Give some examples of everyday vibrat3r kzw41hspxr 0cx j6+ing objects. Which exhibit SHM, at least approximwx6r4zkch13 +0pxrjs ately?

Is the acceleration of a simple harmonic oscillator ever4+;zep xp x.wu zero? If so, where?

Explain why the motion of a piston in an automobile engine is approximately sim t 2ejo2zvq:wi bsvs 44k;8 mzd+e ;.gtro)st*ptt28 4dov*eiers t42v:s)z;w k bj;qzgms+ .ole harmonic.

Real springs have mass. Will the true period and freq (,/s*l l- kaudjd,x ka9gr1tguency be larger or smaller than given by the equations for a mass oscillating oast*k l,kx(ug 9gdj1dra /,-l n the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple has3 t/haoz*w t5o2 pplaan b:vdt)/z--rmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical sprg:qx ub - +dreg;j/u.fing scale, and then is released. Describe the scale reading as a functirgbjdu-x.; f:/ +q uegon of time.

If a pendulum clock is accurate at sea level, will it gai/ixdbz +6+.+nn hat wwn or lose time when taken to high altitude? Why?t hw nb++/ix+.w6 dnza

A tire swing hanging from a branch r*r3to(;so9 /ezc if dmeaches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch using only a stopwatch?om 9t(d/fso3z e*irc;

Why can you make water slosh back and brlegp8om(s 331e ym3forth in a pan only if you shake the pan at a certain freqm y 1eom3(3 pbselg3r8uency?

Give several everyday exampc.pt+pk5u c+u les of resonance.

Is a rattle in a car ever a resonance p p;aqm3n+(iyahenomenon? Explain.

Is the frequency of a simplercji i 1 l1itcb7c;n1: periodic wave equal to the frequency of its source? Why or why not?c1ii blr1cc:n7j1 i;t

Explain the difference between the speed of a transverse wsu *l5c/kpf(jave traveling down a cord and the speed of a tiny 5f p*cujk/sl( piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano normally have t-p 1 ;wzlez:uwire wrap:t1wlez p u-;zped around them?

What kind of waves do you think will travel down a hoqqbxt9 p 8 *axpvpzm.s /9z:g4rizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parqp m9:4.gs*x9 qb8vtazp pzx/allel to its length?

Since the density of air decreases with an increase in temperature, but the bulk8ocy,ns;g b:jojuv7 n2 x1h.d d n j.h nbj:;82y1 cguox,sv7omodulus B is nearly 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 amplitude as they tda8q9x cb:cde yp36p3 ravel abqd aypxce83 d 63:cp9way from the source.

Two linear waves have the same ampliteho4; 8urx;7wwy*i8l rtaf3 jude and speed, and otherwise are identical, except one has half the h8etwroj r; 7x*4wa fu; y3l8iwavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of jt6lwnt7x 5w(pt di78 cord as in Fig. 11–33, the frequency does no w85(jtlwt76d pxint7 t change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are 0 x*(u*gir1ij am er;hthere any places you could touch it with a knife blade without disturbing the motion? i;m10xaijuh r*gr* (e

When a standing wave exists on a string, the vibrations of incident and reflectrzffu,v; c0h6xrhsk587l;h jed waves cancel at the nodes. Does this mean ;v 5kljx rfcfr6 ,hz87hush;0that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to another, h3 hw6wx-zx*iq :v k- lf*wy*ziow might we determine whether the energy was being c*vx kqz- wf**h:l 6i 3yx-iwwzarried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total 6 5ljy;+n -zf:ui p7ajxdc-jpdistance it travels in one pez:j + dip6x5;7f-luan -jcjpy riod?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs fr j hx,p0yp*ld+r wq0cdl, ijab1l::i;auau*1om it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of :yj +plp1rl,h:u*c q1,ubi*ax0d ; laja 0id wthis elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm 9pcz ,b f)+nurf3nl i2t8wpv; when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequency of nlubr3p9;2t8c)fv zwfn,p+ ivibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-d(v; r n:e(s56sqc3vmfd a+jpkg fish hangs from it. (a) What is the sprinsm;5qcv(+6nda3f d(ve rsj p: g stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a m74 heilw 1 fx/v2lxpt9ass of 0.60 kg is hung from it. What is it2lxlfewx /h 1i 7t9pv4s frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x o 5*zvz;gblsb(xv5n y 7f the mass in Fig. 11–2 at times t = * ;5g x5(nzv7bblvsyz 0,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web. Th-sp)p4gz+s+v vq, m1vb 3 gcjae web vibrates predominately with a freqzggqjc- 14a,pv)psb3+mv +sv uency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a 2s c)k uk-n8uo7c l)fbspring vibrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the value)ou )fc2 - 8skkbcunl7 of m?    kg

  A 0.60-kg mass at the end of a:+ h qc2cao ,5**hzche + z,gdympa-kn spring vibrates 3.0 times per second with an amplitude of 0.13 m. Determinh 5*an+he*, mk+ ypo haqcz2z:,-cgdce
(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 v3-ey/z 9. udl (tppzbm1k6yiaalpz 9k 1lt6e.(apb/uym di3 -zyue?$\approx$    A

A mass attached to the end of a spring is stretched a distanc2b pu)xqu q2a2/ 4levue $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. If the spring is stre apj1 y* a.rll+;lqg0ztched an additional 0.130 m and released, how long does it take to reach the (nr;.+l1 pgzlaa*j0qyl ew) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffness ,xmj1pr u) zumav/2 x4b3sm.pconstant k = 280 N/m and ixbmz/ m2vu.amrp)j34 1p,suxs executing 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 comkp3pj:1 w hx/,;jwhfopress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will theopwk wp: hj/h;,f3 x1j ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface irrsob82k+qj p (g *cq,s 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 expkq+ qp8gs bjo,r(cr2*eriences 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 = 0.45cola8 n7ibhgpne7 ;g2:j s6.4t where x is in 78jplng;gn2ebha: i 7meters 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 equilibruk6z*wf2tgv a8, l.; rkys 2a,pved:z ium is the energy of a SHO half KE and half PE?z,2*zk;d6wtfurap.elvs8:,k g2ya v ±    A

  If one vibration has 7.0 times the energy of a second, but their frel) r7: ldz2aodquencies and masses are the same, what is the ratio of their 27od:r zll)d aamplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanginn-m:lkqql v13g5d t 5qg light spring once every 0.6t:ngll q351 qv5mq-d k5 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 s(zs c5,22pkwqibc bk+ 6htdi9mm 8x/pupported by two identical parallel vertical springs, each with icmh(k 2q ,m5 b 8w+bs/izcdx92 6pkptspring stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates d;i-))*r 0nphv jpw+4h02ps yzs dtko according to the equation x = 0.38sin6.5t where x is in meters and t is i0 r z yphi*sv ppn2;dw-ok0htj4 ))+dsn 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 exam p -)mnci,iz9.vor ;8iw 7mppgples 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 theix0 d88zqwf :ztq f:4q end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial4tqz zfiqd :x8:0f 8wq 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 stiffnessk*qwcrn0u9gc)7d /gdy: p b6y constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass p d g7c9)bn0qdy:p6gyr wc *u/kasses through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring stiffness const nwd6 y55une*xzfd /v1ants $k_1$ 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 ho7n -/fb2 s,lboqfif+m3 u0q tvrizontal spring whose spring stiffness constant u,0l-i tbvf 3o+fbsf7q q2mn/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 bridgecinhs8jpql7.y8 5uwus j 1.6 v. After reaching his lowest 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 th7jpwn 5hcji. .8v6uy1qu l 8sse 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 ,f 6wo 4/ msxiwtz*xi860 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it ise3x0. hww)lgxslg*4e)i (zq p to make exactly one swing per second? (That is,zlh)wwlei*.(x4xqg gs 0 p e)3 one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth.q czp 9:1 ep:g6xeak0s What is its period on Mars, where the acceleration of gravity i: x ag6z1ekc:es p9qp0s about 0.37 that on Earth?    s

  What is the period of a simple pk)*l;jm ldh(f endulum 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 bob has a mass of xw(0j 2u yr4ad365 grams, and it isy2dwua xj4 0r( 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 pendulu1ujftwa.o icfg9dy0ec 0*/b -m has a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the lengthy 9-ec1dfo/0. 0jcgbt f*iwua of the pendulum? shortened by    mm.

Derive a formula for the maxv0z f,dwltr k1fcl 0y k4r(c,6imum speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. Atdozf 8g 27z;ym it is released from rezy2mo d ;zg78fst starting 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 anchored boat eve fr3xhbkh57izwveyupj3w8 473i7i z0ry 3.0 s. He measures the distance between two crests t4w3pzhr05b 3jkiwex7i7ziuv y 83 h7f o be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and tra t (oeg :m qp;io3uk;pin*7s6uvels with a speed of 343 m/s How far apart are the wave crests (compressi*3pu7eqmk(o sn;;i t:uog6 pi ons)?    m

  (a) AM radio signals have frequencies between 550 kHzzq+gtjmrbrl c/tn ):/z+90cn and 1600 kHz (kilohertz) and travel wrzgl+ jn 0mr/9 ct+:tzqcbn)/ith 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 longit. rj*ddbc4j5ey eo9p3dntj3w5dp n.;udinal 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 densea96y(l:.egoipo:n fl as the other. In which rod will the speed of longitui:g69yn oapf. ol(:eldinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched*5.zi6jr/a v bdxo ha/ between two supports 28 m apart. If the tension in the cord is 150 N.brajv*/d /hai z5ox6, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of lengtmp vi77n u yd/b8;(jmth 620 m and diadtjb /p;u7nimm8 y v(7meter 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 side of his ship j l:pgre 7ma7c-o ga /jop5c(n6ust below the surface of the sea. He hears the echo of the wave reflected from the ocean floor l g5 e(:oap6a cj m7oc/g-rnp7directly 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 th6/zoj85; remau9 yh*cq zf)ph is difference helps in locating the earthquake “epicenter” (where the disturbance took plac6h5fh*paojcyz/u 98q rze) m;e).
(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 surfaflf, gs+ 9isp+5a px5ace wave can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (is g5ax9f+5saf+p ,pltypical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensitieb y :kwhy vtj6p:(xn494rwz )ls, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km p x4z wytn kh lrw96:(yb)4v:jand 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing teipsl6; 0opf o4c;q+x u1/h dwhrough the Earth is measured to be sxplui/wqd;4; 6ceh1 f+ o0op$ 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 portion of eftwf4nwyr,b7aca-6 u9m. -o the Earth, but one iow-cfa96 7am.-f nry ew,tbu 4s carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same freqfa,q7;90.rujk1qm cwe -a jnu6 zj3ecuency, but one transport1cwzu9jme qk f 7,reau0.jn;6-3ajcqs three times the power of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down a total ver(fq nl0kyie:0v /z /cbtical dist( k:febc0q/iy/ 0n lzvance 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 factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving f/l7/k xk4/weh.jnvztoward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the k f k/vjxn/h7z4.ewl/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 vidv: :xm3 j-g uhbij.c0brates at 440 Hz as its fundamental frequency, what are the frequencies of the fd3 - vjjg:humibx c:0.irst four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at g ztxs*-(be;d 294 Hz when unfingered. At what frequency will it vibrate if it is finx -d;t *bzes(ggered 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 resonates in four loops at a frequency of 280 Hz. Na zt y,vqm , .uueq5wdz,y)1nse3+b)pgme at least three other frequenciyn5bwzevm d,z1.,pq+)3 y),uusq gte es 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 standing7u,pq*:z qpv/ 1coqsz waves is 1,zq: uo7pcq*/q vzs p475 Hz, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz ana 2v,r5 2v9yy*.cczi4 rhd ruhd 350 Hz, what is the frequency 4a,uz*.rhvd cyrc2i9y r 2 h5vof the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. Tjt7uu,t4y.4r mm8p)kro+;sbd sle v8he distance from the bridge to the support post is L = 62cm and the string is under a tension of 520j4eru)yt+4l8k ;usmv sm p b.7 8rt,do N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string smhye7 rt v/t:,iwow/+z6 ze9 gd(zy-is supposed 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 cgtv :hzem69y i/w r (t 7y/o+dwsz-ez,orrect the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it is measurv*mewvm 6/n j i1 9jdt9fzj2d-ed to vibrate at 205 Hz. By what percent should the tension in the s 9v2w md jj*i/mj9nfv6te1dz-tring be changed to correct the frequency? decreased by    %

  One end of a horizontalftt7,3 t qrur x coo/,slj sj3d(b3*f* string is attached to a small-amplitude mechanical 60-Hz vibr3*3 s3qltbrf(t r*,sc x/ 7,ftojdjouator. The 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 may be adjusted by moving the pulley.yp 6n)olaftf/ )1 i 5(qsudus6cb3v k6 If the hanging mass3u vaf q( kpb so1)ysl66/fc)unid6 t5 m is fixed at 0.080 kg, how 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 righk 2kdm8n7ll 1oeo- 4oht frequency, the water alternately rises and falls at each end, remaining relatively c7ld2n4 h1-em8olook kalm 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 km/s ,s9xh+lgld)a ig60 dn m(v+zhstrikes a boundary within the Earth between two kinds of material. Ifd,z )vl(sg0dhg+nmix +hl9 a6 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 underwatereoz.e.i4y 18 f6+r3h)dh jx bk9(p7y pm nikor “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests make az4(f+ emh9kyo .6pri)jeio .b1xd hy3n 87prk 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is travels0d;io+h+5 xiw f*pay ing in warm air when it hits a layer of cold, dense air. If the sound wave hits psixfhdo*w5a;0y+ +ithe 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 wave strikes a boundqmb 7n m6fbfq9yfm-. +0.l ovaary between two types of rock at aqm9 7 nvabf-+6obyl0q m.mf.f 38 $^{\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. Acco ng g(c jn5npd/1xrfw99;w uxc30vwb 5rding to the user’s manual, the dish has to be pointed in the direction of the satellite, but an error of ab vx1g9 3p ucd5cw05jr;9 bng/ nn(wwxfout 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 acrqp p . gwq06q8sub+q3joss 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 during tsunamis, some of them attracted to the shore to see.q qppq3g60bj+ w s8qu stranded fishes and boats.)    min

  An energy-absorbing cax*(xra/ 8q.(no wg19qqt g7 eodle3k mr bumper has a spring stiffness constant of 550 kN/m Find the* do/goqalwnr(e.98 1qqx 3 xgme7kt( maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below,wz ltz*2iew7 + which stretches the net 1.1 t2w7w+z *e lizm. 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 spring. The maspjnt xm)(/h7 js then falls 33 cm before it stops and begins to rise.)t7x(hmn j/ pj What is the frequency of the oscillation?    Hz

  A 950-kg car strikes 6dw k0xx/5ubg a huge spring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring 5 uxx6d kbg/0wstiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just thp7- 2km2olmwn;u eou; e right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the spw; me;l onu2m 7uo-2kpeed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a s/kv:tt9e*emzuy.*j pg:ny ii* jh;033-rpm phonograph record have a wavelength of 1.70 mm. What will b*k m:nj et0jzepht9:giv y .y*us*;/ie the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the-xvqu1 djrn+)w :f 2bl equation x=0.650cos7.40t where x is in met) -jxl21wq+fb: undvr ers and 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 oscilla 0;rjx:yd0yk4/q wq vates with frequency f. What is its frequency if it accelerates at 0.50g ( ;awqdy yr4:/0xj 0vqka) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a eg (qyh9u c l 3/(invjeg3ab2,(ibd5s75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for a wij(e 2eg3 l /9 qi ((nsyag,db35vhcbuhile.
(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 musxfkw+a3d oy53ical instrument are tuned to play at 392 Hz (G) and 440 Hz (A).+ dw3 ax3yk5of
(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. 11–33. D m:i fgi7q -mml .:1yhibd*i(cetermine 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 frequency is the same in both sections. Why?) (c) Is the waveleng fc:-i1d(lhm7 bi myim.gi:* qth greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 vyk w:yj c 61/dv8s bjwt0+i*cHz, and the tip of each prong moves 1.8 mm to either c+w6 v 1wsvjyt y0b *k:8/dicjside 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 oscilla 0jxt(oea+adg( -qx)c7c3qwytes with simple harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed they7-( d0oe 3+jwgct(qcaxx a) qre (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that endc2vzh*g eqb2e6*l h ex8.al 8l is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the reso ve l2.h*68e2lxzlh aq*8gcebnant 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-wamyu 8q;elvk9ag (in 7 y9w((soy swing takes me8( 9v(y;(lsa ni7 yqo9g uwk1.000 s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertical g -p.rmpww*unn8 t (p5direction or can swing as a pendulum of small amplip85.ntpw -*( wrpnm gutude, 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 stretchexxuv re*bomeq)v:a:; uy g ,h ug9*du8f6j-8n d under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is geuu bu,8y-fv:ed*qh86o :na)m g;uxrx9v *g ejnerated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by ne*x- (zzbw.e(yw )gza spring with spring stiffness constant k. A zbz.n(-w eze)* (wy gxpenny 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 junkyard80ccc 4z8- ia no8g.uel-ie t ;.lbdxm. The steel crane 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? -8 loec-edtl;ni0g.cax8 . 8imzu c4b[Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Foub s8v2z1cy /vd q+8tig. 11–58 (which also gives the dimensions of the block). You push it sidv8uo8 +tzcsvdqy1 /2beways 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 modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz