Give some examples of everyday vibrating objects. W oivy cd4,.pj:.o+ flwhich exhibit SHM, at least appr wci4,d:+.y l.vf joopoximately?

Is the acceleration of a simple harmonic oscillator-cb *3yuq/k5r zz034lx1ltxu gg9 aa(4es toi ever zero? If so, where?

Explain why the motion of a piston in an automobi5kfx y:6;qb elle engine is approximately simpb:xlq;e 5yf6kle harmonic.

Real springs have mass. Will the true period and frequency be larger or v )equm ( k/+0il6ntfusmaller than given by the equations for a mass oscillating on the end of an idealized masftu)u nel 0k/ i(q6+mvsless spring? Explain.

How could you double the maximum speed of a simple harmonwyh3mf kiwe 8yke5gm*- l(cu+ /6f(m7dwwo5yic oscillator (SHO)?

A 5.0-kg trout is attached to the hook(gedcqpb y*ink5.25i5 w kka( of a vertical spring scale, and then is released. Describe the scale reading as a function a5g5kb qcd(ii(ew*2k.kpy5n of time.

If a pendulum clock is accunm0 h3j *xkb:trate at sea level, will it gain or lose time when taken to nj hm: xtbk03*high altitude? Why?

A tire swing hanging from a branch reaches neg5w x*6vzllrx: /g ;sdarly to the ground (Fig. 11–48). How could you estimate the heigh l:wvd5/gz6l*xxg; sr t of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only id ti k5bu1pe 3k17hrb.f you shake the pan at a certain frequ tud15bp.3ik1hbr7 keency?

Give several everyday example 5ura0* r4vg7/hw/d thgprd 4j- s9bnls of resonance.

Is a rattle in a car ever a resonance phenomenon? Ex f.d,gri(q7u tp 3cma2plain.

Is the frequency of a simple periodic wave equal to j4fdy aj :,(87h nqyvpthe frequency of its source? Wh4 j v8pdny( f,aqj:7hyy or why not?

Explain the difference between the speed of a transverse wave trazhy e+ a1mp0i5veling down a cord and the speed of a tiny piece +m 05pzyi e1ahof the cord.

Why do the strings used for the lowest-frequency no h3v( ro:0 q4uwnhpzj;tes on a piano normally have wire wrapped around uz:p(r4v;o jhh n0 3wqthem?

What kind of waves do you think will travel down a horizontal metal rod if you /m c58()3kvqh2dofdqtgg p0 fstrike its end (a) vertically from above and (b) horizontally parqo/03h m8f dk2v5)fgpq(g cd tallel to its length?

Since the density of air decreases with an q x :tjznl1 ),u)o7rhuincrease in temperature, but the bulk modulus B is nearly inde )1l:uqjx o ruz),t7nhpendent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular c j0u .p8.nxoc eik.1rai xv6)rg5/wewater waves decrease in amplitude as they travel away fromer.xu g 1 wjr .085ncx.i/6e opkavci) the source.

Two linear waves have the same amplitude and speed, and otherwise are identicp tgll 5h x/ic-/ko9)cal, except one has half the wavelength of the other. Which transmits more energy? By what 5ilc- k/xh9g l /otcp)factor?

When a sinusoidal wave crosses the boundary between two sectvvm))1l4 xdtk ions of cord as in Fig. 11–33,k t1dvv) xl)m4 the frequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segmentsx1 *ex1n0; lkbr4zl gh, are there any places you could touch it with a knife blade withl*xz le14x r0g;hbk1 nout disturbing the motion?

When a standing wave exists */jpo7hd fzhl9 :.vdtdnsw.08 d 2eslon a string, the vibrations of incident and reflected waves cancel at the nodes. Does this m ldp* d07fhhln9o vjtsdz/82s .w:de.ean that energy was destroyed? Explain.

If we knew that energy was being transmitzij ,eb31 pmx9ur edd76c+ 1xrted from one place to another, how might we determine 7ec+pi,u3xexz9jrdd1 mb61r whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergyz+6)tih3q*o 23/ osf caaar boes SHM with amplitude 0.18 m, what is the total distance it travels +qr)* 2/yhztbooaa6f a33s c iin one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it r4 zj q;tc9y4bbut is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of j9z4ybq;r4tc this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm whe qd, g3r :e1aqd-b(ldvn its 68-kg driver gets into the driver’s seat. db-,d :1q q3(dv gealrIf the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (a) b4 w32n3kczf df(4 6d7o zwq y)y+xlnbWhat is the sprinbcbzzfn(nwfy qdk)w+ l xd673 2y344o 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 4:unna:tm /3ubvyd; h9uz*j s7ge9xvwhen a mass of 0.60 kg is hung from it.9hu: *:m;g4 yeusjv93atnbv7n x d/uz What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x kh7ua/)q xz0rm3pum 4t34 ifx of the mass in Fig. 11–2 at times t = 0,xip4 x7/3 furmt3m)hukzaq40t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 v;psu1c r4:rx1x e.hbsibrates predominately with a frequency of 4.0 Hz.srxcu4p xrs1:1;b. h e
(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 frc atn0ewv:/8l equency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60l : wtva/enc80 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of n9gy-b2o4 q cia spring vibrates 3.0 times per second with an amplitude of 0.13 m. oy9i-g n b2c4qDetermine
(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 speedk0tjb3ap 43 sw3c( vsi of a SHO half the maximum valtss b33wa(k vj i40p3cue?$\approx$    A

A mass attached to the end of a spring is stretched a diszms5wo 7gnc)x64 ks6ttance $x_0$ 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 stretc ylii akab7-a+v5 +g4ched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium position again?g -a l7ca5iya++4vbki    s

  An object with mass 3.0 kg is attached to a xj:s)dw6yw1xt+w ( fz spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. 1)t(df :x+wwwysxj6 zWhen the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring oagc3z .0 p9eldf a toy popgun 0.200 m to “load” a 0.180-kg ball. Wiz 0g c.a9e3ldpth what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, fric c6cc2v2i 88 .zona1rflc2uyxtionless surface is attached to one end of a spring; thzcc6. la1vru ncofc2x288 2 iye 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 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 vibrate4vxp)m 9x gg/s+)-qew6uwcj j s according to the equation x = 0.45cos6.4t where x is in meters and t9) /g+)u vjmepgj xww-sx4q6 c 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 energy of a SHO half KE and/)q.tp.ztq cv half PE? ±qc).tv p/qzt.    A

  If one vibration has 7.0 times the energy of a second, but the0x)q-3klgsd*s6 yr0 azub k8kir frequencies and masses are the same, what is t6kakrzxgq-*u lks)by 830d 0s he ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates 7jneit(,9f (vlg kpo/from a vertically hanging light spring once every 0.65 s. l9 (ek/vn o,fj7pi(g t
(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 vertical springs, 5.koge r/ef(cinr -3w6 4q rbveach with spring 3 iw6fe.r bvg/krr n5 (q4eo-cstiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates accordi+brun1,dm 5q. vj 4qhjng to the equation x = 0.38sin6.5t where x is in meters and t is in, 5+b .j 4nmujhv1dqqr 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 t45++(rks5 xgsb(dnndl vn )wm wo examples 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 the end of a horizoq/r+kxl jbaz.cb a+ pe5g--;kntal spring (k = 124 N/m) is struck by a hammer, which gives the mass an in.+ a-a+5 ekjkbrpqxc/gl- ;bzitial 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 wi) nfd; mzg(2cgay91x 0oqzh pzi4i ue)r9e+0cth spring stiffness constant 305 N/m vibrates with an amplitud1gu pc4yzz n9gx;() 9 ea0io)0 qh iefm+d2zcre of 28.0 cm 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 spr; 0lp/e y*htij dlv9a3ing 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 g 0)6o-cg 3( 9qkjedb rh6avaxattached to a fixed horizontal spring whose spring stiffness con xdarg6 oa-)09b 6jg3ehvc(kqstant 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 bridge. After rear 4xw79 :q0gjvuvp f8zching 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 the spring stiffness constang:97u v4jzxfpq0 rv8wt 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 its6 m q*j+t at0l-bq:vcz
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if ;2cjujvr,de(g;n d7n it is to make exactly one swing per second? (That is, one compl j7; c;gv,(u 2dejrdnnete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.8q knq5y6s- n4 xncftz8ti9a9hc 57;it0 s on Earth. What is its period on Mars, where the accel59aq47st nhnintf ixt6 qk9c -;z5 yc8eration of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 8 ye4m(qzg e*07k7ztnc0 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is*c); 8ccl9,jk4czh jqquk yp2 0.760 m, the pendulum bob has a mass of 365 grams, anu cqyj)j4 lchpc829z*qkc k ;,d it is released at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 m. If the clock losmpq9zoein69 x 4i2m: 04sffztes half a minute m zinf94ozi4xtfems026p9 : q per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the ma (n+14zjp( cwnn3w)spf.o)jo tiu +w uximum 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 oscillatesq8 wvz mvc859cb0v+s o at a frequency of 2.5 Hz. At it is released from rest starting vzb0o+5msc98w q8v cvat 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 pa/5da8k3+ot+y tppwhly9t + n ddnx41 ess the bow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m.t3dhn4ped+nt 9+tly+pd/ 51awy o8k x How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz cnmzs/5n.s; 56y k;*dwhdyw c:d) cgjand travels with a speed of 343 m/s How far apart ared5yyndskj)ch.ww5;sdn * mcg6 z; c/: the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and t j. r4uu/2b;u8hcylr 1600 kHz (kilohertz) and travel with a l u/j;8yrb2 h4urc .tuspeed 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 lo/zzs0dif2r2/i hq f5cp+ e5p nngitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elt7mt j4q6 ;acxaf5+j uastic modulus, but one is twice as dense as the other. In whj4;6jq7ut t+m5 fxacaich rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two suppn 31rxogn9l4hg d07 0r dwbc-vorts 28 m apart. If the tension in the cord is 150 N, how hgl0d17c0bvrro d3 4n-9 nwxg 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 cc8hk o: wt aolnt:-k2jp2*0mgable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps int2 h t:an-wpk2o gklo mtc:j*80o 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 j7.i:uudfn et;z*5cr uust below the surface of the sea. He hears the echo of the wave reflected from the ocean floor ddzitr 7.uuf;u n *:c5eirectly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at dif5+jdfnc e 8r9cz756lrs vu ;v 7:xoztmferent speeds, and this difference helps in locating the earthquake “e78zrf6; rnsd5 +cx mv:5ujtce9volz 7picenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated by a sinusoidal transv8ybgx3loo1s2 vkg- 2c iir: ok+-mej: erse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of s:+igl2 i8eb:ok3k-j 1v goyc- o2rmx 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 x93 c7d2ld(hxzlulh3xzih1 9 (a) the intensities, and (b) the amplitudes, of an earthquake P wave passing through the Earth and dete9zl1xuhlli x d39c(d7h3 z2h xcted at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured to bu. x. qc.w:qp9nfl* 9d 8qwssun0 pir3e w8.us.x ppq. ic9u:rdsqf0w39l qn*n $ 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 port9vthoqc. 2*lh ion of the Earth, but one is carrying twice the energy. What is the ratioqc.tv9o h*l h2 of the amplitudes of the two waves?   

  Two waves traveling along a stretched string h*p 4c 9h6;zzdtm wqw3.ga*ge jave the same frequency, but one transports three times the power ofawcm*3 we g.6jz9*4q;ht gz pd the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface o4fbx9(hi5ncls aqbqo) /0os/ f a pond is observed to move 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 ( as)/4sqn 509b/oflqci bo xh4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) Sketch tt4b bq-n7aajcd58a zj7 xee*t 2bq*3bhe 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 adt z e 3qjjb8an4bcea*x77- t5abb q2*t this moment?

  If a violin string vibrates at 440 Hz as its fundamental fr +:vmg)zjew-b49v3 x uvn6wde equency, what are the emwg9zvxun4d: 3wbjv +e) v-6 frequencies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates ate 7r3kf/fo4reh; d0zl 294 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-t7f0eord/h 4lkrzf; e3 hirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency g,f-homt(xz evz + 9+dof 280 Hz. Name at least three other frequencies toz+f+- e v(m,hzx9gdat 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 frequencb, )r85rxsy-pca8w;ahvdma e m 26n)sy of standing waves is 475 shb5)n 26ac8-d 8 ,rwayr )sev;pxam mHz, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz andjl 5.uuk n1hq; 350 Hz, what is the frequency of the fundamentalh.;u1kj l qu5n?    Hz

  A guitar string is 90 cm long and has a mass of 3 pz1c q/7 aoq, 5l rtkllw8bpr(r49rz;.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension zt98wb7lp kracoq/z;r rl5l4pq 1,r(of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate vbf49b( nyyl9 at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent shoul4(yfv9ybnl b9 d 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 stringedfeu8oc ;tk04 -cou b/;)ms p is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what u ks0btf/-c eep ;d;o)8 muc4opercent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is adpn5je 3to 7a;ttached to a small-amplitude mechanical 60-Hz3jdatep7 5;n o vibrator. 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 k-ayx r+g*7 jgbe adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wav-a* gg+ xkjr7ye patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and fo:nl5j: khmj44 j :mlcbrth 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 65-cm-wide tub is 0.85 Hz. What is the speed of the water wav:m4b: nk l ljjh4cjm5:e?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundako;)qpt+f7btf *sm; en 3z1e h.nm-rery within the Earth between two kinds of material. If it approaches the boundary at an incident angle of;ktb 1zmee.e mffo+;*hpqtrn-73s n) 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velocity chzb:+1 kf:oa*d iv* .bjpaf.sa anges from 2.8 m+faoi*.dj.p zbf:*ba sk 1a:v/s to 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 when kp7 mv48ow,aqu*-a g 26 uwjtkit hits a layer of cold, dense air. If the sound wave hits the col,ukw 6jw2qp8ak *vgu4ot -m7 ad 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 between two types of roc utf69 ;zmz4fpk at a 38 t f;z9fzmp64 u$^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m in diameter. According to the user’s manusq gtesdn6 z x53yyly75 1+n9mal, the dish has to be pointed in the direction of the satellite, but an error of about 2 z9y5d+s mqyng5x3 tesy6nl 17$^{\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 the Pacik)6ll+0t8sz jn, mpwcfic 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 attk0m6wc,znl 8ltsp+) jracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant*dvp 1,h hcb0o of 550 kN/m Find the maximum compression *dohh0bv,c 1p of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which stretches t10v5 c i(spsdy0ry,t phe net 1.1 m. Assume that the net behaves like a simple spri( ds0rv,s0tcyyp5ip1 ng, 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 spguow n 1w55y8pring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of the osciw85u p1nwg oy5llation?    Hz

  A 950-kg car strikes a huge spring at a sc :d:czl.kl fwp6 ;j)dq.m:hmpeed of 22 m/s (Fig. 11–54), compressing the spri6mhdk.:)c fpj; dc llw::z. qmng 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 of coffee (diameter 8 kbu-qlwm- f6 )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. 11–55). Estimate the speed of waves in w--mb u k)f6qlthe coffee.    cm/s

  The ripples in a certain groove 10 w.g ekt. p5o9 )qs:ltj)1wvhl)n)bv9kbhn)b.8 cm from the center of a 33-rpm phonograph record have a wavelenbt:l) vj5v9 kwep q.wtb9)k h.gnblho1s) n))gth of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to0zet6z-a f5z+ hni.bh 6he 4oz the equation x=0.650cos7.40t where x is in meters and 54.0+h6eo6fh b atn-zzh zi zet 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 frequency;4o vpvv 7/7qfl ,q*aag-pbgt f. What is its frequency if it accelerates aq-4,at7v lpopab v7 q /gv;fg*t 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats aw9 -:a mm;zjeon a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raf:; jwa zm-em9at 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 1gls0xdec. h903qlivplay at 392 Hz (G) and 440 Hz (Ash0lc iq 3lx.9eg10 vd).
(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. t24 akev;a /c3irpge z9k6kxc7x7 u;iDetermine 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/ap k6gkz x 4eu;ecxirkc7i9 a27; vt3. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and z*nt-mpwmqj7 7)lz5uthe tip of each prong moves 1.8 m7zn5 wtpl7*jm) u-z qmm to either side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of frequency+6ucyxe8 pc9c+r :ot kc; sfx- 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order:scfou ck xyrxep8;9+c6tc-+ 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 attachedu,)0xeul r: m kn)rbnb+n)r4q to a ring that can slide without friction on a vertical pole (Fig. 11–57). Deu):rl) be+,qnnx4)n 0mrkurb termine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way t;+ nw.7c.2 aiosr:stxhek0:+wgjjmswing takes 1.000 s. .0sr:+t ct ;hgasx mnj2 wj+weo7:k.i
(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 v di3e0p6yp5ioscillate in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Wi0 5i dppv3ey6hich one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched under a tension of 255 N. A p (jni;xnp0a6g ulse is generated at one end, and 20.0 ms later a second pulse ing (xaj6p;n0is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring wd sf9s of4qn m1xy3 t7tu/d. sbbik -2)ajk,1rith spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscilla a,3)tnsfqo1kyb -ut2dm7drs.x/s1 4fji9 b ktions 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 cra0g i8-rje r6g2hkjs z,ne 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? [, sre-k8 gjgir026jh zHint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (whic ydih)78xuh 6dh 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. Inxh6 87ihdy du) 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