Give some examples of everyday vibratingi jc2)ra95uyyj fyx80 objects. Which exhibit SHM, at least approximatelcy yaji82f5j90ury x)y?

Is the acceleration of a simple c k7:p.wavec*z9y )yxharmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in ank qfkrv).fl4a0 umv j;z1d7l*17 okkn automobile engine is approximately simple harmoni kdm0)* av1 f71fnl jkuk.lv; koz47rqc.

Real springs have mass. Will the true pey-l4u d)a u26o(iv 1 5liimsferiod and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized massless spring? Ex5is iu(u1m6-4l i el)vyfa2d oplain.

How could you double the maximum speed oh(nke8c 5k/ykf a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attacc2br ze;p2h*9 nbey vr8 l8a8zhed to the hook of a vertical spring scale, and then is released. Describe the scale reading as a function of ti2 b8b ez *8rrnyl9cpz;a82vheme.

If a pendulum clock is accurate at sea level, will it gain or lose time;aapjwl/g9f(eelm/ / when taken to hifja( e gelw l;/9a/mp/gh altitude? Why?

A tire swing hanging from fj)o u*, mh*el:czc:ha branch reaches nearly to the ground (Fig. 11–48). How could you estimate the height u*) c z*ceh :fm,l:ojhof the branch using only a stopwatch?

Why can you make water slosh back aqk,gys6j5.a(s3gdu6 ) cc/ +zxslyl t nd forth in a pan only if you shake the pan at a certain freqgszuy)6cl+3qcy (ag t5jk, sxd.sl/ 6uency?

Give several everyday examples of resgr.0g gv .m5xnonance.

Is a rattle in a car ever a r9vx+ l *dp/pawnit* 6vesonance phenomenon? Explain.

Is the frequency of a simple penkn 04pth y2 5nqloq2+riodic wave equal to the frequency of its source? Why or 2 pl nhqn5tqok2y0n+4why not?

Explain the difference between the speed of a transverse .in-w*xxh0 - rnxk6be wave traveling down a cord and the speed of a tiny piece 6eh-b*x0-. wrxnxnik of the cord.

Why do the strings used for the lowest-frequency notes on a piano h.,. izymd 53adki/tz normally have wire d/hy5d..m, az3k ztiiwrapped around them?

What kind of waves do you think will travel down a horizontal metal rod if , mg4 ;ghf;u34h vum 0axyr 8((gtrbckyou strike its end (a) vertically from above and (b) horizontallyv;u43hcgbu frrg 40tm,( ;ghaym (k8x parallel to its length?

Since the density of air decreases with an increase in temperature, but /ib, ic 6)lgzathe bulk modulus B is nearly independent of temperature, how woulgz , a6/ilicb)d you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as they traorwjtb a0g u 2- 4evcbv1493nlvel away frw23tg01nvob-r4julae 4 b9cvom the source.

Two linear waves have the same amplitude and speed, and otherwise are identicalmo/h9bgx0r.4c8o q uh , except one has half the wavelength of thor.ugqc/h0 h9o4b8x me other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary betwelb* csk2) v7vzen two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Exps7kzl)vv2b*c lain why.

If a string is vibrating in three segments, are there any places you could toug6bjeqmhm/ f9) 4zia(ch it with a knife blade without 6f/g 94 zhimeqj(mb)a disturbing the motion?

When a standing wave exists on a string, the vb x9o +l4mq:pegd4 7diibrations of incident and reflected waves cancel moli b gqexd7d94 p4+:at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one placygb/ru 2: (dhr+ jt,ype to another, how mighrdh +2tg /purjb:y, (yt we determine 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 totf;gusiyu:t r2q4og3.al distance it travels in one periog rf4u;3y qgi2s. to:ud?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it b* i4u)fx z4zlqqqqnzg)22etk9 t(:xaut is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of thx e9*4 xz ng 2fz):z4qkattqq2)(uq ilis elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver gets into tj pn73u2tpl1me5:zs khe driver’s seat. If the car 2l:u 1p3js5t7z mkepngoes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from i( e:w5 lcesmd5t. (a) What is the sprineslm 5 cwd(e5:g 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 - ai02ao+gwza(x f(/qzumpfk; .(hlldvcf2/ frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 fgu2a(ix +c(dvl2z/fhqa a.(om fk0;-zl/p w kg hangs from it?    Hz

Construct a Table indicating the position x of thepj-c)z0x* umj mass in Fig. 11–2 at times t jm0*u) j xz-pc= 0,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 w cxk)7/*6sijo w;xcraeb vibrates predominately with a freq6cj;ak)xi*7rxs /cow uency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with f: .guwbum e9l9n x1,aa frequency of 0.88 Hz. When an additional 680-g mass is added to wu axbfgm19nl9.: e ,um, 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,;4ab s)wmk8h1ki 3yddkkb 6b times per second with an amplitude of 0.13 m. Determ ykk)bb3d,1hsa kwb4m8i k6d; ine
(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 g:oiutem5*)f a SHO half the maximum value:gmo* u5te if)?$\approx$    A

A mass attached to the end of a spring is st(pl/*ri 1dim5kxg ld5retched 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 is stretcb 5h+p/bwe *s*ayu2 ydhed an additional 0.130 m and released, how long does it take+bb*/we yy5hd2au*ps to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffness cons/x-i dst4t7+azn dc6 0cj:t hdtant k = 280 N/m and is executing simp- s:hz+dndd6j0x t 4ccia7 /ttle 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 t apok 8q1cg)w)he spring of a toy popgun 0.200 m to “load” a 0.180-kg balwcqo)ag )k18p l. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictim)wnddhq 0: 6j: u nb71plig9yonless 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 mass is released from rest with the spring comgdihq607:) w :d9mnlbpn1yu j pressed, 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 t. 7wsnwob 8f5jll/sx7o the equation x = 0.45cos6.4t where x is in meters anb s7.snf/jowx5w8l 7l d 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 ejo1hrvj 2a 4m:quilibrium is the energy of a SHO half KE and half PE? ± av o2 jhj4mr1:   A

  If one vibration has 7.0 times the energy of a second, but their frs2z9egx*n5kg b ot* 2fhfb j84equencies and masses are the same, what is the ratio of their amplxfsjg n4of9 8kt5 * gbbhz*2e2itudes?   

  A 2.00-kg pumpkin oscillat6i1m 1i25ioj (uxyoaoes from a vertically hanging light spring once every 015o(i moioayux12j i6.65 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 spring3xt r+w 7huvxy +eh2f-y+dmz.s, each with spring stiffness constant k (Fig. 11–497m2x3t+w.hfyry xd+ z v+h-ue). What will be the frequency of vibration?

  A 300-g mass vibrates accow gw 4,plye(60( pm+kju 9yjxzrding to the equation x = 0.38sin6.5t where x is in meters and t is in seconds. Dete(my z, ejk6(l +u90wwpx4gpjy rmine
(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, lab 8 og-:d+jv( izb0wrkteled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal spring (k = 124 N/ek.g1s2sq u 5am) is struck by a hammer,.1sq5gsau ek2 which gives the 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 stiffness constant 305 N/m vibrates with an amplit ls7 whwx puv)1p)x38xude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity at lx1xxpp)hw 8s7)vu3 w
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring stiffness constant3 zts tyz)iqyv6drj5.) j5t:j + g5jyys $k_1$ 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 5 z 2uua4qp:mtblock attached to a fixed horizontal spring whose spring stiffnpaztq5:2 4uumess 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 masbp9 wgnb3w5t.s(gpr)4ino 8 h.bknv w ;+ 3uyys 65.0 kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight ;)w ipn8(3b + h5 wbpyuvns9wn k4..gyr bgo3tmore 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. What is its)*he*.8chz(prze rid 1 ue0bq
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it +n frt/(xhdc md.1oa7is to make exactly one swing per second? (Tht1m.f(a/o c xndr7h +dat is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Ej6d4d;s*5h 1bnebirqarth. What is its period on Mars, where the acceleration of gravjd*h5;r de4sb6biq1n ity is about 0.37 that on Earth?    s

  What is the period of a simple pendulxm mk4y x),oulvf4 ;a 2f44:6zydathv um 80 cm long
(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 pendulumz9jtufdvp g1u-rn/ n-f*vllw, 3(yp( 6,v cw t bob has a mass of 365 grams, and it is released at an angle of vlc / j1wufr*3t,(py g dpf vw-vtz-l9n(nu,612.0 $^{\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 1a/pk nsmsb5; (ov9co length of 0.9930 m. If the clock loses half a minute per day, how should you 1s/os5ko(m;n9 p c bvaadjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum speed -(/ftk x swyorkzo*v. yp ;t 0oxf3f64$v_{max}$ 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 iap3 upp6hf/ vym83vt8 t is released from rest starting pv /y8863fp mp ut3vhaat 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 pass the bow of his anchored bou2,glm- 8h 11ofpkhj wat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the waves travelihj wl 1h,ok8f-2ug m1png?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with i9,nz/ dewcp i;si o6,a speed of 343 m/s How far apart are the wave crests (compressions)?oidi9np,i e; 6czw/s ,    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kiloher5/ms.(qpxjj 7k ml* cg 09oz6umwcb5ttz) and travel wqbmw zgsj5 m/kp 50( * uc6olj7.mct9xith 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 lobnuprt 3, v: ij4,cc8mngitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastiec*e4b j )n g*b+d:xf/ukm5arc modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, and by what factc5:4bar+d*xe* /fb)ej un mkgor?   

  A cord of mass 0.65 kg is stretched ug qdvs7, 69kmb)e/6gtsj4qgbetween two supports 28 m apart. If the tension in the cord is 150 N, how long wil6kbqtm7g9/e u ,jdgg6 )s svq4l it take a pulse to travel from one support to the other?    s

  A ski gondola is connecbv03f8t v* b3c4aroqkted to the top of a hill by a steel cable of 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 0 f b4vb*aqock3rt 38valong the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the surface of the sea. Hu 4vd;s0 9rpq(tewokk49sn h2e hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean ;ktu4kn2r0sw d ohpsq9ev (49at this point?    m

  P and S waves from an earthquake travel at different speeds, and this di9jlz26de zwo b/3cob7bz ;at/fference helps in localbzzb2t/odw j9 o e3cb7;/a6zting 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 can be approximated by a-o m fs2xmz2/11bl4ea*l u qxg sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects bgobmqlfe2 /m12sx*x au 1-z4legin 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 ear.hhj k:.gcxrt cfr-v 7x(/u+f thquake P wave passi.x f: -gtx (ch/h7rc fj+ukv.rng 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 through the Eartj9etrqezbo(/u 6+ a-y h is measured to be y qjteae br(o6z-+/u 9$ 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 sam09sy04m s9 fww1fesw95(cffqhfuwr2 e portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of the two waves?r2 f4f(sh00fm9 qfw9e wf15swu9 wsc y   

  Two waves traveling along a stretched string have the same frequem8jpubpb4)gx *q;4 ynrn+ 4grncy, but one transports three times the power )ug4+;qxy4p r*bm4gbn8 rnpj of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface tzpqv*0b86,wi:- jzbfp nyj. of a pond is 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, by what factorfb :i-q . y bjptv0zz6nwp*8,j does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52vf(d1 jgm4 l/y 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 lateg dj(fl1v/4ymr. (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 moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, what are x7s 4w q;wwf4fthe frequencies of the first four harmo fw7s;x4 fwwq4nics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency wu-6no+n/ 5nnjdn)w b0,nhrmpill it vibrate if it is fingered one-third ,5m nd/n r)-pj0+obnnnnu6w hof 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 at a frequency of 280 Hz. Namn4plj 7z8ko g8e at least three othg8pl ko48nj7zer frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If thd9o,-cjm i.te : rt8zhe frequency of standing waves is 475 Hz, how far apart are two adja,rc-tzjd8 :mti9eho.cent nodes?   m

  If two successive ovyov8 i bclhou .-49:nyertones of a vibrating string are 280 Hz and 350 Hz, what is the frequency of the fundaml4vc: -o h9.i8buoy nyental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance from the brru-o un50 5atbidge to the supportubro0un a -t55 post is 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 string is supposed to vibrate at 200 Hz, but it is measured vwvq5 vss 8)*gto vibrate8w )vvg*svs5 q at 205 Hz. By what 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 200 g wi:kf;bv6e6x5-7pj(llu sj Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the st gwi uv-jjb75:;x6kfe6l sl p(ring be changed to correct the frequency? decreased by    %

  One end of a horizons vu+ufbou(pm3hb0r6h8v)s 7tal string is attached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass po6r +)3bshpsmuu v(7 h8ubv f0er 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 le1.g2i h klt6kungth of the string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave pa6gtl1kuh2ik . tterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the right frequence 2d.qh1erg a1y, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce sucq1 hd r2a.eg1eh a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at ,ddal09ze2z l5n x5yv k.0 km/s strikes a boundary within the Earth between two kinds of material. Ifzdl 92yaexl nd,v z505 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 und*wvj; yaxm0 7werwater “shelf” where the velocity changes from 2.8 m/s to 2.17awwm j0y;v x* m/s If the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer of cold, dense am8l ljm3wk+ ,byj0,zair. If the sound wave hits the c0+mkab8,j j l,ym3zwlold 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 boundary5miavsw onbsa-d2 i786ub t,4 between two types of rock at a 6a7b2ibd 4oma uw n5vss- i8,t38 $^{\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 mbtw8 n//0086rzq4lbbq jrjeuser’s manual, the dish has to be pointed in the direction of the satellite, but an error of about 2er mwtr8qb0/ nj/b04b 86jlzq $^{\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 acre,c p 2g8etd19vkzpfq7h0u/yoss the Pacific Oced 8c0tk pqzg1 /92hp ,yefv7euan. 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 boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant offyo-rw u 7gw31 550 kN/m Find the ug31yf w-w7ro 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 conservation of energy.]    m

  A 65-kg person jumps from a window to a fire j b/bjgr9-f,s net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a simp g jr-,sbjf/9ble 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 spring. The mass akfm * ,qo/t,ethen falls 33 cm before it s kqf,t, oem*/atops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring t3zx: /h6oyp/ yh,bfr at a speed of 22 m/s (Fig. 11–54), compressing the springhy/f /p tozx y,3br:h6 5.0 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 cm) at just the right9x-tj / 6z w ,ta*copllabp(a5:p,nm t pace of about 1 step per second, the coffee sloshes more and more until eventually iatx/tb5jp: ca,9t- *pa, po(l6lmznwt 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 hi42 0 je8(gu.k nfygfcm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. 8jiy.n(4 20 ghff eugkWhat will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650co5j/la3 r.gw bxx ,u 4og54pisls7.40t where x is in meters and t in seconds. Determine 53bgu,4x5lgxa psr4 jwiol/.
(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 freque3uv vrzq +b+gqwp.xz:gk+ny8 efb109 ncy f. What is its frequency if it accelerates at 0.50g (a) 3ggzb++.n9kyq v+8 zvepquf 1b wx:0rupward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raftna3b+p ./2pexk1ecc g , it sinks 4.0 cm deeper into the water. When he steps off, the raf1gkp exb.c23pa /ce+n t 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 44 3eyib va v505xynb-q0 nl;ae50 Hz (A).5vn5;5ilb bey0 v ya-a 0xn3eq
(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 streyw y1aa8 a+pb+0g2 ilrtched two-part cord 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 t2 a+18gy pi 0yba+wralhe 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 4/jrlkh,a6fcq)r v gox7qx+ (8x zho :of 264 Hz, and the tip of each prong moves 1.8 mm to either sid +kvr: jcah( f8x7zox) qoq,4g hr/lx6e 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 simple harmonis)qinz7ye l 0aztt 1+4c 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 peby t1ln0t esq7z4+z)aible placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” endj6ts t.qc.xl8ykr o3w)y 0j6q if that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the rerq0tx)y8sw ykj.cl3q oj.t66sonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of (r2qygu -4;cfr y vldc6-k :alexactly 2.000 s — each one-way swing takes 1.000 s.l;(d2aq64 u yc :rgvky-l-crf
(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 verhn u a 6ype*lkxj.:9c+tical 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 vertijc6 .+ p:u h*k9lexyancal 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 tens8 y5i6 i0r g4 aitxz)k:opr-uzion 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 pulsxipti z6i-5)rrkyo:80azug 4 es first meet?    m

A block of mass M is suspended from a ceiling.kfi(6g6g dl r by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay ong 6(grli df6.k top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cable 1ai7zk//v nbkis 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 iknz71bv k/a/period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a py04 kxk lr*y tdb1*ez-12 hifilate as shown in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibrationby1 *4 kdlhftyixiz 1 -*2kr0e, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz