Give some examples of everyday vibrating objects. Which exhibit2m o yx7uz*k ,exwx17l SHM, at least approximw1xxo2 yex mz,7*k 7ulately?

Is the acceleration of a simple harmonic oscillator ever mhelz 4 qr;tpvd9;:7rzero? If so, where?

Explain why the motion of a piston in an automobile engine is approximatelynhp-d lx c4yywz0;;fq f/r99j simpl9q-pfrzy;hn4jl 0c9f ; /d ywxe harmonic.

Real springs have mass. s-tlc oi3owjh- ,o( fm(0m; prWill the true period and frequency be larger or smaller than given by the equations for a mc (jpmow,-ro(ol-;3 s0 t hifmass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simta 67b- ax(oorple harmonic oscillator (SHO)?

A 5.0-kg trout is attached toxg6uhl*jhp1x 8j;30k.ep :g3l oessg the hook of a vertical spring scale, and then is released. Describe the hl;h6:* e3 8.g guk s1eposl pxjj30xgscale reading as a function of time.

If a pendulum clock isofc8x/fz 1-d p accurate at sea level, will it gain or lose time when tak8 fx1od/-z fpcen to high altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–48f1 lse :d+ 4nbq2mg+s0yf :jbo). How com nfeb :0yl :sdgq1sfjb++24ould you estimate the height of the branch using only a stopwatch?

Why can you make water slosh back and ci 4lm i)3dlw(y /9suzforth in a pan only if you shake the pan at a certain freqdc)w3/zy4l( islmu i 9uency?

Give several everyday examples of reso ggl. q:jyw;-r; ifa)lnance.

Is a rattle in a car eve; 8p vz4b 8iiqmm786qqdsf. yxr a resonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to td9qp n h1d:ww.ugw(j ,he frequency of its source? Why or wj1 u ,q(.hwwwndpdg9:hy not?

Explain the difference between the speed of a transverse wave travel4 mrh/gdol /d iz (q2;r ls)nu.ya*)aying down a cord and the speed of a tiny)lr/( )qr zg;ahi*ay duds lym/n24o . piece of the cord.

Why do the strings used for the lowest-frequency notes os1*lj l 7rl rl;zd6ax)q odhnr;9;k(jn a piano normally have wire wrapped around th9 *;h )(ldjl1qsna ;korll7rdrj;6 x zem?

What kind of waves d/(a he)w6 t+m ;tna:pekoms w4o you think will travel down a horizontal metal rod if you strike its end )t w/6na4em ktohpema(+ :s; w(a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase z z/ rx4yo w3fbn7/s gco(1xv(in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary wit(n cg(vs4fyozw3xr/ xo7 / z1bh temperature?

Give two reasons why circular water waves decrokzwx33x 8cx;k/ ouc )ease in amplitude as they travel away from theo wc/x8;3xz u cx3kk)o source.

Two linear waves have the same amplitude and speed, and otherwise are 81 lwd y(z/rs:tctn 7qidentical,z tq1cl/tr8(ynw 7:s d except one has half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave croscdoo 3)4 6oaew02fvro ses the boundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocityor 0ocd)w4 6a2oefv3o do change). Explain why.

If a string is vibrating in thl3rbw 9(ien; eree segments, are there any places you could touch it with a knifn;ibel 9ew3(re blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of infurwf3s .twy;kw.: rcam h*2*cident and reflected waves cancel at the node*k; f wmruy rwt:3.f.a ch2ws*s. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmma7hjq-gt. /q a68v jpitted from one place to another, how might we determin g/h p87vqt jaa6.j-qme whether the 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 distmx,5gb1+ a ddbance it tra1x ,abg dmb5d+vels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs ft3l:- sqfztk2d1kk3 rg v x2j*rom it but is 85 cm long when a weight of 1zs3*22t:rk3kkxq f ltg v-1j d80 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver getsnzxd/ bdl3722ru8 d*4oykjyx into the driver’s seat. If the car goes over a bump, what ukzx n*l4or dd2/2bx87 d3yjywill be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a (0)g ,u squbyr2.7-kg fish hangs from it. (a) What is the sprrs,qu)y( 0gubing stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz whezuy8*j5 s *qte7*2 oeq;hmltc+y ya /jn a mass of 0.60 kg is hung from it.;lsqh+8q t*mey u/o e*y25az*7 jtcyj 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 at tych69kza 4 23ep0: *cdtbzot oimes t = 0o:t 9hz3bd20c yp 6*c4oezka t,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 n8 ,0cspjo9i q f/p,hl0.25 g is caught in a spider’s web. The web vibrates predominately with a 9,/i0 s nhcolpqj,8p ffrequency 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 vibratqt3qbcrrxi+ tg0)n et;(9i7whk ,n* nes with a frequency of 0.88 Hz. When an additional 680-g mass is added to(3e*0nnnqt;riwk+7i b )tq,tr9cgx h 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 vibzux q x0vg67(arates 3.0 times per second with an amplitude of 0.17xvqza6 0 (uxg3 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 5) a t;a-r gblwr1xb7pspeed of a SHO half the maximum valu7r5lar b bp 1w);x-tage?$\approx$    A

A mass attached to the end of a spring iu7q3m /b9lrdb s 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 vertical spring 0.315 m. If the sutgjwv0l9*8j n+n ey, pring is stretched an additional 0.130 m n9,w gjle *tyvun8j+0 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 stiffness co 6hc.b)iq ohwscq v+;d /;wias;g;mz/ nstant k = 280 N/m and is exgc;a6/)/qs siw ;;h+qzdwh.;i c bvomecuting simple harmonic motion. When the object 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 to compress the spring of a n 5d2wzbdf8a6 toy popgun 0.200 m to “load” a 0.180-kg ball. With whnb2fwz8 5dd 6aat speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is atta 1w; b22eh)qeid5i na bm;nd2qched to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the w ;b )2id5hndb2n ei am1;e2qqspring 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 vibratepu cxbs 0v,42bi,*peoq/4-lnwb6 q wis according to the equation x = 0.45cos6.4t where x is in m4 b /ieu2qso,bw*bxlcp 6vp w q0n,4-ieters and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from eq d4x/cjfc7 gd/uilibrium is the energy of a SHO half KE and half PE? ± ddg/j/c fxc 47   A

  If one vibration has 7.0 times the energy of a second, but dpdl8looi 7d.2paf38 unqz7ww,i4 3 an+.wuqtheir frequencies and masses are the same, what is the ratio of their amplitudes? o l8u ad2n.3qwi.zpni7oq3 8 7df+ldpuwwa4,  

  A 2.00-kg pumpkin oscillates from a vertically hanging lig81xukeqb 0f d:ht spring once every 0.qd: k eb18uf0x65 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 supported by two identical parallel vertical sprin v w:p8;ln0etogs, each with spring stiffnesop; wn8: tv0els constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates accordin: bsmr87t fopxm+98fjg to the equation x = 0.38sin6.5t where x is in me+ 7:r sfojm8x9mfbp8t ters and t is in 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 *m t*yy9cqklhzi.9p 3SHM, 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 horizdis7-wje63z zontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed od -i3 z67eszjwf 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 sp,yx* qs5(dughw e-)naring stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm eh5ysuqna() ,xw* d-gwhen 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 sprim*qg1koo2) k j x(xc,ings, 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 horizontal spriwps )c svc(r;rw-4kq2ng whose spri ;wv(4qs p2-srk)wccrng 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(pz acn7 x7kj3 65.0 kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hittingxpz3 aj(n77c k a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 60 s 55 jtzn3)rd s ,)nkmp) lllc9nu8.lua. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one 5iy a 8 zi98r orhpk8tc54q1fkswing per second? (That is, one complethirai88pq fyzr1k5ot c9 k584e vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, whph9k:v . .tqsl w /e p;jxpu)o6xz1t*5uuw9tqere the acceleration of gravity isqq tl*v9z6 u5.; xt9 poku1e)wxw .up/jhtsp : about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm long 37xha5hjrwjw+c eao x 071 lx7
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, kg 54;1x22igzwvakzx the pendulum bob has a mass of 365 grams, and it is released at an akvxiz; g1z x2aw2k 5g4ngle 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 lengts(;40- fhhx-s ygmzdq h of 0.9930 m. If the clock loses half a minute per day, how should you adjust x0ss( gmy-hf;d-4q zhthe length of the pendulum? shortened by    mm.

Derive a formula for the maximurw rfpi-vsod 1,xi e8489ih y+m 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 released fro2va ezjez6 .l(m rest startinez e6 2zl.ja(vg at an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pasjl mg2y+rg3 x ltid1l;o1jf00hyf)+ms the bow of his anchored boat every 3.0 s. He measures theo0x+tj gr g+1lmfly3y )m 0i1 fl2djh; distance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air 0q68z( )p3gr )8wv o,qfeuseyaoe* pw has a frequency of 262 Hz and travels with a speed of 343 m/s How far apart are the wave crests (comp6 o88 r3*ap zps qwyeqgf 0ev,oe)(uw)ressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHzbdjq,el2)pn pu 6px1 * (kilohertz) and travel with a speed of up6q2x ),p pd1 *eljnb$ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal waves 4 tiulxjh p0kx9zj9le 51mi* 6in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elaqep 3wq.xht(33h *ixpstic modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be grea*3 txqhppw.( eqi3x h3ter, and by what factor?   

  A cord of mass 0.65 kg v5nz/ f2qysz4 /oxav6is 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 suppos/av4n/qzv 2 fxoz65yrt to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of length 620 -uyk -n,j/dq qm and diameter 1.5 cm. As the gondola comes to the end of its run, it b-,dqyqnju/ k-umps 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 setbc-e acysei: m935 *b .c,pdua. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is thb:p-c5 ue ,39.mes*a ctyi cdbe ocean at this point?    m

  P and S waves from an earthquake travel at different3lql,bm9. ig;cqlu (z speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbance took placei9( .ll qqlc,gz;m3u b).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated bymx3i/a 7,n ulc7igz; z a sinusoidal transverszcz,7ign/7 mal3iux; e wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of an earthem q4jnzx25 ) xs:o8 2rh1zmjjo3(cus rrz 22yquake P wavsscj q) x25zo m1m:rnh 2ej 2(z34jr xru2oz8ye passing through the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing m 2d;p8u9jra pre8s5u 2j+pp athrough the Earth is measured to be ;25dps 2e+au8pj 9umpa jp8rr$ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency travel through the satymx4ur 4 +xi.;0,(cf, jwrtqx.fyw3 w ufh:bme portion of the Earth, bj r:w xhcf;y(,y4x x3u ff ,bwt .4.tuqiwmr0+ut one is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequ xs (dh1xscv696kx p(;m059c a ndkwuaency, but one transports three times the power of the other. What is the rath(dsx196cmuc9v (6nxxaa5k0 ;psk dw io of the amplitudes of the two waves?   

  A bug on the surface of a pond o. 6px k(6+pkl o7hgmwis observed to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm,h6 km k+opwg plxo7(6. by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig y:dhh3.h/ncm4 /r7tnr7h*uyoue bd ,. 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. 7h* n: ud7y,hychub43 re/d. m hront/What has happened to the energy at this moment?

  If a violin string vibrates(kqd63238lc en p y l+fz6arci at 440 Hz as its fundamental frequency, what are the frequencies of the first four halzy f+i 6lc8e2ncd3a6r(kp 3 qrmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingf)c; qn/rk4 /qliv7w8uqzlrg j7* g6gered. At what frequency will it vibrate if it is fingered one-third of tqn) jq6icg 7fu/;l 7wggzl8r/ kr*qv4he 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 at a frequency of 280 Hz. Name atk5vdj; dx) jic/4fqq9 least three other frequencies at which it will resokj) q4i9xdcjv f;/5dqnate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s qg +h- wi(b4 ,pnnw0w2xu,k;uc :unwin -ac5qIf the frequency of standing waves is 475 Hz, how far apart are two adjacen,u(;c4 aqwi0b:ww2n,wh5+pnxcki - u -uq ngnt nodes?   m

  If two successive overtones of a vibrating string are 280 Hz andw-g175*z9 iww;si dy 0xiog uo 350 Hz, what is the frequency of thwu s z*w1 9;gii d7i0o5woxg-ye fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The dis9 fd(qdzsoyd7gb;19lkjq+ u;tance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the fre 7qb1od+9 ;u9lzy ;kf(g dsqjdquencies of the fundamental and first two overtones?    Hz

  A particular guitar string8;sfb t +v:y 8 dn0,e/qlfnv1n4va ezg is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percen nzg 88dy+nn4ve;lfs/fa1 t ,:vvbe0qt 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 i qpq;hnuq1g:-f l36 nds supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent shouldd 3lhgq un:q;-qn p16f the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to at2 wa-x tkf ph.v:3ee1 small-amplitude mechanical 60-Hz vibrator. The string’s mass per unievp3f h.te :1wt2xk-a t length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be 9arb6 ,wdv vj)la9 h(xadjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave path (,d6 r9alwa b9)xjvvterns 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 justaa bsfy;c/,w* the right frequency, the water alternately rises and falls at each end, fc,;ysa w/*ab 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 travelintm1//t :x,hfki pgws)g at k.0 km/s strikes a boundary within the Earth between two kinds of material. If it it:kp /hxswg1/m )f,t 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 underwx n 1f:s;l/fyt0t+ jw/(zg engater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests make an t/se1j(wn/0lyz:+ f;gfx tg 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 airrb ;yd +m,*5kx4zl hci zv.u1i. If the sound wave hits the cold airyvz rbmi u*1h5,d+.4 kx;ilcz 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 wa0swx ,fb)ye*r+efz g- isvg*8ve strikes a boundary between two types of rock at a 38,) z8egfw bigs-*sr* +vyx fe0 $^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m in diameter. According to the user’s manuy)2jw q ojaof+te -(*cal, the dish has to be pointed in the direction of theoe yqwo-+tj* 2(cfj )a 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 ac 1y,;nvi,1txr p p5yhgross the Pacific Ocean. As it;xip n,rph,g 11yv 5yt 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 boats.)    min

  An energy-absorbing car bumper has a spring stiffness con8 6w6lu2xeo ynstant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg,6oexlun 26 8yw 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 4t)rqpukvk+g k x- 0aj0n0i- gfire net 18 m below, which stretches the net 1.1 m. Assume that the n)qg0g+4tp k0k0-v -rkuxji anet 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 sprsv7 j; tq:aw2 sa1nsq)ing. The mass then falls 33 cm before it stopst n ss;w2q aq1av7:j)s and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at aqs0ona8 6y:h fs i1*qx speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spri6nqq:ossi0h* fx ay18ng 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 right pace of abo1 vey(2gqtlo6t mhk9.ut 1 step per second, q eglho1ytv 9k62tm.(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 from the center of a 33-ro stafd ;qu0 4ri:/qf-pm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sound uir;f0s/- da4ot qf: qemitted?    Hz

  A 2.00-kg mass vibrates according to)l kdo3;ixq ;o the equation x=0.650cos7.40t where x is in meters and t in seconds. Ded3);xloqoi k ;termine
(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 oscillj0a(i9nwzr d-;oe *prates with frequency f. What is its frequency if it accelerates at 0. 9iw0;n-ezro( pr j*ad50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a *4me: 1w*wj3), (pos9afuyyx/o frdy sqt r(p75-kg man stands on the raft, it sinks 4.0 cm dx ,w1wq/(rjf**mo u 3perpy(oys)f 9yt ds:a4eeper into the water. When he steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play 1d5k 9em5uewc at 392 Hz (G) and 440 Hz (A 55uec1k mew9d).
(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– :c*leutmqu vs*0dn8033. Determine a formula (a) for the ratio of the speeds of the wave in the :0uqnlcu* t *ev 8mds0heavy 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 p/8x jtsobr:6.y ze4esrong moves 4j/e .o8ebs:6y rxstz 1.8 mm to either side 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 osciln- vrwq,sg9-puq,m* klates with 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 that a pebble placed there (Fig.up q,gm rnw- kq*v9s,- 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 awzo 9qnz9pk6jq7 i+*t czdwn y :*d05q ring that can slide without friction on a vertical polewokz*6*dqd 5 nn qzqij0yt :+cw97zp9 (Fig. 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 — each onegfb,jo1qi0v+ q.lm *n-way swing takes ,qj. +gfq10mni o* lbv1.000 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 vert0warecn8ov2qh l7 5 y-d 9b2akxr;pt*ical direction or can swing as a pendulum of small amplitude, but not both 2a 92n07tr cdl5kxaq*rh; 8 o epw-vbyat the 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 255 N. A pulsehdvn8om dp+ -x 6m7ty4 is generated at one end, and 20.0 ms later a second pulse is+my7dv 84hx odtn- mp6 generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspendel7ozrz:uq*c4 s z;o6 p 8h6ymid from a ceiling by a spring with spring stiffness constant k. A penny of mass m islh;yqu zp*6o m 86scz:4irz7o placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at th86qxhip 7yu62vlaz8e e junkyard. The steel crane cable is 22 m long and has a diameter of 6.xu az62vp8yh7 qi6l 8e4 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. 11–58 (which also gives thu7 l8glw(crnqc0)3sl e 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 spri80q( c nu)rll7lgwcs3ng, 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