Give some examples of everyday vibrating objects. Which exhibit SHM, at 6zz5a:3cl+i(yw9 xt c j qv:alleast approximately 69a+ 3 l lazc:vq5:(ixtwczyj?

Is the acceleration of*za 8sik0j.bz a simple harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approximxl zqlwm5w *n; 47(8prqejt l1ately simple harmelrm5p l w4;j1 n7wxl* q8ztq(onic.

Real springs have mass. Will the true period and frequency be larger or smaller 1d pns+mf ;fm8than given by the equations for a mass oscillating on the end of an idealimdmf ;s1f pn8+zed massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillator (SHO)rol3legh* c8f)gp92ix:dwe : ?

A 5.0-kg trout is attached to the hook of a vgq r9+ueo 23mnzfrug j vqku/y*xv,fz)6* (/bertical spring scale, and then is rbrvuk)9je q 2uuzz(g*f/xfg v* yq, 36n+m/roeleased. Describe the scale reading as a function of time.

If a pendulum clock is accurg:wvom8buyef2 - 7 xf5ate at sea level, will it gain or lose time when taken to h5bovw f:em8xu y g7-f2igh altitude? Why?

A tire swing hanging fr ka.4o(8gg 7ek ldfck1om a branch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the brana1g7eg (k lk4f.8kdo cch using only a stopwatch?

Why can you make water slosh bmognas 84-s f4ack and forth in a pan only if you shake the pan at a certa48-mfag oss4nin frequency?

Give several everyday examples of rki) 9 :e.m qma9ol, .oh0o+a( +hl ym)paruanmesonance.

Is a rattle in a car ever a resonance )8hhr4m70pords..: u-ibznb ln8k qz phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of i 8 1if;axt2bfkts source? W 1bxf;a i2tfk8hy or why not?

Explain the difference between the speed of a tranes sj-w/vyc5vzcwa/sz4 7n, 8sverse wave traveling down a cord and the speed of a t 8n4w zs/7es/w ,-a yvzccv5jsiny piece of the cord.

Why do the strings used for the lowest-frequency notes o 7zs8*xk e p2u:)poaypn a piano normally have wire z )ypop:p sek87ax*u2wrapped around them?

What kind of waves do you think will travel down a horizontal metal rod if yo +3oihql5 qm;(jdnp:c u strike its end (a) verthi:mq;3+c qjl d(op5nically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in tekkz-a ; k:tty5mperature, but the bulk modulus B is nearly independent of temperature, how would you expec-kykat k5;: tzt the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as)p ).o2fuahky b/wt j0 they travel away from the p)at/yf0)kj2huowb.source.

Two linear waves have the same amplitude and speed, and otherwise are identical ejjxn2k a6./.e-vc prup /vu*, except one has half the wavelength of the .e e2a6j*/vpx.cv-npuj u r/k other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two s2c7 oi alhv5f-ections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and72lo-iach 5 fv velocity do change). Explain why.

If a string is vibrating in three segments, are there any places you couldmx bil)* :ph9a touch it with a knife blade without disturbinpixbh*9 a)m:lg the motion?

When a standing wave exists on a string, the vibrations of incide . g,stglj2bkxpiza8a4j*d;9nt and reflected waves cancel at the nodes. Does this mean that energy was destroyed? Ex b,j4g9z kl p8aisa*gjx;td.2plain.

If we knew that energy was being transmitted from one place to another, how 8obq au1av7 4u+c4s* qp:yzyhmight we determine whether the energy was being carried by particles (ma 4vyu+s78q ayophz*abcu4 1q :terial bodies) or by waves?

  If a particle undergesl-p2x0; ay soes SHM with amplitude 0.18 m, what is the total distance it travels in olspx-eys 20;ane period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it t,ea*ow h-8b 0m/ymjm but is 85 cm long when a weight of 180 N hangs from it. t *a mo -8y/ebj0mhm,wWhat 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 gets into th3wwf2l )nn ;v/pvneikq) 7i)he driver’s seat. If the car goes over a bump, what will be the frequency of vibrati k wvi;v))lenfw2i/pn 7hqn3)ons?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-pvf9yi,*3ac vgd : reeio0x 1-kg fish hangs from it. (a) What is the spring ,*p- agcy vvx f19id0re:o ie3stiffness 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 when a mass of 0.60 kg i;3kl y4mhkn 5nb 5pwv*s hung from it. What is its frequency if only 0.;w4 khk35*bvlny n5mp38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at timesc2gi7/m /hy7fo1at+ n jri e;j t = 0,t / + ienyjg7i17o2;crjmtfa/h = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 web vibrates predo f.aw-:ls drq*kn 6-w98hb cxominate-:awh -6 9 r*nolcxsbdkwf8q .ly 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 ad7j0p 4kfz-rm spring vibrates with a frequency of 0.88 Hz. When an additional 6k0md-f47rp jz80-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 seco y y3;t8cl0nn/b)tkb0qr tpdmahx7-.nd with an amplitude of 0.q;.3 nc0dt bty-kr n8m bht)70/xy lpa13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed of a SHO 0 +fj)tu*sbd rh5 3r1am+k n 7eq*.r e5ybmfcmhalf the maximum val)7eka0*1n musfc*5 +fmyhb+3 rejmrr t5. q bdue?$\approx$    A

A mass attached to the end of a spring is stretched a distanc0lhiy.ugay0e q f8cpqc ;k.bd6uyi/.11 hmi.e $x_0$ 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 sprinhpu7o *c9c+ 2wm*osf/p:f k ang 0.315 m. If the spring is stretched pu/h*mo9cf okf:c *pws2 + a7nan additional 0.130 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with ,i;nda, ib blektbox*76z .1 7xer5apspring stiffness constant k = 280 N/m and is ez7aad,,6* e pl7inxxo5i1;. rtbbkeb xecuting 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 compres03ghr rnt2in kn5)p l-s the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the balllnrg20ht3rpi5 n-)k n leave the gun?    m/s

  A mass sitting on a horizontal, fric363iy45 sqrfad b o3rntionless 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 compressed, the mass experiences a maximum acceleration 53 soa3r43dbnyq6ifr of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x = 0.45cos6.4t where x n9qnud4+z q e3is in d 9e+uq43znn qmeters 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 equilibrium is the energy of a SHO haibe65k(k4 j b,kjjr ,zlf KE and half PE? ±k6j, bi 5, (k4zjbrkje    A

  If one vibration hasw,gko*76e d smihyem426vrh. 7.0 times the energy of a second, but their frequencies and masses are the same, what is the ratio vy7e4k oms gi6 ,r6.dh*m2weh of their amplitudes?   

  A 2.00-kg pumpkin oscillaeyg4ex 5.m0gz tes from a vertically hanging light spring once every 0.0gx54 y.zemeg 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 verti +l/h2oncn+ fgcal springs, each with spring stiffness constant k (Fig. 11–49). What will behc/+2lo+ nfng the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.3* vd,b ytkkv+vz :;u /,kz96hf1y zfay8sin6.5t where x is in meters and t is in seconds. Determin/ *zu,zv kvfzbtay+hyd k f61 :;y,v9ke
(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 example3bw5 uyfi -fm.,xd2x93 h3+;ekry9z up itnats of SHM, labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal spring (k =m*/rw1 uoqk2 q 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Detew1*/2omqkq r urmine
(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 p p-1 5-t 0ptvxz.45qfpu bdg q.bloe7N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positivx4qlpt pte -0bzp1 . v ug55-pdf.oq7be 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, wr9l f a9m9se3gith 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 horizon020 zrsmfq8pw9 0n yhttal spring whose spring stif ry 0sz80n2wmfqh9 t0pfness 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..wv 8xwxuva kus/.j. 65.0 kg jumps from a high bridge. After reaching his lowest point, he oscillates up an8j. . ka.ws.vuxw/uvx d 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.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibra1r,,w tdkd bg4tions in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one sm8pt,phw hc*zkicr g 1s50 7v3bl-b*f wing per second? (That is, one complete vibration takes *h*, 8b 1bgr- smz5 ft7v0hi kppcc3lwexactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on hcbpa )9f4ryy0zn6w5 w;c/ c zEarth. What is its period on Mars, where the accelebzf/c6 cyp4wyn a50hwrz 9 ;)cration of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm lonut;8(yad:c6dhz 0a x w a7sq ;u+1ifqbg
(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 masst b8wi-irt6uk8 05 zyzs1o -jg of 365 gram i5s8w-g86zy 0tzj -t1r uokibs, and it is released 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 c.x6 g) ztyouk7lock loses half a minute per day, how should you adjust the lenx. 6t7uzy)go kgth of the pendulum? shortened by    mm.

Derive a formula for the maximum .t9 qvk m+nx2/zjjjmh;dj l5+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 gxzbi lp*9* 5y/qkcz:4 /rsex of 2.5 Hz. At it is released from rest star9xpyi *5bz/xe*g/s q4zkcl:r ting 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 thaxohhkl -559ut*y 2lh*hqx y m)t wave crests pass the bow of his anchored boat every 3.0 s. He measures the distancq k t y-5 59xyh**lxhl)hh2uome between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels wi u.u4;9lf/bsffuz- ) s+cuton th a speed of 343 m/s Hoft/;fl4u+f)nc u .bz-uso9 us w far apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz ab*;i.i n+a z7opum4(u fi )swand 1600 kHz (kilohertz) and travel withmaif4u.n o ui*7)zwi;+sb pa ( 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 longitd:mxgk e,* ofdyu61i8udinal 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 twz2biw qp ;+ 50,xs dqzj)zlhn9ice as dense as the other. In which rod will the speed ofhz;bnzl 5d 9isw2q,z xpq)j0+ longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two suppoctl9ek 0kg1jdnn 89 *a ue7if8w jn9gr* e4s(wrts 28 m apart. If the tension in the cord is 150 N, ho**g8lwn1er7t09ksc nk 9e ngji8 4 djef 9wa(uw long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connecgm 05c-fvwq +pted 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 along the cable. It is observed that it took 16 s for the pulse t0-+gm vp5f wqco 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 (3r4+(avta60e 0 cv dfxgnpyb gxqk 84sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s latea46 q4 ( bvxg(a8gv0kctnxre3fp y0+dr. How deep is the ocean at this point?    m

  P and S waves from an earthquake trph(ul, ou sz4(u /os;iavel at different speeds, and this difference helps in ,posu u;luih s(/o z4(locating 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 /7pkh (io k8mjby a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually includ io(hpkm/8j7k e 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) tpq*a w(;j-mn+kaljz 6he intensities, and (b) the amplitudes, of an earthquake P wave passing through t*a( jkz-6j;wl ap+ nqmhe 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 Earth is measured tbp;zk i*78 xw(2temz do be wt(pe*k8xz di;zm 7b 2$ 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 frequenu9 8y++yl28i 6vzhws nhgkg-ecy travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of the two wav29ueh8khl+8z6vyn-yi+ g wgses?   

  Two waves traveling along a stretched st ;zzr1; fmsr6a /zv,p8np7m ejring have the same frequency, but one transports three times the power of the other. What is the ratio of j6;1; mr8 zenpz/p7r asz ,mvfthe amplitudes of the two waves?   

  A bug on the surface of a pond is2elm-bkk(y1 ds 7p g ;4+inwnk 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 f4g;kl+wnmy-db(n27is p kk e1actor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are movingt bs(a(d -- vpuv-(aqzd1qh- e 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 pu-taqd dpvqab-1hvuz- -(((e s lses 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, .i6qb(i;0rjj* f 6wvnpr8ag +t s8nbp what are the fri.68wj s*f +rv a(t86b jripn;bpqgn 0equencies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz wh+9s y6;,bultbs96d y ewg8 koyen unfingered. At what frequency will it vibrat d99 sb8oy+ 6lygeuwb,sk; 6yte if it is fingered one-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 r xu4iks;y,2xe pe.ra / 5,-f;evjdkcgfd:;xoesonates in four loops at a frequency of 280 Hz. Name at least three other frequencies at which it. f:dex xr,doi2kk;c g y; ex-j;u4saf,pve5/ will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency ieu;:w 7ek+4 0onvzvj+jt1 d bof standing waves is 475 Hz, + 7ze i0ojnu1v+wbtd;ve:kj4 how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 3) )ejjwsc,ajm )b3 n/4:ncofm50 Hz, what is the frequency of the 4 wmjjnc/e3ocman :bs )j))f,fundamental?    Hz

  A guitar string is 90 cm long and has a mum)a jl0; gdsxj qpc0 8ynd:9+ass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequenciesgjd;j lm 0+as 9c8p:y 0)dqunx of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 H cx/*p+4krl b(z-ua8qztr7ic z, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequencies /z tlzb 8kr- i7*4pcq(cuxar+are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string iel5- yg nuf;q9s supposed to vibrate at 200 Hz, but it is measured to vibrat;lfqy9 g n-5eue at 205 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal7+ p8f/mvcd:8bb)an 7 (qjvzz7zex wd string is attached to a small-amplitude mechanical 60-Hz vibrator. The j :bqn zc7( 7m/wdzv8x78davzpb+fe)string’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string*tff 3ye x9ln. may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying3xy9nle .*ftf L between 10 cm and 1.5 m?   

  When you slosh the water back and 0b bxlsusm kw: /l +gaq-5:+ccforth 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-wi::bmcl-0kxl ws/ +us bca+5gqde tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary within the Earth (zbf py *sae6fz- lr(6.l e6bnbetween two kinds of materbrb(6 e-sp.* fz6l6fn ye( azlial. If it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velocity changes fromcc4;w f)iugzsm(d /t- 2.8 m/s to 2.1 m/s If the incident w /(m gcdzi)w cf4-ust;ave 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 ao wu5 .n8m1+h7m y)aq+ agwfrvjx; o,cir. If the soungxm, wo ounj1hw 5 v+m.qacaf7+)ry ;8d wave hits 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 ;uov ns 40u/kewe 9;a5lul3ne -qm x-vspv ,d)wave strikes a boundary between two types of rock at a 38;); nesklsn 9,-4q5pvluxwde ouvum /v30 ae- $^{\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 manua a,7k 9:,+veci h,pjhpjb8fzd l, the dish has to be pointed in the direction of the sabzc, k aie h89pj7f,h+vdp:,jtellite, 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 across th3ve1kkz5vwna+ee 0 3 qe Pacific Ocean. As it approaches Hawaii, people observe an3enz150qv v wk3ae k+e 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 stiffnes/ck h ywi79yh 5fz .abk.u5kt1s constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Usezt f7c.kkhu/. b15 k9 wyi5hay conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m belic znvq2wy1o e5 )/hl/ow, which stretches the net 1.1 m. 52vo 1q/ wznyclieh)/ Assume that the net behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hanging sp4cmlsyo2d ,74a: e;iktrqf/e* w/xqp ring. The mass then falls 33 cm before it stops and begins to rise. What ix*q 4ypr,dsef/i kloa/cmwq;7t4e 2: s the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed oj+ *e8zewq 5bpf 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of the sp*b8e +qwe5zj pring?    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 co1yclo3 * 3eewup of coffee (diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually ito1 c* lw3ey3oe 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 z*4ryiz) d3nl33-rpm phonograph recor3) i*4ndzzyl rd have a wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x= 6i3fel8qinm40.650cos7.40t where x is in meters and t in seconds. Determefliim63n q 84ine
(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 frequ:09y wrp0 iweaency f. What is its frequency if it accelerates at 0.50g (a) upw90r ai:p0ywew ard,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-.1 ; c :t)cb9ozdrzirehc/ r/wr+1je akg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steoceret/1 +9r:dcrw c;ra/h)z z1j. bips off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play at 392-m)sj(h26k ctehsg n)nwa1t* Hz (G) and 440 Hz (A). k* -tsn) h6(hecwjm2 s a)1gtn
(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 o/:qudy1 ;mo cb:n w4 1n;fzzcg:mipr0f Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lig;qy g ndcfizp:c1m: o :zu4rmw 0b1n/;hter 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 es i3n2ppp-y+ v:1s qmthe tip of each prong moves 1.8 mmssp+ :p1i2-qme 3ypnv 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 oscillates with simple harmonic motion of frequenu;9b hw 6m1ddwcy 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. 11–56) will not lose contact with the board during the oscillatih1 d;ubdwm w96on?

A string can have a “free” end if tht :k2 ttmtv,6bat end is attached to a ring that can slide without friction on a vertical pole (Fig. 116vbt :tttmk, 2–57). 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 o.:3ncv thclu +f exactly 2.000 s — each one-way swing takes 1.00vc.ntu:cl3h+ 0 s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertical dru /atg josg3cp5k 0:/irection or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longe tk/rac0gsjgo /3 5:upr, 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 stretche4m1pt ()h+ply 3nmhpu d under a tension of 255 N. A pulse is generated at one e m )hp4(y1umht np+pl3nd, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spf i my6):a)ap;mw o)btring with spring stiffness constant k. A penny of mass m is placed on top of the block. What iomma ap6):y w)f )ib;ts 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 cra6 ow +)554kp/ ljelfq.gdlipcne cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the ca/p.d )4ljpekciwgl f l6 q+5o5ble. 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 thetd+/nk5h rr*ra0ps)x 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 frequhr 0xr+npdras/t) *5 kency 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