Give some examples of everyday vibrating objects. Which exhibit SHM, c+ o x*xnj(v(vwvz f3-at least appr+- vxnvzvo x(w(cf3*joximately?

Is the acceleration of a simple harmonic osci a +z8y 8zq )kib2lzq)6c) cue.ygtgy(llator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is ap +od pd0(fc9e+eossp: proximately simple hars+e e:o o9+dfc psdp(0monic.

Real springs have mass.lhp8l1n )2h u lz-m4oi Will the true period and frequency be larger or smaller than given by the equations for a mass oscillatil4lh 1zinm8-p ho )l2ung on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oqs+gzx):jup*t l i0g9scillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and t4a8rfk4xrp l; m wp22mhen is r2wka rl;xmm4p4r 8f2peleased. Describe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gai)lhj mnm l7h85n or lose time when taken to hig8hm lj)n l57hmh altitude? Why?

A tire swing hanging froesm 1z;*vu hx:xi+g+ ym a branch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch using only a stopwatcsg:x zeiu;*h+mx+ y1 vh?

Why can you make water slosh back-kqzg 1x4aa8:qzz3qf and forth in a pan only if you shake the pan at a certain frequency?3kq1zz: aaxgf- qqz8 4

Give several everyday:kue+y 6nea, f:tvaz np;/2dt examples of resonance.

Is a rattle in a car ever a resonance phenohfl dz4d7g3 k(menon? Explain.

Is the frequency of a simple periodic wave equal to the frequenc42 y,0:gvwtohu ii vw,y of its source? Why2g4yo :u,hiw w,vitv 0 or why not?

Explain the difference between the speed of a transverse wave traveling dowxpksd.hl+ c:uy :adu:lb l1-e)k 2o7vn a cord and the speed ad -xhp.7:kyl :l2+:o beu1)vkslu cdof a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano normally have mav)u *1ikyy8u3 1zjywire wrapped around themv1 )i83yuu*amzyy kj1?

What kind of waves do you think will travel down a htrq bp ,+r;js wq+ma:3orizontal metal rod if you strike its end (a) vqq;jba ,ptm+rw:sr3+ ertically from above and (b) horizontally parallel to its length?

Since the density of air ;)(s tcz65ecaq 3bzhr decreases with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in acsa )6cez5z3q(r ;bh tir to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as theu: . ,u4ycjc 6c+czh5sx uh*lxy travel away from the source.* u . ,ju4lx6su+yh:cxzc5cch

Two linear waves have the same amplitude and speed, and oth 8 /ws,/p/ 8dczhln:ozsrpa6z erwise are identical, except one has half the wavelength of the other. Which transmits m 8c/a/ howpspn8/,:zdz l6rzs ore energy? By what factor?

When a sinusoidal wave cr. whjc: 5/6cvocsh1cf osses the boundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do chan. s1hfjc /c6co:vh w5cge). Explain why.

If a string is vibrating in thr avsg r*9dl2y n yrrci:wt-:;+ee segments, are there any places you could touch it with a knife yri; y+wlcvt 2a:rgd*s:-rn9blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incident and 3 5s ait9-/xgy4nfblfreflected waves cancel at the nodes. Does this mean that ener3lfnax4 -igb9f5 ts /ygy was destroyed? Explain.

If we knew that energy was being transmitted from one place to anots 16i2i+; nodow8hlh kher, how might we determine whether the energy was being carried by particles (d86hs o1wi2i hon;lk +material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what idabme*1x o;+wei (lkf;ijg q0;6 ku-is the total distance it travels in one pgl kj 1amwik0o 6e+(fxedii; *q;b-;ueriod?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it bul5uyy 1 d-d (81dbgosst is 85 cm long when a weight of 180 N hangs fro5dg d(- uo1ls8b1dyysm it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5 hwludt.)1hp6xrqq ten+40 u) .0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what wil lh 4pued+trw h 6).x1uqtqn0)l be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6*unm- 5ezyhj l8*w3mh cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffness -y el8 n*m3zhmjh*w 5uconstant $\approx$    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 frey(d p/.qmwten++b(z c quency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangq/ c tw+b(pmy+ezd.(ns from it?    Hz

Construct a Table indicating the position x of the mass 4 wn5,lmz3 tuncegh,/ in Fig. 11–2 at times t = c/z35g ,et m 4nuhlw,n0,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*cksamg4c -l; is caught in a spider’s web. The web vibrates predominately ws c;gaml* ck-4ith a frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frp2b- a.fyr5 gyequency of 0.88 Hz. When an additional 680-g mass is added to m, the freque5.y2rpfy- ba gncy is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second withyy.4bnu+ cza- an amplitude of 0.13y yabn+z-cu .4 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 equilcnk 4pj,cu 8xcii 8;q7ibrium is the speed of a SHO half the maximum valujp4;cikxci8 7 u8n,q ce?$\approx$    A

A mass attached to the*n * ;.4yz4tmmo 0v9vtmhb oco end of a spring is stretched 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 spriniehktl8j(dtp(/nw7 *g 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new*d ph(7ttw8keji/(n l) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a sye 3sfehe;xud:02d;yn:o;w q pring with spring stiffness constant k = 280 N/m and ih:2 ;;fs weeuno e:0;y 3ydqdxs 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 compress the sp;g zm inu3u4y 9;zg7oy2vx 1nyer0 ;vqring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what spee; nnxyyo0g97mg zrqzy4i3v 1ev2;; uud will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one end cl*kf po3*i)l of a spring; the other end is fixed to a wall.ol*ic )*f3lk p 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration 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 1ewsl s5zk vb7gr;bzav p4264= 0.45cos6.4t where x is in meters14v;lsgz 7bw 6zb25 ravp4kes and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energtpow t*i ld 2/s5*2qx0qnac )ry of a SHO half KE and half PE* 2 p25li rq *ttd0oc)/qanxws? ±    A

  If one vibration has 7.0 times the energy of a second, s1woyzoj6)tqtc hq fa 5/ d40;but their frequencies and masses are )oj1zaft;t0 hw o6d54 qqy/c sthe same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring on1 lw1 avbchmuz*o;27du/idp)7w q.jsce every 0.65 s. q*u7z7dsl /u;1icv h1 j. bapmo2)d ww
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallel +o) n44nd8(: dqbang4m vm ;j6fn xbzvvertical springs, each with spring stiffnn:n(voa4 gxd;4+ 8q6mzfnb nmb4j) dvess constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according tofn+zii,osi +w;f 3nqd9a it0) the equation x = 0.38sin6.5t where x is in meters and t is in seconowst+;f 3,)n ifiqi09 iz+adn ds. 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 oml*,nsxed+75r c0tsp9cyd c ; fg h4p8f SHM, labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontalcm;*hd( 9k+ dxlx in v6yc0n9w spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/xl *k90mwn 9idncvhc;+d(x6 ys 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 s da:oc941kvq upring stiffness constant 305 N/m vibrates with an amplitude of 28.0 cmkud:4q o 1av9c when 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 connected to two springs, with 6 emt 4z)*lwg lj/l9q3p8ceqn 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 horizontals i 0:z(iyir;g spring whose spring sti0(ysi i ;zg:riffness 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 kgsq p pnr2 c(kz/w6.qzjdl8 g(7 jumps from a high bridge. After reaching his lowest point, he k/r((nz jgdwq2cp6q 7s 8lz.poscillates 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. What is its u*1u,o:ygxv we jvt ,+ 1tu*qv
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is jn;dx 2v8*y5 qbm37muzb7npwup+ q z* to make exactly one swing per second? (That is, one compnu*nmpvw jb+;5 q77qb8 mupz3d y*x 2zlete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What hcx a;h7rv,.n is its period on Mars, where the acceleration of gravity is about 0.37 that on nha ;7chv,x. rEarth?    s

  What is the period of a simple petgpq lg508, i4f* m gnf(tkek;ndulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum f 1hjj (tpdj vj. 11pihp2.af(is 0.760 m, the pendulum bob has a mass of 365 grams, and it is released at an angltfp p1vph1jdj1jij . (.fa(h2e 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 r4 :ut acuf+vx 3t/y0mclock loses half a minute per day, how should you adjust the lengthxumf3r: 40v+tc/uty a of the pendulum? shortened by    mm.

Derive a formula for the m ,rh.zqhy.d8qaximum 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. At it is release4e;yiy)w k e-u(l2 llkd from rest starting at aeywek2k;l4 lu il)- (yn 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 crvgn2 b6 zf3b0nd4g)ngests pass the bow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How g0gvzbgn bd nn )46f32fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed ott thhusyi*5gf+yc l+ v3q)5 3f 343 m/s How far apart are t3ucl v+)yqsiyg3*tfh +5t h5 the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilohertz)gnxq n.7 ;/z tun7dg.n and travel witn7z. . g7x;q/ dnnutgnh 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 longitudinal wavefwf bffp33m)cv9c3- g s in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastk oy9jym-:.uc;noqm 4 ic modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves9kmm oncj:qy.y u;o4- be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If th )yuvku)8o: uje tension in the cord is 150 N, how long will ikuu :)yuoj8 v)t 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 lengtjp 3x vdh*hz4)h 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that ithvj) *d34 xpzh 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 be,i z j3e0x es-khk8f3qlow the surface of the sea. He hears the ecxe ks0kzj3fhq3i-e , 8ho of the wave reflected from the ocean floor directly 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, l)v4akt o3rt/8 azoc a 7/mb/jand this difference helps in locating the earthq//4a87 )lvmzra3 o ot j/kbtacuake “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 cags*zgd 6 77q 4lz ow-kr;b9uzwn be approximated by a sinusoidal transverse wave. Assuming a frequg; -rs u6zqzolb w4gd9w77*zkency of 0.50 Hz (typical 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 intensities, and (b) the amplitudes, of an earthquavniu*pb /d .iu46bwu4(l0ndrke P wave passing through the Earth an4r/( nnui4bv.lb0i*6d udu pwd detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through /azr0y,d 8jo; vb kvw+the Earth is measured to be 0aw vod zk,/y br8v+;j$ 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 samji+ r0 8: osgjbu6kna2b smv.7e portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes o+8mbo6a. vkg:sbinj 0rus 2 j7f the two waves?   

  Two waves traveling along a stretched string have the same z som+ v(:kwc1tvt6d 4frequency, but one transports three times the power of the other. What is the ratio of the amplitudes of 61m s4wk( oz:t+tcvdvthe two waves?   

  A bug on the surface of a pond is observed to mop2g8q qf9*;usifdf9t,j ps8 t ve up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, dst,tfi q;8gf*f2u8q9sppj 9by what factor does the bug’s maximum KE change?   

The two pulses shown in Fp3h rhz67 ly, *pqpp8dig. 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 string is straigd6 *hp h7py38pqpl,rz ht. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its 1vh;h.icr1i)s9 pwvw fundamental frequency, what are the frequencies of the shrcpv.w1h91i )i ; wvfirst four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294xvz9 6r.iyt b0 /kobc, Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wai o6vt ykbx,.09rb c/zve.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hs dfi f3kzn n -9ul:x9zuypbc;l.kmn1cz-6 ;7z. Name at least three othe9;flz;- 6n.c9:3ukpulz- d i ykcnmnfb sz7x1r frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the fre6gp;*) x91qqv ay p: j,kbwiiyquency of standing waves is 475 Hz, hqyx;ivp1 bw6j, g* 9pk)aiqy:ow far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are/3xf23s d enqy9;nx qt 280 Hz and 350 Hz, what is the frequency of the funxqy x3s 29;dn/n qfte3damental?    Hz

  A guitar string is 90 cm long and has a mass of 3. eqn)9 2i9tz3b c:qh;9kbgojx bz2p7i6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tensk ci:nxz39hoe 9b2qq)gb tj7z; 92 pibion of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is me) 61tucakfq.wasured to viu w c1at).qf6kbrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but y tk68wyrkcz;g-frsxeh )0c : ho( (m5g)jc 5nit is measured to vibrate at 2c:kr m0k etrfch6sw-g) x;gy8 (c()h5nzo5 jy05 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attachemn t*e,j d(-q. u0ejlyd to a small-amplitude mechanical 60-Hz vibrator. The string’s mass per jte0 yq.ln *-(dm,uej 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 t0il1 :; r-keklrmh8l,o8 rnpohe pulley. If the hanging mass 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 ;1pkel,kr8 h0oo-8lm:rrlin m?   

  When you slosh the water back and 3a5m phlo0pbh-kb j27forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 6 3ap lj0oh25kbb7hm p-5-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 / y*uo1w81kproa2yl lw4 hc9 tstrikes a boundary within the Earth between twoyoalo29uyh k18w4/r* pwtc1l kinds of material. If it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velocit ;aw e9a ojsy97r-9w6a-dzkmry changes from 2.8 m/s to 7jm9o-sa6krz ; ww 99-aayrde 2.1 m/s If the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air w 5vay7a2en l54s:,x+jt cpd lphen it hits a layer of cold, dense air. If thespjp7ayl2t d5, :v nc+xa4el5 sound wave hits the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strik:rc +e 2p,cyua(w 6jbtes a boundary between two types of rock at a 38 b62ayt ,c(+:uwrj pce $^{\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 th/gpglptch*-,t 7igr8 e user’s manual, the dish has to t*7 -,p8rg g/t lpgichbe pointed in the 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 750 km/h travels across tqxf x/uz*o9zk f5:c6hqwu( 2ahe Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they hw9:ckuuxax5f*(q o z26hzqf /ave 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 stiffneivsm(( 87;0;zdfm sp wpmib(ess constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, colp mze((v;0d pf wmsi(sb8;m7ilides 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 grjai 3,k2 cy9ovlyd3 we8t;)m below, which stretches the net 1.1 m. Assume tha2y 9d;3e3t,oag)i8cyvj rkw lt 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 end5+zl v;9zifmk6(m 4iq olrt0dwq5 qi * of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is th5qtvim4d q*zzl 9(oliq rmk5 +fw6 i;0e frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed oy+ z: kt,nu2k6 yz+zcff 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) Whak n:t +,zz uk2fz6+ycyt 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 coff4e; pgbis-2/9bvs geahku(t- 3yf dd(ee (diameter 8 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 (Fig. 11–vy3s u-f(-2de/ethbs 4a 9kggp;(b di55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certa zb.d rb1v5xx;in groove 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the rdzxbb v.;51x sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t f *h2qmm d+0tte .ktb3where x is in meters an +*3km2 q.thmtf0bdted 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 oscillates with frequenc, 5xp 8yyi-phi4 2awu dg*os puawy/63y f. What is its frequency if it accelerates at 0.50g (a)ipd6h s38p4 a*ix/-o,a uw 5yyugw y2p upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When 76k ibyhg0 ru01mu*tg a 75-kg man stands on the raft, it sinks 4.0 cm gt*irk0 uy7 1ubh m0g6deeper 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 to play at 392 Hz (G) and 44045dpnd/vcpe j buwa08 kf4v(8 Hz (A afv84 vpd(054pwujdnkcbe8/).
(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. z73z i2z s9h .ovk1.mugmo*ct 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 wavelengths in the two sections. (The frequency is ttm .3oh 9zk1*2ovuzi.zgm 7 cshe 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 264n wm;7 n dq-3,zllq7gi Hz, and the tip of each prong moves 1.8 mm to either side of center. Calculq-7n ;liw7 g,z dmqnl3ate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motnkbc29 yhp7l f,+ r9pbion 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) will not lose contact with the board during th lrcnpb9fyp29+ ,7bkhe oscillation?

A string can have a “free” end if that end is attached to am yp1ld1 ml (fz0zf:8o ring that can slide without fr0y:( fopm mll8dfz1 1ziction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactlyc4 sx ,0 nzn(h (kp1jq4;mleam 2.000 s — each one-way swing takes 1.p0e, zn mk(4cla;xhq(41 m sjn000 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 dire7c 4n xmzs9k5k 5f1zkection or can swing as a pendulum of small 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 9mezskcz4f x5kk715n : 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 1lgx+ ieqz; lr ;7bu+f o 1.*:mfrnn9jw23 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 will the two pun.gz1+jf9 iwq;+ blno;e:ur x lm*7rf lses first meet?    m

A block of mass M is suspended from a ceiling by a spring with wa/qownmmgl-b+ly h 1(1(8vtspring stiffness constant k. A penny of mass(m1 w ml/v8logbwya- + t(qnh1 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 4q 1iot,pji2qcrane 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 tho,4 qj2iitp q1e period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fi bg8;m rxwnkrya coh:: h53h3*g. 11–58 (which also gives the dimensions of the block). You puw3b *o;mrh:h3a5xk 8yrh n:c gsh 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 modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz