Give some examples of everyday vibrating objects. Which exhibu2od2 ko* ti38ji4eu nit SHM, at least approximateloteu onki d*428iju23 y?

Is the acceleration of a simple harmonic oscillator ever zel lsn3gp/vig+ fa)4: tj4s5jyro? If so, where?

Explain why the motion of a piston in an a 0hbsfyg- cpe7y +tmp p-;-jv1utomobile engine is approximately simplef1e0v+tc-bpy7hpjm g; y -p -s harmonic.

Real springs have mass. Will the true period and frequency be larger ory 8j.lx-p) ptaoe vx92we25 ar smaller than given by the equations for a mass oscillating on the en-ae )y2jpreo9al5 v 82x. wpxtd of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic h-, b6c dcjw:/kl wea5ipr:y,by 6;lcoscillator (SHO)?

A 5.0-kg trout is attached to:e. asbq c2su/ tk+r 2/wzqkq+ the hook of a vertical spring scale, and then is relea2 2 eq +:r+.zckqtk /awq/sbussed. Describe the scale reading as a function of time.

If a pendulum clock lh3k 1jb qs as3r9/x2uis accurate at sea level, will it gain or lose time when taken to high altithsx rl9 a k21qsju/3b3ude? Why?

A tire swing hanging frya j+-1.l vfo 2wbkbc8om a branch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch using only a stopwatch .o-+cbk2fjbw1al 8yv?

Why can you make water slosh back and forth in a pan oqgf6 mjnza*2j yq 3*42yy abmdgr1x7* nly if you shake the pan at a cnmj a*q g7d36*4 yzbjmxg1r2f*qyy2aertain frequency?

Give several everyday examples of resonainc; u*qw ph56oyvk3xqz--* pnce.

Is a rattle in a car ever ipyr6 ) )pv+eja resonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to thexx )q dnb)66zommu:, p frequency of its source? Why or why notxz)x,d ombmq:) pun66 ?

Explain the difference between the speed of a :a1o fzw aba9 0(mfap(transverse wave traveling down a cord and the :ao b0 f1fam9a(w(zpa speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano no3bnt(m30sq,avh arb 3rmally have wire wrapped around3a(b ,aqn tb3v0 3rhsm them?

What kind of waves do you think will travel dow3c1.eip-;ui27dg fusv kj o 8wn a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parallel to its leng-j273 kdu;i8fp ge1uco.iwsv th?

Since the density of air decreases with an increase in temperatur7f xj*i 5ymr-gd5s+ hye, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air ti7+ fh jm5*5g-d sxryyo vary with temperature?

Give two reasons why circular water waves decrease y*lx2 syhr+3isvk 1(xin amplitude as they travel away fro+ 3yvislr(yksh* xx1 2m the source.

Two linear waves have the same amplitude and speed, and otherwise are identicalv d tdj19y*kavnwfx*v7eia2a8.c,+1 lok -al, except one has half the wavelength of the other. Whichkvo+ 8 w*t7ic.a1x1 9avydl- 2, *dafanveklj transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of corrji(px5/ a.mo1 ;739fsqis 2rdiw ixvd as in Fig. 11–33, the frequency does not change (although the wavele/15wxmii;fdv (39asror 2 i. isx7jqpngth and velocity do change). Explain why.

If a string is vibrating in three segm, bk3+*+nej2 (sbs2mqq x we0ynyoyn.ents, are there any places you could touch it with a knife blade withon en0.*b2j3+s+ kn,2 yymsbyw(qxeq out disturbing the motion?

When a standing wave exists on a string, the vibrationizh l/ hkm*hv3: *(kqes of incident and reflected waves cancel at thm( kl*3h*q hz vhiek/:e nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one placwvn60 2dfo o)+-2ctqv izxnj -e to another, how might we detedco 2+f- 02qvotjn6nw)- zvix rmine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0 ++z5rcjmtd1i.18 m, what is the total distance it travels in one peri1rc5++jdtmzi od?    m

  An elastic cord is 65 cm long when a weightwacb,qf.1 3lj-3kc wk4q a)f x of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” consta3-,xc4wf )j bafkc wq k.qa31lnt k of this elastic cord?    N/m

  The springs of a 1500-ql69 +p8mmq g1fo ma;hkg car compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequency of vi 68;mqh9 g1ml+pmqa ofbrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fiw+6hlo h(*z qysh hangs from it. (a) What is the spring stiffness consta+ylo6qh(hz* w nt $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mass of 0. m/0wpgt;m i6+q swfz360 kg is hum;p f6t3 imw /qg0ws+zng from it. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating o : r3a/srfdu/the position x of the mass in Fig. 11–2 at times t = 0,t o / duf/3r:ars= $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web. The web yk9r,a ;5)951yy o(odua -hxjjfbwidvibrates predominately with k hd 59r5boo)xi y,af;jyw(-d 9ayju1 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 spgt0b6ux l,.alq 0p i-zring 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 t,gp-tli0.l x0 qua zb6he value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times perc bgue/ +6nt1v second with an amplitude of 0.13 m.+e1gbc6vtn/ u 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 equiliubb.d8 6c: ipakx7rz -os7s4fbrium is the speed of a SHO half the maximum valu-.ic7uxap fb46z7 :rskdbos8e?$\approx$    A

A mass attached to the end of a sprin5:qht6 vlza5/s;okq 5h x msd,g 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 /o3srb*3hspmc-.dn1 w;ed as spring 0.315 m. If the spring is stretched an additional 0wass/b 3n*csmrde-o3d. h p1;.130 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffnxduk0njq64x+ nubhc.8d 6b 2 yess constant k = 280 N/m and is exe d6qk+80cn.nx bu bdyh42xj6u cuting 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 the548kiylx* fi1rsft67 vd 1tke spring of a toy popgun 0.200 m to “load” alk7*6er45ifxd kstvfy 8i 1t1 0.180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one end ofuh ,6yn:c +z43 s yk-kb)qwzjglpv8w) 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)6+ yhzsk8:kw -u)q,4 wljg3vc pzbny 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 = 0.45cos6.4t where x is yk6 rzzqw2/ 0y6;cv , xdr(recin meters and t is in seconds. Detqx6cd,k6yr;wyvze/ ( r zr2c0ermine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of a SHO half x7 . vdma)luh*2i.i;s5j qnmbh4kjy:KE and half PE? ±h5 ajh;.s4ld .xi q2un)m jvimbky7*:    A

  If one vibration has 7.0 times the enerb ;tsnv*f-ue7 (20xongii ie:gy of a second, but their frequencies and masses are the same, what is the ratio of their amplitudiix7o*fse0 - :enb nt(v2gu i;es?   

  A 2.00-kg pumpkin oscillates from a o*,tw 9*2nj -tdbemff vertically hanging light spring once every 0.65 s. b* o-w td,*tjf fem29n
(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 ve2kwlo+q-gs)ntj 3o, y rtical springs, each wi3t )wg ,k2 lqjyo+n-soth spring stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38fnj,bsl 0hkt y-j(1 9 i8daf-psin6.5t where x is in meters abi-0t 9(8pf1dsj njhyf -l, aknd 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 exam4:tv, wj y1vxaples 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 g32q qyf7u 4nw.d x9nox/xgq6.zw c8ogdr9+ gon the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass aggqxcw 92qg8. y+uqndogz3dn4 / f97xo6.rwx 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 .y 3s5y35gqddg.fogt stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm wf yg.o3g dq s.dyg553then 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 spr 0v7 r,mro:rlgje2f+ming 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 djsvk9: de5xzyike8 :rw58;kblock attached to a fixed horizontal spring whose sprin :5x8:5;esiwrydkev8d9 kkz jg stiffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a higxtv s2v()y6 ru;) xmtkh bridge. 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 the level of the bridge. Calculate ; 2t )k(xrv)mys6xvutthe 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 oi2edkse p141s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simpleu1 l *.ejtosw8 pendulum be if it is to make exactly one swing per second? (That is, one complete vibration takes exacelj 1wo.8 *tsutly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is qmqr4g yqtns c* xy,i3k7o *5*its period on Mars, where the acceleration ofrq7y** qxty o g4kc 3msi5q,n* gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm long f7uq 90(sph gatw --rnt; :bc3 eijq6p+ n0orz
(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 362t7y( t1wsxufbuw2pi 0h ji m)q23ru)5 grams, and it is released at an angle0 bjw7q3h2iu xusitp(2))rft2wu1m y 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 loses h5q-x ocf3aj)rl k*sz-alf a minute per day, how shoulza5l3xcjks *of q)r-- d you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maxib zos9(;/(p t .wwgoecmum 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 (xw1r,hss0u 6wgp;oa7rgq wm v0,,0 0npqwkb2.5 Hz. At it is released from rest starting akx(whb60rr,sqp0, w0 goqmagwv, ns170; wput 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 thgg.vt4 z; h8ugat wave crests pass the bow of his anchored boat every 3.0 s. He measures theg ug;8z4g.ht v 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 of 262 Hz and travels wio a)w2j+/wrs,j3ylzx ,w2 vecth a speed of 343 m/s How far apart are the wave crayo+ c3lx/,2 sw,wvrw e2z j)jests (compressions)?    m

  (a) AM radio signals hah) x6m5wf x/ gm1l- agm.4kepcve frequencies between 550 kHz and 1600 kHz (kilohertz) and trave/wf x 1c- hp)xmgk almg.564mel 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 2uzv1oz- w - jjcyty+;longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modul+ ic6fa tnh(i5us, but one is twice as dense as the other. In which rod will the +t56i chnaf(ispeed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 72 n-a wd6gwexm apart. If the tension in the cord is 150 N, how long will it take a pulse to travel fromw7gd e6-xnwa 2 one support to the other?    s

  A ski gondola is connecantg2 xx zl935xuf7v2ted to the top of a hill by a steel cable of length 620 m and diameter 1.5 cxz t39un25lva x7fg x2m. 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 just below the surface of the sea.l 2evxtz-g2v . 2f-c gkc5mf9g He hears the echo of the wave 9mtzc g5x-2lg 2f e2c.fkvv-g 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, and this differ,*w3:lshv- w ea oezmu+j ;6awence helps in locating the earthquake “epicenter” (where the distuwj+le*w os:; w3h6,aa e-uvzmrbance 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 su/jinl r(ts+:srface wave can be approximated by a sinusoidal transverse wave. Assuming a frequency 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 ( s j:/nsitlr+with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, xqq(wu .gr: x3 -zke (geqgya+p/,.jaand (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 2yw3 gp/eqruq +.xx :q.a(zg ,(ga-k ej0 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is sh vg/;meaa vx,(k--bmeasured to be e-k (a/vv ha;x-mgs ,b$ 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 sdiujn -, pcht7y v85l+ame portion of the Earth, but one is carrying twice the energy. What is the rati7-+h 8ji,ltd yncupv5 o of the amplitudes of the two waves?   

  Two waves traveling along a stretched string haveb9p2bwb(u/b gh 47l e o9z+zpu the same frequency, but one transports three times the powewpz7l/u( +h bb e4pgb2o bz9u9r 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 do7eq 5joe9lxvff-h(9 m wn a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5oh(f- vl fe99em qj57x cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–59y y/u8b3.fl)prv quwm9/ b oa2 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 straight. What has happened to the energy at this mommquywop/)r39b v / ay8u.bl9fent?

  If a violin string vibrates at 440 Hz as its 55w 4/2 4qcs c4dlofmk9iwv ypfundamental frequency, what are the frequencies/9w pm2iwcd4flcks ov55q4 4y of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfi+4oug m*h 5tjyngered. At what frequency will it vibrate if it is fingered one-t j*o+m5hy4t ughird 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 inw :p /;it1fdgi four loops at a frequency of 280 Hz. Name at least three other frequencies1twg:ip/ id;f 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 theg0.3jy5lbhh7weuq ,q*q c)wh frequency of standing waves is 475 Hz, how far apart are two adjacent nod,3ucb7hwhqq)g0 *e l.qwhj5 yes?   m

  If two successive overtones of a vibraty)+ict ;:qtp+89wuwg edk/ncguc2 4 ming string are 280 Hz and 350 Hz, what is the frequency of the fundamedut;cukcm9qyp4 2w ggnw t +/e i+8):cntal?    Hz

  A guitar string is 90 cm long and has a tn thv :lg sh38jgs3n-*:+ogumass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two o gj3l:th nos3ns8g+g :thv*u -vertones?    Hz

  A particular guitar string is supposed to vibrate at 200 w0 n.5hzmx tfol8qhs6k 8k3j( Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the str3jq(6l s.50wh8kf t hxkno8mzing 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 it is measux*qisi q7c 67jred to vibrate at 205 Hz. By what percent should the tensio cqxqi *si7j67n in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-ami3y-rkqx8pk26 t xp i4plitude mechanical 60-Hz vibrator. The string’sx8p-64pkti 23 yxrk qi 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 movi4r vz*lcj 4matz2(,pqy92j b eng the pulley. If the hanging mass m is fixed a* p,lbrvty944(2zmj ez a2jqc t 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 jugesi3m52-(ii u5 fy30izstv2s u2 u wlst the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequenim5uvu-22se i gsi 0 iu(sy2lt3w5f3zcy 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 trave.sb bz p-v:qi(sqp1e+ling at k.0 km/s strikes a boundary within the Earth between two kinds of material. If it b-eqzbpsv s:+iq .1(papproaches 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” wyz;m.x- zmjx-.)g 1qxo h,ynthere the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests make a-q xzzm-.y1, x;moh y)txjn g. 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveil h kknu/ jlzf4p,+5 k(/s+ncling in warm air when it hits a layer of cold, dense air. If the so++ik j,nplfkns5 k(zcul /h4/ und 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 strikes a boundary b*bg29.g ekk mgetween two types of rock at a 38 g* bmk2e.gk9 g$^{\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 0m/vhnd p ki/- q ,()vb-izalc(3r9be x.5 m in diameter. According to the user’s manual, the dish has to be pointed in the direction of ti( hr3 vv(cl-k)-pien /zxmbqabd9,/ he 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 acrx*iv m*p5jqn 6oss the Pacific Ocean. As it approac m5*i j*qpnv6xhes 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 stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring sflwf 0ha99v i7/jy.f+j j2s+ efnn/85 mvifrstiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, cvvr2j 8yii se /njlfhjaf9fsn w+f9 f7.m/05+ollides 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 the :pfhwyb r -z2m;lq2+m net 1.1 m. Assume that the net y qzf-b2:+ mrpmhlw;2behaves 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 sprin bbeb1k2v mf;f0ht3 t8g. The mass then falls 33 ckev38mtfb fh1 t;b2b 0m before it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fiwsq;s xw*+m1+k-3z1t yc khklg. 11–54), compressins lyks1xh*wtm3k1 c-q; kz w++g the spring 5.0 m. (a) What is the spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup oo dabfp9 +:;* ddbmx+bf coffee (diameter 8 cm) at just the right pace of about 1 step per second, the coffdpm+d:*9a bf+ ;dx bobee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 3ihj5 ,t 0wqy0out7 6dg3-rpm phonograph record have a wavelength of 1.70 mm.7o u6whyq50i g0 tdj,t What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates accoz xfqnymsq-oh cqe0w955w-, .rding to the equation x=0.650cos7.40t where x is in meters and t i ym 9.sqhnczw5qqw5o e0--x,fn 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,1*fyj9-v1rzx ab yzktes with frequency f. What is its frequency if it accelerates at 09yjzbky, zxa1 *f-rv 1.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raft, itc0 eibyx 6/t7*e6iz zt sinks 4.0 cm deeper into the water. When he sbz0xeziiy/et*676 t cteps 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 4*,)uhswjbqau43 k() fzv*kzr40 Hz (A). arf(h,zv *43bz qwsu*kj )ku)
(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 travelingns)oxh vpng *nj6:zx)6ci:c(b z;bj( down the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavibn)6pjcv (z:s; jzo:n6 x x*cnhi g)b(er section of cord or the lighter?

  A tuning fork vibrates at a frequency vc8 pg2ogl4eu(dp+e0 of 264 Hz, and the tip of each prong moves 1.8 mm to either side of centeree2gug+o4 p8dplv0(c . 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 simp-udpan2hc,8 tqg7 y .lle harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the 7t8gcq2hupdl.n ,ay-end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attachedv qa.)89cy vbc3cx8bc+1hee6vj as8y to a ring that can slide withve8yys+cq6 cv 98e)b3a.vh1xcbac8 j out friction 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 z/2*)p4lgclljlf* 8u( tf(a8wbafvce1cs t3 of exactly 2.000 s — each one-way swing takes 1.0/* wgllc41 f28cuj(sct()z*l 8flta3v fb eap00 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 thevp jya5,s1ax+ vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the a +s y,v51ajpxhorizontal 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 un0zfd0m onj 4*dder a tension of 255 N. A pulse is generated at one end, and 2 dzo0n*dmfj04 0.0 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 fromvz,gxg l ht-cuwzs1. sl(; earw 7w.*h4lg(v 6 a ceiling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximzsr u .vh; ag l-.cwh s wxe6zt4gl(v*,w1(7lgum 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. 9ha 3er. :wzsyidcj+ ,The steel crane cable is 22 m long and has a diameter jhyi z3cse.w9,+dar: of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on aut(3f2 yg3 hoa plate as shown in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibr a( oty3ghuf23ating 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