Give some examples of everyday vibrating objects. Which exhibit SHM, ah xbz*s ga8s/5 2xn)tvt least approximatelbx nzht8gax*s )5vs2/y?

Is the acceleration of a simple harmonic oscillator ever zero? If so, wheresl3 fhtyt4x9f,w .e 6t?

Explain why the motion of a piston in an automobile engine is approximately sia241e (r(nxmjsrlm9 t 6qp a3zmpla1xmt3amr(ez jq9 snr(p 4 l26e harmonic.

Real springs have mass. Will the true period and frequency be larger ozo b 9i49elj1n,r,ylxr smaller than gi1noeizl99r, jl4bx,y ven by the equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of arpxsn9asvg);-l jywq we+x;6t- 6,nc simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hookzwwg7f9g: ;eg3 xslp 9 of a vertical spring scale, and then is releaxf9ezw9plg gg:;s7 w3sed. Describe the scale reading as a function of time.

If a pendulum clock is accurate at s.hvd8 u kauv6ea00jh (ea level, will it gain or lose time when taken to high altitudekahu.u v6v 0dhe( 0ja8? Why?

A tire swing hanging from a branch reaches nearly tl; yh0+gc4y p ,n 6e0opo0)4iiqvzymuo the ground (Fig. 11–48). How could you estimate the height of theh0yipy0v,;g 4 c)mol+n iuyz pe 6q04o branch using only a stopwatch?

Why can you make water slosh back and f+e ho*0wdto /wzqq 5m7orth in a pan only if you shake the pan at at57 h*w z/qw 0ood+emq certain frequency?

Give several everydar nkv 6,df/1ksy examples of resonance.

Is a rattle in a car ever a resonance phenomenon? Explain. 5 ln 1wkxulrgh ooa4z8*u: q*z5fu,p.

Is the frequency of a simple periodic wave equal to the frequency of its sourc-+flswe*st y.g ffg8 q/x-a+ze? Why or why notw-s-a+yq 8f+ggxs./ e f* ftlz?

Explain the difference between the speed of a transverse wave traveling dl og e 4(r+nsqghk dg6x5,2(weown a cord and the speed of a tiny piece ofwoe , g25xq 6h +endg4lgk(sr( the cord.

Why do the strings used for the lowest-frequency notes on arzma6r07/ tf y piano normally have wire wrapped 07zmt6 y f/arraround them?

What kind of waves do you think wi u rl slt5rj))jn1z8gd(7h w:yb0 o/oull travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizont rl sjhto /uo)8lnryg1b(:jz70 wu 5d)ally parallel to its length?

Since the density of air decreases with an increase in temperafeu 76ps)dymsi .n59zsun 9;k ture, but the bulk modulus B is nearly independent of temperature, how would you 9ueu zpny5fd;kssn.m6is )97 expect the speed of sound waves in air to vary with temperature?

Give two reasons why cfljsj6r104 u rircular water waves decrease in amplitude as they travel away from tlj61fs 4jurr0he source.

Two linear waves have the sc6v:h uc gtm -dp3j1z9ame amplitude and speed, and otherwise are identical, except one has half the wavelength of the other. W3 9 u1v g-chczjtpdm:6hich transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary beej5z)t0.b; zpzvyc6oy -8zx ttween two sections of cord as in Fig. 11–33, the frequency does notv6tjz 8)ypzy ;cbx ze5-t0.zo change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any placivrg zhn.h7856 4w ycaes you could touch it with a knife blade without disturbing the motion?8a6.i 4c vwzr7y hgnh5

When a standing wave exists on a string, the vibrations of incident and rojf ,:,vcjaq 1eflected waves cancel at the j,aq1 ,:fjocvnodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to anothh4ffsq 8ee; y68l gfi,er, how might we determine whether the energy was being carried by particles (material bodiese4f8 gf;hqye f6, sl8i) or by waves?

  If a particle undergoes SHM with amplitude 0.18q3*ab v +i)wgw,1dya7x kd kp; m, what is the total distance it travels in)*b3a +;1,pxgiq k7 akwvddwy one period?    m

  An elastic cord is 65 cm long when a weight of 75 N:x hwaer3x9s4+k c 8lp hangs from it but is 85 cm long when a weight of 180 N hangs from e9 x lh wr8a+3scxkp:4it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when ih 39 yp-etzp*q-ma bh-ts 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequency ohp- pbq-t-hzam*39e y f vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (a) Whoy6emn1d;d3vbm ( u k3at is the;u n 3e(63mobkdyv1 md spring 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 vibrate6ewp5r8ep i z2a*yk 3es with a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is ieiza ryw6 p*3pe e52k8ts frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at timesmn; uc .bx.h.(md fldg+1ck*m t = 0,t1lmd(* +d ;xchn.umg.m kb.fc = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 we v/o 45jkj9p37 a-rdouoev xq.b. The web vibrates predominately with a frequency of 4. 3ujooo7/jvqvx59rped ak.-40 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 vib1s (mvw0im+jyi* ayqxt8:s -p rates with a frequency of 0.88 Hz. When an additional 680-g mass is i:q+*s( 0mm a-t y8visypjwx1added 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 vibazhq)g/ a bv fuh-/ tn)e80wx4rates 3.0 times per second with an amplit 48)xvfzetqw/u a/b ) h-0ngahude 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 the maximum vbx2y rxv9 h.og)qfeml8uzn ;(h 52sw- aluhon x5hq rwve(8) ;29f -mglsbxy. uz2e?$\approx$    A

A mass attached to the end of a spring is stretchloz yh;35 b.s-d9d bk r84n vida;rhn*ed 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 3epahze,7+cm the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equili,e3 mh +ezcpa7brium position again?    s

  An object with mass 3.0 kg is attached to 1rqwq /trr 1k9a spring with spring stiffness constant k = 280 N/m and is execu1k9/t rwqqr1 rting simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a toy popgun 0.200 m to z+s6.2hobbbk. l ml w )mb)95xe3v qf:/tvefb“load” a 0.180-kg ball. With what speed w). bevblqvx/3se9b)mbmfok+6tw 5b z:.f2hlill the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one en1yd x1*8r/6lgx(ytl;.m ljtrfg gk 3od 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 releas1 fg gylkxjo;*mdt(3g /xl 6. 18tyrrled 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 the equation x duc3fsa(2 ohd+* lk*j = 0.45cos6.4t where x is in meters and t is in seconds. Determine kjco2 d+*h* dl sf3(ua
(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 fy f4 hb35ct2lvf (om2rrom equilibrium is the energy of a SHO half KE and half PElc5bo(f hfv4 t3y2 rm2? ±    A

  If one vibration has 7.0 times the energy of a second, but 9(v -bk zqf-vtl; +1 lhrvdwl2their frequencies and masses 1lzq vf-llh;9r+kt-vw(b 2vd are the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates fath -z 7(gz/oj)pte9xc6 74nv,b gtbxrom a vertically hanging light spring once every 0.65 s.(h9 xzge76xtna /t)- 4c7 ovjbgb,tpz
(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 identicy p9v42lyh9rdk 1 ky9ual parallel vertical springs, each with spring stiffn9r uk9yk1hv4 d2 9yypless 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 i2l+o;j 3 suz5x 3fxjrzs in meters f5xjz3j2os+3x ;zl ru and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and B. For each, what ,m47tkqq5tne 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 sn v09 a (4 ds0*co.jspfm2lqn(k = 124 N/m) is struck by a hammer, which gives the mass an4 *.n9s2dol0qs (sjp a0cfvm n 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 constak7 +x e8jsu 2fwn1id9znt 305 N/m vibrates with an amplitude of 28.0 cm whenkzf s1uw72id j89n+xe 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected8lr c0k4qpr-x1y9f zrzca0 x5 to 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 attxv oom42i6eep nu 0+qhh6j-s 7ached to a fixed horizontal spring whose spring stiffjsxqi -hpu 6v 0e+oeom4nh27 6ness 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 1 sux9m i fuq0lfepg8(/ ey:a8a high bridge. After reaching his lowest point, he osci (ufe/m1la8 9:y8iqg 0fxusep llates 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 rv s c 8x0ra8o)r1w8*j9 uswjgin exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be ifze qn lp) e(saco;5lwp;38*p+pc+zb s it is to make exactly one swing per second? (That is, one complete vibration takes b8pos3;a +s pwl*e+nzle(z p 5cp);qcexactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, wherefmsu6mzo *x 6; the accelerauz;6xm6 f*o smtion of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pe1rwi5 pxo eflv()4- zxndulum 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 pendu/*l8fuz()adw f5vpxz0q i: o ulum bob has a mass of 365 grams, and it is released at ad5pz*fao/lfviu x wz0q( u:)8n angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 m. If the clock l +903doisbvb afxi m ll4d x0ji585g2coses half a minute per day, how shou5v 0gx 3lmxiibd d 0cbjo+48sl2f a5i9ld you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum spwt,bw4:dth8 qbbf1 *d eed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At it is ; im2dd9zlt9;ec1qmc released from rest s ;qelidccd2;t19zmm9 tarting at an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchzp t3r. rwt1 q2ree,/uored boat every 3.0 s. He measur/rq retpte .3ur,z1w 2es the distance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency ok9m ru-u2 ez f4f;an+lf 262 Hz and travels with a speed of 343 m/s How far apart are the wave cres4 m2fzunkue9+ral ;f-ts (compressions)?    m

  (a) AM radio signals have frequencies between /1r2w d;y sbgjd2 am0k550 kHz and 1600 kHz (kilohertz) and trgr ay;/d20b 2dsmjw1kavel with 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 longitudinalbd9y u.l:p2ha waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elasticxg dev)3c,(t dl5 vli+ modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be great gd3t+5vllcvx)( ,deier, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If the tenktlvxvf9u. x3x ph+ 9hffq2,*sion in the cord is 150 N, how l k*+u.vqx3 9,fx hf2vt 9xflphong will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top 5uaw 4s 8*ibap5e*pydyk 7.zxrqba(- pm01asof a hill by a steel cable of length 620 m and diamete4p5* p * adxy1auqma-bpaer k y0(75 biswz8.sr 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(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 -pf7zc pfl) 7oo* gp2f 3zfc+jside of his ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this point? 72cfczffoj7-f pp3+ pz *o)gl    m

  P and S waves from an earthquake tapr17* o wh.+sta ;tnaravel at different speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbance took t*1r .a saha tpwno+;7place).
(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 sinusoub 8c-/q/s+wzclvy q6idal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquaksbq/ u /qwv8lz6+c-cyes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensitievcq/ yf aj-;o r537h7o hzx4gss, and (b) the amplitudes, of an earthquake P wave passing through the j-s7 fgzc73a;y 5 vhrhooq/ 4xEarth 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 ixa6 yquk0:a6 (t - w8dyuz.surs measured to be :w xu6.zut (0yr-86su qdaay k$ 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 t ,/yjfg h0a5ye54i reary-nl+ravel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of the twagi ferhy4yj/0-n,e l5+a yr5o waves?   

  Two waves traveling along a stretched string have the 9p6fi4 wzf(mk same frequency, but one transports three times the power of the other. What is the ratio of the amplitudes of the two ifmw(k46fzp9 waves?   

  A bug on the surface of a pond is observed to move u*4n,bm1 (0viutgkv1v5tzo yvp and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wavzt 1o0ungyt v45,(v vvbm1 *kie passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 arjlv wab .,)0vfi ;1rall9b 2o9pb .mzke moving toward each other. (a) Sketch the shape of the string at the mo9 a ombr9pj0.1,fl.k b vwv;zbll)ia2ment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as i /7+h atzyaaegz71xs0ts fundamental frequency, what are the frequencies of the first four harmonic710atzs7zheaax+/y g s?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz 0yk:/oa phvc sg:i g 5rjcf(70when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (Thag 7ysv:jf/r (0c0k5h ag: opcit is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequenx:fszw/ 4qi pryje7,8 cy of 280 Hz. Name at least three other frequencies fx,: spw8jyi/zr4qe7 at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a stringqk/lp 5tuz+ 1n is 92m/s If the frequency of standing waves is 475 Hz, how far aparnl1 +qk/utz p5t are two adjacent nodes?   m

  If two successive overtones of (y k4 2jh8kb7w2ej5nmecg(wsa vibrating string are 280 Hz and 350 Hz, what is the fr 28ges(5ykjj nk2w4cebw(7mhequency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass v p2bvkeo5 qzw--o 6f)wk2.l mof 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 l zowf)v6w -m po2kb5k-.eqv2are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz,5vg/zfqm desixh 7v4xg.**j; 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 frequencx4gvdeh5v g*q sf;m7/ xi*z.jies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate a2 lv8i-,f *jj3ho6f f*dvyagu t 200 Hz, but it is measured to vibrate at 205 Hz. By wu8y* fj, fg*vlohf2a dvj36i- hat percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mechanical r(b.zx 5 -6nbfkdn7 uz iw9hf060-Hz vibrator. The string’s mass pe0z bd( ix nr7fz6 9.hwkn5fbu-r 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 adjustedyi xrg2l7zxj 07pyx.c3s053t +wwyld by moving the pulley. If the hanging mass m is fixed at 0.080 kg, howjdw770zlyr xsg 2x yp c0ty35i.l wx3+ many different standing wave 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 right fr-y40uud6 lnb-:bd s xmequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produud0:by6 lnd4- xbsu-mce 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 km/s strikes a boundary wih qi4 iw.uey,1 sk hsd8m/3(pjthin the Earth between two kinds of material. If it approaches the boundary at an incidepu e4j38sh/ iw(siqd,.h myk1nt 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 froa3xqj m dkxx0 zig+ tb4 kpda8)u2s,+)m 2.8 m/s to 2.1 m/s If the incident wave crests maketi )x q dkx4)m,xup2 kdz +j83a0gab+s 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 layer7wv3wrrh5e99 rwlc 9k of cold, dense air. If the sound wave hits the cold air in9r 9wck3h7w wlrr59e vterface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary between qpfay5w 5.r (vzww5r5x3qbp4 two types of rock at a 38 ypaqp3 rfwv5bw5qwz(x55.4 r$^{\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 userz33r;vl bmv)s ’s manual, the dish has to be pointed in thev sl3)z;bv3mr direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750m-2e(yr;z*x xlwge z-u q r7hi;;ak ;w km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died durin(ruwq-x;ki*g z haee72 w;xlrm;y;- zg 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 ofjpf (b,7)i:5 vipqrb 0t8lmdv 550 kN/m Find the maximum compres0 b5tj ) (7 ildqpmfv:8ip,rvbsion 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 net 18 m below, which stretches qj z1+-*in jibehkc1jd2eoo q(89q ;ethe net 1.1 m. Assume that the net behaves like a simple spring, nd 9( 1ejz;eb+kjiqcqooj82 h1-e* qiand
(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 o 8uwzohf6ccyrk: a ;*g+,ov-mass then falls 33 cm before it stozy;kc:ghu*o- o6o +f c,avwr8 ps and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a hugg30n +t4z1a jh2xmzf35mfwrzhi 3r3 pe spring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What itff31r imja+5x3r 20pg3h hm 3zn4 zzws 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 82y)jy *wequ61awigat t 96 hk9 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fii 6hwautqkt e) 9*2a9ygyj16wg. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8/ c g3tai -6gbfpu+*el cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. Whte/-p bc3 lg+f*aiu6 gat will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the eqgqy 2q.u;.il ouation x=0.650cos7.40t where x is in meters and og2 ;..qiuqyl 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 osciln9gnw2,zh2)b w0pgu )vhp 1 aylates with frequency f. What is its frequency if it accelbpgh)zna) 212ug0vpn ,9 whwyerates at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a mm6sxg,5erkp; lf,m n.(ea 8alake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibamrs(,mlm ; aef5pk,6en gx .8rates 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 tuneat+.j;1 9)n5lpqmb i ywpij8wd to play at 392 Hz (G) and 440 Hz (A).. m1w95 +wlai jnybipqj 8tp;)
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stretched two-part cord of Fig. 11–5jmczet pook1lcri4;6g f 13j/ii6q433. 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 wavelengths in the two sections. (The frequencm/t1 pz34ei c i6lq r61o;kcjo5f4gijy is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of each prongxh p5*iz 5wfbqgk68 ;o moves 1.8 mm to either side opx*zq5h5g ibk w ;f6o8f 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 ha6 tod+w,ai ;zutah7p)rmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) ) zoua+;adt ih w7t,p6will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a ring that can slide fc/ezay ( hy02jhg (0lfq9w6fwithout friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonantfhy2a9 ylewz(f0 qjc6(f 0hg / 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 swing takes d1at j3z 3mbt01.000 s. dmbj3 0t 31atz
(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 dir/w q20dup(jyyection or can swing as a pendulum of sm2ydu wy0/pq(j all amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

  A block with mass $M=5.0\mathrm{kg}$ rests on a frictionless table and is attached by a horizontal spring $\begin{pmatrix}k=130\mathrm{N/m}\end{pmatrix}$ to a wall. A second block, of mass $m=1.25\mathrm{kg}$ rests on top of M. The coefficient of static friction between the two blocks is 0.30. What is the maximum possible amplitude of oscillation such that m will not slip off M?    m

  A 10.0-m-long wire of mass 123 g is stretched under a tension of 255 Nlniw.7yzt2 a4:w5qlkjsc 40l efe 7q96ko*tz. A pulse is generated at one end, and 2.k y5q 7fw lcstai2te4o ew0n76zl*jlkz q9:40.0 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 spring with spri87mrsf mkd7:jng stiffness constant k. A penny of mass m is placed on top of the block. What imds 7k:7jmrf8s 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 crb(t lp6p omytf1ec0 6:ane cable is 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 period of the bouncing? 06efpm(botp 1lc:6 yt [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which also gives the 6e3 b56va9me xtj* 5u ggpbv*pdimensions 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 sprinxb g5 bg 6 eu3ev6v*pamt9j*5pg, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz