falls 33 cm before it stops and begins to rise. W rrrx6wetah5/ /6 m9rxhat is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed j-bswzqhdnt,z;97. y of 22 m/s (Fig. 11–54), compressing the spring 5.;tzn,w s jqhb 97.dz-y0 m. (a) 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 crs f4,iwoit/0m) at just the right pace of about 1 step per sfo wt0s, 4i/irecond, the coffee sloshes more and more 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 fros5t/mncfs st4s;q2902 zckd sm the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. W tmsszs0fnsd/52c 2q4;kstc 9hat will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according tor)v727o jw2p zeo;k,7 snfr it the equation x=0.650cos7.40t where x is in meters and t in seconds. Det7r, wi27poo t7v e;kjz)2snrf ermine
(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 frequencyq/8 o 8li:q w)/aqsloc7zck;x if it acceleratesoc lxa/;z )qcwi8kso: 7 8qlq/ at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raft, itorz uoj:4 ;52dycp2rg sinks 4.0 cm deeper into tz 2r2:r54guy oc;jdop he water. When he steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play q3 oho87tcic/p( h;qc at 392 Hz (G) and 440 Hz (A). /7t(;hcopic ho3q8 cq
(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 cord of Fig. 11–33xm,g+kdja4 ;v m4 q9ln. Determine a formula (a) fovj;qlm g m+ 4k9xnd4,ar 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 the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of each prong mqb/79car l u b3a/k-8mdpl f(moves 1.8 mm to either side of cbml a8aldu mkf(b 9r- 7/3cpq/enter. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates withom 0jirv3fx w1 +-ees. simple harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order t oi 1-xw0v rfej.es+m3hat 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 ring thallr ,4pe:mc 9lt can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the othl:49cr,ml pe ler free.

  A “seconds” pendulum has l jk*rme47k0pa period of exactly 2.000 s — each one-way swing takes 1pk l4ejr0km* 7.000 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 vew *pd- 3*zsmhrbf7d k32z* hnfrtical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and b7fd* h-kd 2*b rshn3mw *zzp3fy 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 teo*i m 6eh mqd*kk4yt2:nsion of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at t *q:k4tom6e m2ikd* yhhe opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling oh yd;34rz qc5by a spring with spring stiffness constant k. A penny of mass m is placed on top of t c5r d4hyo3zq;he block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cable ihus e;3pxc5bim 3v o5m6 0zf5mj)rl5vs 22 m long and has am5 3 )o5mzsh53 u mrvxl;j6 0ic5fvbep 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 Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. d(zg(l z9 *p0/x ttege11–58 (which also gives the dimensions of the block). You push it s0g(z tld/exe*p(tg 9 zideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz