Give some examples of every y-co )v:6favhday vibrating objects. Which exhibit SHM, at least approximatel6ay oc):hf vv-y?

Is the acceleration of a jvc:w g:ct r* fd-u,0wsimple harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engaff t(7(v f7koine is approximately simpkav7 o(7tfff(le harmonic.

Real springs have mass. Will the true period and frequency be larger oom f-6j ++fu8wyozfq(r smaller than given by 8o oqw-f( fy++z6mjfu the equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic p7j rk*u2c 6pooscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and then is m ie;,vyfclid0u n)0*dnq gc0vz73j2 released. Describe the vqidg20v3en ,)l mjfuz 0yni;cdc 70*scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or 5 s(-0zygh,c (os7g (c4 .vpkykmtrasv m0rq-lose time when taken to high altitude?kmp (a4qtsm50 y,- rscr-( 0kg7ozc sv h.g(yv Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 1k t4x,u;hu y *v)jfr:t1–48). How could you estimate the height of the x;u,j : fhtku*rvyt4 )branch using only a stopwatch?

Why can you make water slosh baibbi-bqv)7l*nv9 b .w ck and forth in a pan only if you shake the pan at a certain frv7 qbb i9-bw.)*ibvn lequency?

Give several everyday examplgw d69y695cdgiu sqy1es of resonance.

Is a rattle in a car ever a ry:oodiz z. w9(esonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of its g z)63rfmgvojz1 s+d. *,ilgp source? Whygrl,p f zvo gd6z)ijs m3*g.1+ or why not?

Explain the difference between the speed of a tran5n00;n;nvs6c2bb rq yvciy3d sverse wave traveling down a cord and the speed of a tiny piece of the c0nc3syrqiv;nvnb 05y c2 d;6bord.

Why do the strings used for the lowest-frzv0t7 f:6 esbfequency notes on a piano normally have wire wrvfb e 7z0fts6:apped around them?

What kind of waves do you think will travel down a horiz8 tfh()azh:c6r9 ehv7pqjkr5 ontal metal rod if you strike its end (a) v kr65( vhfpret8:q j)zha9hc 7ertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in tempebq) vvuk 9dz2ajn, 5imj x6z+x57w1pyrature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperaturevzb7 zmdj )y+w5ixjv1ua qp9, x6k52n?

Give two reasons why circular water waves decre8rd .d2kt)9whxe/6g*ot feru - k 4qjzase in amplitude as they travel away from the sourz ouk2* wrh.t/eje 9 rtgfdxq )d8-k46ce.

Two linear waves have the same amplitude and speed, adj ow7.gj;r mt h.6)nahtpy)6 nd otherwise are identical, except one has half the wavelength of the other. Which tr.opjya .nmd7jr6w h)h6g)t t;ansmits more energy? By what factor?

When a sinusoidal wave crosses the bounts)s+cb : ltwu7k z+*fql* ;ftdary between two sections of cord as in Filtt)q*s+u+zs:k t *ff7wb;c lg. 11–33, the frequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places you could t er)i999vhlfmgtsbc .b9tu2 4 ouch 9isc9.u9g)vber4th l2bf mt9it with a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incident and reflectehw4g hj y/* u-1sihy8id waves cancel at the nodes. Doesiy4i hgj h*uy8- /1whs this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one placevugzm 7- w+xkr4agrw.+k4cd : to another, how might we determine whether the energy was being caz-74+.g +gadmk uxww4ck : vrrrried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total dis:i7: ( ipg4x e st:xzpuv9;ctutance it travels in ontc4; ie t u9ug7sp ::pzvix(x:e period?    m

  An elastic cord is 65 cm lon /2vcyh0zspk7 g when a weight of 75 N hangs from it but is 85 cm loz cps0y7/2 kvhng when a weight of 180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-km4no2vxz7*a ug driver gets into the driver’s seat. If the car goes over a bump, what will be t2* oa7nmzuxv 4he frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.x3)o3gki3b s cr8r w8su-quv76 cm when a 2.7-kg fish hangs from it. (a) What is the spring k8v83uc3r rigxswqu7- osb 3)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 vibrntuh**be8v 0bd/:oqc ates with a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.8 h/td:nvbqo* c*beu038 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Figq/ejkuh 9p7 1 owrj+pnb7 :5n3sgcj0f. 11–2 at times t = 0,o7 nwgppj/ 9:rsfj qbu5+h10en 7jkc3t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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’ n765mbxwo ygh856baw s web. The web vibrates predominately with a frequencyxao8b5n m6w hgby 56w7 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 fx- ;f.aurtco dh( 69dprequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is ucr p;dto(- f d6.xh9a0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates kz5 i:g; b/qoy8rjesk4b1e+h 3.0 times per second with an amplitude of 0.13 m. Determ8/5gj1:br kkoq;eyhi +4bzseine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed zldq/j/nb5 2gya slat,*a9 )dof a SHO half the maximum value?gl/dazd* aj5t/nq bs, )2 y9la$\approx$    A

A mass attached to the end of a spring is stretched a distancu)87j ((m cx (kkmjkf ev5:bzge $x_0$ 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 stre3e c yq;c5t aa;qk(q 8lpo;q3k (dr:yetched an additional 0.130 m and released, how long does it take to reach the (new) equ; eq d p(8qcya3lytkko:;q q c;rea35(ilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spq7 o6a wf4(jxo7215y fc tnjarey/) qmring stiffness constant k = 280 N/m and is exeyaet6y7nof 5rao ()27wx1 j4cqq fmj/ 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 the spdg3, zse bmm8 7fz/l8*ibiba(nhxn6 -e k u-i;ring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave the gun? 7e8l, nkmeb; i-x 6ii(n 8a*/gd3ubhms-f bzz   m/s

  A mass sitting on a horizontal, frictionless surface is attached to one end o) o- fj:oqg:a zpf69 i,mj(lcgf a spring; the other end is fixed t: g6c-j(gij )pfazf:o q mo9l,o 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 vibrates according to the equation x = 0.dh33m-;1)qmar93fnt 9 bx ydohps 0rp45cos6.4t where x is in meters and 9adyr-r nht0q)d1xm m3o h93f pbs3;pt 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 enear.lu nl:;(icau, 9m qrgy of a SHO half KE and half PEl q(u; ,m9cna.r:liua? ±    A

  If one vibration has 7.0 times the energy of a second, but theirskzh;61 v)k:br izkhu,c2 0xg frequencies and masses are the skz20h:gs;rcku ) xk zh6i, 1bvame, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates s/sqgoz w3; 55fnp/,tddk. j yfrom a vertically hanging light spring once every 0.65 s. dwk5o,p z5gds n j3 q/f.ty/s;
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallel vertical springs, each+ql.i) o9 wxqn with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibrationlwx + i.qqo9)n?

  A 300-g mass vibrates according to the e wc fydj9m ulp7f3 + bjs.1x.sb-a.w,uquation x = 0.38sin6.5t where x is in meters and t is in seconds.puj. - ws3wuf+, c.7.y9j1l fbmxsadb Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and B. For each, what ise+ r 7snp5eiofz(97qs
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal spring (k =fiyjs/g vb2z ,p o2.h. 124 N/m) is struck by a hammer, which gives the mg zpi..oyf2/, hjvs2bass an 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 spt.fc2 pcjbf3 :ring stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity at32ct.jfcfb p :
(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, w uz2y,hut6i z2ith 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 strikesq(: .r;mo -3rr7jwedu;vpj yt a 0.600-kg block attached to a fixed horizontal spring whose spring stiffnesrr;e vp.jt3o ;qj-dur:wm(y7s 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 high br (,ejq/ubp cq+s;vk00+rl9 qab6x vblidge. 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 be 09sv0cvl;qqqkjxb eb,/(au r+6pl +blow 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 exacts kcy;4a09 : rzj*huesly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is toa b36u0f24wmt1fn fq 21 jxvxt make exactly one swing per second? (That is, one c b1wj 6 2xf3 unvtqfxmt1042faomplete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of xfe+ ,-)oc fxk0.80 s on Earth. What is its period on Mars, where the acke+,x-ox) f cfceleration of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendfo0w +;jzr -nu4*nu;iop o1u hulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the penduluhrq p) fd o+z)j:oxh:2m bob has a mass of 365 gram:p)fjqh) orzd x+:2 hos, and 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..+f ys upfdc/ length of 0.9930 m. If the clock loses half a minute per day, how should you adju/.su cf.fpy d+st the length of the pendulum? shortened by    mm.

Derive a formula forxh zbz 08.:;cp7fje5cf cqn8s pr)5gw the maximum 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 ysgh+s02 9y,wor4tx - -twzjm:pds8pne.b0 t is released from rest starting at an anglgn+02ps4szj.t y8 whtxs rtpymw- e0-:9 b,ode 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 th2pbyqplv l:mdvcp8 )79i x- (uat wave crests pass the bow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How iv9:y xv7pm qc8pplb(l-) 2ud fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz anmm0/ t bg665mjk*sia md travels with a speed of 343 m/s How far apask5ba6t6 0mmmjm/ *i grt are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and ag8w+u) 5;x rloq:v qv1600 kHz (kilohertz) and travel with5x8q :qwlag)vv+;ro u 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 waves in9hzejx* z)uxhg9 e1 (.y )ipc2 xrj.tv
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same e t*gn r2dxw k* s8sn8k)v+u8dvy*+vbblastic modulus, but one is twice as dense as the other. In which rod will the speed of longitudinab n v8bns**)u +*w8skd 2ydkr g+8tvvxl waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between taoq; 6ox48qffv th2n.wo supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one suppov;4ntqfaq of8h.2ox 6rt to the other?    s

  A ski gondola is connected to the top of a hillsjgakd2 s73.s8nr cd3 by a steel cable of length 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 it took 16 s for the pulse to rec7s83.3 ajrknsdsgd2 turn.
(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 so u4 7+j1j0 yvl*sp)areaptg- hip just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor lu*o) 1jaj-4p0g yter+ pavs 7directly 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 w(l 2,qsjjt/othis difference helps in locatinqjj lw,2ts (/og the earthquake “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 ca6i-.p llxm j6hg)zs:g9+hwk g n be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of + j gp-:m)l6hkl zwxsg69g h.ifrequencies), 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 ac:1 hy+fwgm v ++j8 i*s-cbesrn earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from the source?1grc+j sh+e fv:*-s+b mw8iyc(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured to b;( hjljk g3qn5w6zf, ce qzg;nwkl(6 jj35fc, h$ 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 samyoc0-kgq4(j s e portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of the two wk-gsj( 40cqo yaves?   

  Two waves traveling along a stretched string have the same l3/b/:pxls o ifrequency, but one transports three times the power of the other. pilox:l 3b//sWhat is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and downuqfelw;ee jt, 5 6w2;m a total vertical distance of 6e ;uw5w mt6e2 f;jqe,l.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (af:th7.f)a hq kgly63w9z,la f) Sketch the shape of y 93hh6z: at 7lga w)ff,klf.qthe 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 moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, what are the 5o1f 6*(o2cc o+wq+jh jwyx1vr lica 82b:crr frequencies of the fi lrhrj21cv oo*jirc+x(5 bc 8+2 :wycofaq61 wrst four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At wa7yuw+kjk rp: b/ja35 6bhf /ihat frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the stringj/u rb5ijk+yh:k a6/a7bwfp3 vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at ap*as xvx.n*j ( frequency of 280 Hz. Name at least tx*.(px nv *asjhree other frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a stringc g43orpt9tvq04 x0m8m; (x8e gan c/prvtn3r is 92m/s If the frequency of standing waves is 475 Hz, how far apart are two adjaccgn838(pe/tmt x4 ar4p;ogn00mrt3xv c 9rq vent nodes?   m

  If two successive overtones of a vibrating string are blg 1+ wxf4j,f280 Hz and 350 Hz, what is the frequency of the fundamebj1lfg ,4x+fw ntal?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance fw j v8pvp(-h)irom the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What( 8 )pwp-ivhvj are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibra):y:ioz p y6z px.j.ldte at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in t::o 6ij. pydz px.y)lzhe 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 it is me1 udwiz +t5 ru(2yp yv7h0vm)e7gsuq 1asured to vibrate at 205 Hz. By what percent should twqpyi5mut1 rsdzuue+ (2gvhy 7v1)7 0 he tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amp//eimzuv rl2yr -ef* 4.v2icb litude mechanical 60-Hz vi/ e vf4czei .2vu -blm*2r/ryibrator. 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 tx /ebiyc3wwsg ;0ogsxrj12y y938vv -he string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standinsg ;g3vr x 309s-8yvb ey1ijw/wx2oycg 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 justf6y6emf 10jgnzyu2d2o5trh1 0 l/pgu the right frequency, the water alternf 1feh ygdp1y l/u0z2gr 52 0mu6t6ojnately 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 wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary at,zv)) yzo9w within the Earth between two kinds of material. If it approaches the boundary at an incident angle ))yow v9tzaz,of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velocity changes from 2.8 maq,5z gnqf ,gea7 w),2wr nn4r/s to 2.1 m/s If the incident wave na47rn,wf2g wg)en,q,qz r 5acrests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling inorhoeo /s8 vk )g0x43k0s 0vje warm air when it hits a layer of cold, dense air. If the sound wave hits the cold air interface o xo 3v/v)e0j0sk84e r0ogk hsat 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 type x l;0fu6avvd2s of rock at a u x; vl6fvd02a38 $^{\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 about2t -t ei+ljq nxfw/n.5 0.5 m in diameter. According to the user’s manual, the dish has to be pointed in tt2 +ejn5l/if .xq-ntwhe 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 the Pfv9 0:ud0 kwnpib;xl csux 14v4 j1a5zacific 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, peop5b041jvsc9 xaflu0; :1 nu pidvwxkz4 le 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 stiffness conhzi+o/k r4ib7 stant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.o/bi7 +4rihkz ]    m

  A 65-kg person jumps from a+g +sdabur8b 7 window to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net brg8au bsbd +7+ehaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hanging spring. nt6ena: x)(f; )qz.qy;yul zj The mass then falls 33 cm before it stops and begins to rise. What is the frequency f;(qlyj t; 6.a)nxuqzezy:)n of the oscillation?    Hz

  A 950-kg car strikes a hugeb):8keb5de vszr7sh d/ 7er0zs 6p oy8 spring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant /d es7s vz e y)0kd:rh8 b7s856zpreboof 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 (rc l e,fly,hswez8uhi d84:704 bmom.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 (Fih c8mezd 4h7u :fmw.oiyrl8, e40ls,bg. 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 33-rexs)-nw zh3lj(v :n5 zpm phonograph record have a wavelength of 1.70 mm. What will be the frequzvn5s):hlnj e z(w 3x-ency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the,tgvk i:vc,vt gc9q00 equation x=0.650cos7.40t where x is in meters and t ,it ,:0 9gq 0vckvgctvin 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 withhlm-pm p,u5 7)xlid7t frequency f. What is its frequency if it accelerates at 0.50g (a) upwt7lm7-i5 udh)mlxpp, ard,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on tlmikb.l81t1w-1+/v rm)s n4fcgu zar he raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for )z.1rc8l-b umnvsrlg mwf+/ 41 1ta kia 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 392ltp9 xw33j2t c Hz (G) and 440 Hz (A).j2l w39 3tcpxt
(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 v.y nk7vy ti3h0( ykf6the 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) Isv7in( kyy.t vhy63 0fk the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and thd/ j1pej*5 zh5i5ayov e tip of each prong moves 1.8 mm to either side of cehoi1py 5zeja*5jv5d/ nter. 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 a-ez.dk 2b*paharmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contactebzd p.a*ak -2 with the board during the oscillation?

A string can have a “free” end if that end is att rij:4y nj3gsx0qwc) ,:hl g(rached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with oneqsr ng3xw) i,j:hly :( cr04jg end fixed and the other free.

  A “seconds” pendulum has a perivd:4 z u ynv:90 ;cdymtgpi0z3od of exactly 2.000 s — each one-way swing takes 1.un9 3ddz:0 :iyv4y zg;pc0tvm000 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 -i7yhsn/jb4 qfdc,u5 spring can oscillate in the 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 horizontal swings, and by wniy5s ,u 4cb7-qf/h jdhat 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 under9 kt *s+bj/hwt*vfy ;cgfiji4f4 *c5w a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the o+ ;k* cfc4ftt *w iwv*b4y9fig/j5jshpposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring,t84ea8u inckhbrv)te1d iut *1k9k(,l z1t j with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the ht)kt,vn a uz e8kii9(8 41tu1kjrde,1ctlb * penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. )vabs9i:xt)o1. jc u l h.c:xhThe steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at thxha :i)scb: c)lt9vh.x .uo1je end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which also gzxsx 4i2u 2lv b1-zli2s-x8c hives 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 vibrating on a spring, estimate the frequency of this vibrb4svhiz c8iz21 2-2lu sl-xxxation, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz