Give some examples of everyday vibra8k a5s+g jusr9g(f;fn) oti e2ting objects. Which exhibit SHM, at least appro9 s(sgj; n fk582it+gorae )ufximately?

Is the acceleration of a simple harmonic oly 0s:;y*dvr x2xlz:2jpd r(7c-yy lg scillator ever zero? If so, where?

Explain why the motion of a piston in a7lfja5zy h 28mn automobile engine is approximately simple58jmh 2z y7laf harmonic.

Real springs have mass. Will the true periopdy 3e,;(6y/ti93des f vtqwhd and frequency be larger or smaller thfyvh36 y,t3t;s qe/dw(d 9ipean given by the equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double4xu h.j2sxka+ the maximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to (gg,/k4qjg -i bqhk 8i uik49lthe hook of a vertical spring scale, and then is released. Describe the scale ri4kj8qgb(h gigklui9k,q-4/ eading as a function of time.

If a pendulum clock is accurate at sea level, will it ga d ws2278k-j dc2ckg(5t s:mzpp d(keuin or lose time when taken to high altitu m2ud wc2p(j-8kkss5 z 7cd:ept(kd2gde? Why?

A tire swing hanging from a branch reaches nearly to the groung.ts;ri/te 6oi2 k so2d (Fig. 11–48). How could you estima;6. sei/2tsk io2rgt ote the height of the branch using only a stopwatch?

Why can you make water slo o*pf31kev j-rsh back and forth in a pan only if you shake the pan at a 1vorfj e-3*k pcertain frequency?

Give several everyday h(2c2 tvr9 xzsmlhd ).examples of resonance.

Is a rattle in a car ever73wvyc rvwp b w5 so/8/9in5yr a resonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal9aw ,gd 508c*xfl6mhczw2rh f to the frequency of its source? Why or why hwaglzc25hf w,d9 *rfm6c 80xnot?

Explain the difference 0e q+c0eqs+ ewmph ,p-between the speed of a transverse wave traveling down a cord and the sqe,e0 p0+ph cm+e-wqs peed of a tiny piece of the cord.

Why do the strings usehu q)( o sc8o)6ygh0krd for the lowest-frequency notes on a piano normally have wire wrapped around theo)s( cyq8krh06og uh) m?

What kind of waves do you think will travel down a horizontal4iw vxg+-bmuns +u:f. metal rod if you st.s+:i 4m b-fx ugvnuw+rike its end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in te,pjl89 rruy-w mperature, but the bulk modulus B is ne9pwjr lr,u -y8arly independent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplituay,wg 1*)zklzdwr obr *s).1tok1o 1kde as they travel away from the source. zo .dwwa)t korgsr1ykbo11*,kl z *)1

Two linear waves have the same amplitude and yj. jnn+r6t,h speed, and otherwise are identical, except one has half the wavelength of the ot.jr,+hn 6njty her. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of c4 osp197s qjfoord as in Fi17sj qfop9 so4g. 11–33, the frequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrat )p4ld jr9 4q2m1lyfpjing in three segments, are there any places you could touch it with a knife blade without disturbing the motp q91ml4j2 dj pr)yf4lion?

When a standing wave exists on a string, the vibrations of incident and re l9j)c r-i 4xnkk8arve z(f)z)flected waves cancel at the nodes. Does this mean that energylv if r)nzz9 k4k() a)8cjxr-e was destroyed? Explain.

If we knew that energy was being transmitted from onyi:k ,wvko 5-ge place to another, how might we determine whether the energy was being carried by particles (materi5kovwgi yk: -,al bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the tod j7fr,tw nnb+y4(gs/crn;h9 tal distance it trw rfnyg +4 d;s79jtr(,nb/hncavels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but .h05eppddcx 22kx)( jr wt t0ois 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this elast22j0x5(hx ctw k) otep.d 0dpric cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm whe6nztr16xffu* n its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequ*t1 f6u frznx6ency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches1vb+beo6xtx1+w qk(d,prtoi2 o6,+k x fv/ea 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spik1 ,v(e2q k tf/xvb+1xtb+wde66a poxr,oo+ ring 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 fre62va0g g.qh kxquency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frekg qv06.a 2hgxquency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position wmyfqkgoml:9.) 10ma j(u y ,ax of the mass in Fig. 11–2 at times t = 0,t =.1f m)okal9(aq 0j ,gy mwyu:m $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 u*+bzb3u y j0- be7mewin a spider’s web. The web vibrates predominately with a frequency of 4.0 Hz. 0zj 7me*ub+bue3ybw-
(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 a frequency of 0.88 Hz.oyfk f-o.8:e,i e-rcd When an additional 680-g mass is added to m, the frequency is 0.60 Hz. W:ck8e id,-foofe-r y.hat is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second with an u g d h ed;9w*m5o,zskdwv23j.amplitude2k gszh dj5wd*,v;9 ome3wu. d of 0.13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed of a SHO half theq+1 qypfs; tw8 maximum value q+ fwsp8yq1t;?$\approx$    A

A mass attached to the end of a spring is st+)b/ 7yg wbq:wpcsg:lretched 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 0.3e9wjjl*yymc.o2bksab 1j6xm + i ;96x+hgml *15 m. If the spring is stretched an additional 0.130 m and released, how lomyj9msjb6ly2l ae* i .91b*6 gc+mhwo ;xx kj+ng does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring qafhrkxq8;es73ng) 555o 0wrkklj gt.fnw 9*with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, itwlkk8onx0 hkt rwn9f r )j5e*f.3q;qgg755sa 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 skj hoar 39p9i*gja4t (fa,bqe k n*:o*pring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave the guht jb9a er akfaj49n,q(*g3:*o*okp in?    m/s

  A mass sitting on a horizv i0 (t))5qxazca+oydvso+v)ontal, frictionless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is requ)vty)zq5+v cov id)(a+0x o asired to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to t/)jccbvt 5w ig5 (9*9oyvdodbhe equation x = 0.45cos6.4t where x is in meters and t is in y9oci5 g*( /9odt) jbd5w bvvcseconds. 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 i s4b6wm(8;hzj -dsr +i+))uslbxl auw s the energy of a SHO half KE and half PE?(w+)jlb)4s+z8l; m whaxu6 irb d-su s ±    A

  If one vibration has 7.0 times the energy of a second, b3 2 39rfna9m blypnxj2ut their frequencies and masses are the same, what is the ratio oly32rfn2a 3pmnjb9 9xf their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging+ik4tai w: ;v ag)f*sf light spring once every 0.65 :viwktf a;f +agsi*) 4s.
(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 paral):avo zb9c w6)e32yx i evd1p*c3fp:lxb yn(llel vertical springs, each with spring s2vi:pyy*cabc33ln)wbf( xedp z:v 9) oe6 lx1tiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x a hz*am,a*st w 9ddp+:is in meters and mpaad 9d+ws ,*t:hza* 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 SHM, labeled A and B. For each, w6gax ey.+7 ci g:gjb r5yp13hnhat 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 horij9n yth/2 :1dwh/cjagzontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/y1h9d:j tg/w/a2hj ncs 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 vibraio; 1-xk tl,qjtes with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity ai -tjxq,o;k1 lt
(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 ( q4guwf*-8rt 3st ai97hhn byto two springs, 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 hor5x1 eun 46apluizontal spring whosene51p64uluax spring stiffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high br86iw ve((ytgg1 :iuufidge. After reaching his loweegvwiu:g ((uyft8 6i1st point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
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. W*55ptj) kbail o rjrik6l 8k:)hat is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exact uq8*s6omom i3fs/v 3tly one swing per second? (That is, one complete vuvso 3*tmo3m/ifq68 sibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on M9wds rp*wz 9v7ob -p)nars, where the acceleration of gravit *ozw9-p 9rvw 7bdp)sny is about 0.37 that on Earth?    s

  What is the period of a simple pe9hxh6(e gyb) cndulum 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 pendulum bv fphk6:: 1 yfueiy2k(ob has a mass of 365 gf yiv:(k1 yuph:k62e frams, 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 0.9+r4888bxf( +m gbpqpegq7 smi930 m. If the clock loses half a minute per day, how should you adjust tmqfrg +msbb(i8e7x q +p88p4ghe length of the pendulum? shortened by    mm.

Derive a formula for the mao 0wb/l20nr tizm 69lj8 e0ajtximum 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 frequec/ /*ri2y 2byplq4:sc3 hm d/ dl,twbmncy of 2.5 Hz. At it is released from rest starting at an angle of 15 ilw dyp4hdtmb/2l rbsy *c,:qm/2c 3/$^{\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 boat every 3.drm7y*- ( q1r 6 yxqqnqstxhk/5u+oy )0 s. He measures the distance between two crests to q y5n(qh*t xu+6k/) dqsryq7-o mx1yrbe 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a tgin g4nd /wbc (d-+k8frequency of 262 Hz and travels with a speed of 343 m/s ibt w-d 48k+gdnc(g/nHow far apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilohertx+;q3rai,5yez zs ...s msdetz) and travel with a speed oy3 i.5asztmqse;.ds.,rx+z e f $ 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 flkagtd5yq4k(f-dl8 y 7q v 3)of longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as dense a mwr9jb my.h gh6z8:-0 .k uoz yyuj63bnum2s1s the other. In which rod will the speed of longitudinal waves be greater, and sm bj uhbz8 60m go.nr-9uyw2 yj36:u.h1myzk by what factor?   

  A cord of mass 0.65 kg is strol*02)o weji r/wbd*ketched between two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to trjkwdb)w/r02il*eo * o avel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cabmc.fb6b4voz g yio .8ngh/g8jql + l02le of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its04 gj+ oobml/lggi26 q .bn8c8vh.fzy run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the surface of the sea.ircw kxd:-, k; He hears the echo of the wave reflected from the ocean floor c: rxkkd;, -widirectly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and this o5;ihnx 3z-le6mjjl 4; x,tzndifference helps in locatilm nx;5zlntx63;e o-4jhz i j,ng 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 sinut-c .ya8md7wh mmvg3g.z-;susoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frdghuy8m.-. wm-;gm3cszv ta7equencies), 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 amplitudz vw nc1rbkhbkd jht)6) 3k3, z78xn3ves, of an earthquake P wave passing through td3)hkzn ,3)w c3b 81kxv6 zthn j7krvbhe 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 /q hbhf pwi 1nu1+xm)8is measured to be n) pib+wuqf/xh 1mh 18$ 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 same p blq pn3vk lk+(xut/++ortion of the Earth, but one is carrying twice the enetp b/k3v+x+(+k lln qurgy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched stri2zwu/q 15ng qucdkjzbs 5k:w4 wm2*+tng have the same frequency, but one transports three times the power of the other. What is the ratio of the amplitudes of the two wavebz k 2 4+zm 12knjw/ w:qtw*c5ugud5qss?   

  A bug on the surface of a pond is observed ttoj(b /x iv tb9r3(wb6o move up and down a total vertical distance or tbjx9 bw/vi(t b3o(6f 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig.u ntsax,stw+;xkfld2x;1 q(kgh2,o 4 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 strino+(;t,kfs,n gkxa ut;xwq2lh2 d41 xsg is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental fz (8qgtnv/ f3xrequency, what are the frequencie/gz8xnf v (3qts of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrate w)5w-,sx*gilt.ngk x s at 294 Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of t gkx5 sw*,ixg)wn.-lthe way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resona3 ,ftlvo3 w09q4kyg0b/njuj r tes in four loops at a frequency of 280 Hz. Name at least three other frequg/v4 o33 w 0ftljkb yruqn9,0jencies 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 the frequency of scl/ 3nljwmv5m pxx/( 8-jebd 5tanding waves is 475 Hz, how far x(/n mjv/w 8ll3xecdbm5j p5-apart are two adjacent nodes?   m

  If two successive overto*r 0uyda oh9u;nes of a vibrating string are 280 Hz and 350 Hz, what is the frequency of the fundamenh* ou0yurad;9tal?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance ;prekir9a 317j bqhc+/c. w1jhidd5g b -7brefrom the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtonesibhc.q-1 b+chadjwe/bkei 97;grr15pd j 7r3 ?    Hz

  A particular guitar string is sup1k wxpbf,mbg v:fop5 a-h(/7jposed to vibrate at 200 Hz, 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:7f/vajf-x owb 1bg hmpk5p(, three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it is me0 lxfub; j3kc3asured to vibrate at 205 Hz. By what percent should the tension in the string be changed 3x0cl 3b ju;fkto correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mechan dngmp7tf1 oep ;:-kqf(,.ig cical 60-Hz vibrator. The string’p- mi g;.7ekfog (:ncqpdt1f, 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 may be adjusted by movir7 )z7tk xzj88qt76 ak +yrdzmng the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wavz8 7dma6r)t+rz8jxtkqyk7 7 ze patterns 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 kblsr: -d gape842mj: l4jd8l right frequency, the water alternately d-g sj e8l8p4bjarll2:4kd :mrises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 kmknk ,)*3mj v wqql789doyayr )/s strikes a boundary within the Earth between two kinds of material. If it approaches the boundary at qov 3klq9djr8w)y mn ka)y*,7an 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 velociaa6txh uf 5o;pymt(tk. ,hu 1,ty changes from 2.8 m/s to 2.1 m/s aft ,u o(p5hy,h ;at 61.mtxukIf 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 air. I jg ))8*jn2bwx67bc8hu lm +)eooybm nf the sound wave hits the cold air interface at8uc)mj h7lno6 bobngye8) w) j+2bm*x an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary between two types of rock 27,gq 7ripjcu at a 3cg 72u qjri,7p8 $^{\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’4sehm4 gadk vo 38//his manual, the dish has to be pointed in the direction of the satellite, but an error of aboutg/ 3v4dohhaski8/4m e 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 1e ma*-64lfcbp h rf w2p(yi)cand velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people o*pf-arcm w2ly hc4i(pf)61eb bserve 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 of 550 j 77/lu4tcpg4z kuop g 5ssz-,kN/m Find the maximum compression of th,clp tou z j/ -g54g4u7skzps7e 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 net 18 m below, /1z ilgioq -v0)l im1wwhich stretches the net 1.1 m. Assume that the net behaves lik i ii/w)-1lm1vgqlz0o e 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 sprinj3zc4n-q+easv3g1 jm g. The mass then falls 33 cm before it stops 3 cs-4ae1mjjq +3zgvn and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed u/cn rd;sf o udaf-:40of 22 m/s (Fig. 11–54), compressing the spring 5.0 -o dacs fd/u40n; f:urm. (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) atxkt0+y )v/qbq just the right pace of about 1 stytk+/)x 0bq vqep per second, 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 +b6cscn7 eq n:cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sound emitt qes:c +7ncb6ned?    Hz

  A 2.00-kg mass vibrates according to thi8w(g2x thtg5e equation x=0.650cos7.40t where x is in meters aigtgx52 (t hw8nd t in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum osd38g.)8f : c1b d,enyk xizeebcillates with frequency f. What is its frequency if it accelerates exfgiy1ck8bdbdn )8:3e,e .z at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. Wh.jjf)sr e u+v6en a 75-kg man stands on the raft, it sinks 4.0 cm deeper6eju+j)fsv .r 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 tot:x7 ;k9ivg3jyl;buqs (ko -v play at 392 Hz (G) and 440 Hz (A).9 o(kx7b v3 ugyv ktl:i;;sj-q
(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 dza bl3 i/um8j+own the stretched 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 the waveleb/lm3ij+z 8 aungths 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)envbw2;v6n d a frequency of 264 Hz, and the tip of each prong moves 1.8 mm to eie)dwnvn b6;2 vther 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 qz7z +2vikf g8simple harmonic motion of frequency 1.5 cycles per second. What is the m fzk7iq+zv8g 2aximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end ihd7wz;la8.h x s attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determd7.; xwh hza8line 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 one-way (7ju1: xz8ssfhd ut; sswing takes 1 dh(zujf7usss 1x ;:t8.000 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 ogtch sfn;ya:305twr 6 scillate in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of twg;5h0tr36syn t c:a fhe 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 mas* b,)2zm lxciss 123 g is stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where w)z,s *2cl xmbiill the two pulses first meet?    m

A block of mass M is suspended fc7 6c)ta u,o*vmvc9yerom a ceiling by a spring with spring stiffness constantctcc,v a*) uve 96ymo7 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 on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel cra04-( mft gmx hpl2ikd)ne cable is 22 m long and-k)i2d t40mg( lmp xfh has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which also gibl ,/ g6u:n/rbu9lamqm1 ckb/jym8,zves the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulju ,ka/ umq8b bbc/ lnr,9m/ym z6:gl1us (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz