Give some examples of everc7y3t9tv7y:.d g n sljyday vibrating objects. Which exhibit SHM, at least app.tdy:v3j7 y9ns 7gc tlroximately?

Is the acceleration of a simple harmonic oscill:nrp309yobk a ator ever zero? If so, where?

Explain why the motion of a piston in a5lfpx j/ch)dt14j 9 npn automobile engine is approximately simple harmlpj n5h94j1xpctd)f / onic.

Real springs have mass. Will the true period and frequency be larger or smal:* xdqhx: /dp yiy-fu3ler than given by the equations for a mass oscillating on the end of an idealized mafxxqydui-*/ :p d3h:y ssless spring? Explain.

How could you double the maximum sp5ntsm,z:) z,xosp i( peed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hoo w7lbxk:mk/c0k of a vertical spring scale, and then is released. Describe the scale reading as a function 0/blx:ckk7wm of time.

If a pendulum clock is accurate kg*;1r 1*) vnzhmw adzat sea level, will it gain or lose time when taken to high ad1mzw avzh*;r) n1 gk*ltitude? Why?

A tire swing hanging from a branch reaches nearly to the gho/6jnksd;wm.1m +v fround (Fig. 11–48). How could you estimate the height of the branch usin dh +s /vmfwm6k1;on.jg only a stopwatch?

Why can you make water slosh back and forth in a pasghuf;/h a8 q.)j0x op;xnouk-(lb+ k n only if you shake the pan at a certain frequency?up-o/ xqgh (h;nx.jl+;sb k0 f8ao u)k

Give several everyday examples of resa+lqu/jp,hs *) v;:*wbmgr 9jtcmoue 8b0ie3onance.

Is a rattle in a car ever a resonance phenomenon? Expla2wwgb/k w.hzn cr) zmrjcka5 *42*v7cin.

Is the frequency of a simplv d(h 04q2i.d r.4fle vmxlvc9e periodic wave equal to the frequency of its source?0 .ldhv4cif.2l mdvex4q(v r9 Why or why not?

Explain the difference between the speed of cshummojc 3y613 33h. bxqkc3 a transverse wave traveling down a cord and the speed of a tiny piece of tyj.qc3h xbu33c6comk3h3 s1 mhe cord.

Why do the strings used for the lowest-frequency notes on a piano normallyps4uf,gfe.rud: h jt 0pccd9j7c 2c6; have wpp h ctju6g.d;0,c 7urj: fs 2c49efdcire wrapped around them?

What kind of waves do you think will travo8xfn88j m0 ehog ug 1jzn-3 vd6rrk*;el down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizong0 m 1odn-8g;fkjre8znxhr* 8o3uv6 j tally parallel to its length?

Since the density of air decreases with an increase in temperaobwf4s e gi2 k)iy5/4kture, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to goke fk244 5/bywii )svary with temperature?

Give two reasons why circular water waves decrease in amplitude as they traw1 d6+)+y jva0 yfkmisvel away frjy f6)d aw01++ismyvkom the source.

Two linear waves have the samejb)n ;v +l1ecjh s-j;h amplitude and speed, and otherwise are identical, except one has half the wavelength of th-lbn;j )j;jvh+csh e1e other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of cord1tk(rzlm wsijg;e ;hz;/x)k.c(c /jb as in Fig. 11–33, the frequency does not change (although the wavelength and vexc1jk;c (lsw.;gz rjtm;hkib/ e/()zlocity do change). Explain why.

If a string is vibrating in three segmentsv;py wi(+/kr3ftb x8q4sywhg )gzx:0, are there any places you could touch it with a knife blade without distur;0/3w p s wty+rbvghx kf8:q(y4giz)xbing the motion?

When a standing wave exists on a string, the vibraky/k2qg* 2s*ckqsa 9r tions of incident and reflectedq cry**ak/ kss g22k9q waves cancel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted welr 2.zubr,,)nu:hzes5 5lpfrom one place to another, how might we determine whether the energy was being carriedrlnu5s,.e,5z) lwr h2:bue p z by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitpmcer(4 ;qc)d08 ury*u.it hf ude 0.18 m, what is the total distance it travels in one peri 8c h;0dep (y muqc.rr)ft*u4iod?    m

  An elastic cord is 6+5qz amg f7kjpz-j0j)5 cm long when a weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k o0a+ gj kmzfpj j)-7zq5f this elastic cord?    N/m

  The springs of a 1500-kg car com 6-npa8x5z9 h0tsrl +o4asvj ipress 5.0 mm when its 68-kg driver gets into the driver’s seat. If 4j89h s-svl+npz5 ix 6a rao0tthe 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+x*ogeac3z-ztan5u 0 ) What a-xo*c e5 0z3zt+an guis the spring 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 f u jlhl:2 tof7* .u2o8mua;;qx1pc ojnrequency of 3.0 Hz when a mass of 0.60 kg is hung from it. ;la2cot2ln jm1.q 8u7o: jou*f xp;uhWhat is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at times t emt8 z-u8 e k5yj)ur)aul ,h8c= 0,teetrhza) u8)yk 85-ulj,m8 cu = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 vo(pq lk(b346pcf/3s w (s jdf0.25 g is caught in a spider’s web. The web vibrates predominately with a frequ j3v3fskfb/(q4scp( lw 6o(d pency 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 frequency of 0.8.ozz3n yp 1xi rpo89/8pea2 br8 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the value 8yz 31 xn28p ro/br9zppioa e.of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second with an ab k4;rw;bb4mp 0ilqn .gh8: zsmplitude of 0.13 m. Determinebi wbkb8 ;4gp0rzm.n4:qhsl ;
(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 zkds odln71 bc7 c6d(/z)y9 ujspeed of a SHO half the maximum valu6boy d(ku7jdczsz7 d ln/ 1c9)e?$\approx$    A

A mass attached to the end of a spring it o(1 *7jvm qp9q0zfsgs 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 spring 0.315 m. If o y+x n+c8bd*b wli5yaf6 l-(bthe spring is stretched an additional 0.130 m and -+(xbcy8nbw5a6yiblo l +d *freleased, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attachec:0 )8* abqpqjgg:ausd to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.02 :8: b qg)asguqa0c*pj0 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 ovwqh, ny(u; ,zf a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave thevu;(wq y,nhz , gun?    m/s

  A mass sitting on a horizontal, frictionlmw(*ce v.,c ehf.i/*3 dug)t8b z uayaess surface is attached to one end of a spring; the other end is fixed to a wall. 3.0d)h* .ca. *yt/ cvfz3u8 w,ueim(agbe 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 acbi hgc 5v-4-fbcording to the equation x = 0.45cos6.4t where x is in meterv ibch-g- 4fb5s and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the ener bmrk bi73. guzwj:a14gy of a SHO half KE and half PE? bigbk u 7r:m.1z 3jaw4±    A

  If one vibration has 7.0 times the energy of a sec6aqw3zx-k9pr ond, but their frequencies and wq-p3r 9xkz 6amasses are the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hangingm 2wxg(e04q tv light spring once every 0.6wtq42vx0(m ge 5 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 sprlbp 1,4 hyrn-f k-)nbrings, each with spring stiffness constant k (Fig. 11–49). W nl 1-4r-knrbyhf)b,phat will be the frequency of vibration?

  A 300-g mass vibrates according to thq p7vunnkdt 0k,-sqx t6y+t/4-ybu) x e equation x = 0.38sin6.5t where x is in meters and t is in seconds. Detp-,7/ ty4+qnk usv0byd -ktnu6x )xtqermine
(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, whahc;w7 +;(g0l2 gjdg ubys mx.u 0ba*ott 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 horizgh)lant-yn/v5d, )c wontal spring (k = 124 N/m) is struck by a hammer, which giv gna/v)-w5n lh )cdy,tes the mass 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 spring stiffness constant 305 N/m vibrateswf,xpsiee q4rf+so er,-2l jh3 f7r11 with an amplitude of 28.0 cm whrf w-f+hi3xf 4,1jeoespe1sr2q 7l,r en 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 sprinq7+ypwi2 dxnkw7r ghw;lz2jy93t m7 :g 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-kgvpriie) y:2/ e block attached to a fixed horizontal spring whose spring stiff y 2iiv/e:r)peness 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 9k) (m.05glykpswt ugmass 65.0 kg jumps from a high 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 the spring stiffneus klym w(59.g )kgtp0ss 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 exact;h k-wwza 6b0j2ax4tsly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exact zngjg1( xpnb:iui .,8ly one swing per second? (Th,g iub:n zn(g81.xpijat is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its periodqpx1 k .3 +z/cx )8jg5d4ppnwzmqc(m w on Mars, where the ac/ 54 k.31mzxc (wpqzm +gjpnq8 cwxp)dceleration of gravity is about 0.37 that on Earth?    s

  What is the period o7px m /2vq;hycf a simple pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulum bob has a massx)n 0rsqwn2-tca v: 5x of 365 grams, and 5tw0q -cx:vxr)2 ann sit 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 peyrq9z:up*qd :x+og3g v1,tozxdw* r4 ndulum has a length of 0.9930 m. If the clock loses half a minute per day, how sd4 drzotvo1py:3+g9x u* w:xg*rz,q qhould you adjust the length of the pendulum? shortened by    mm.

Derive a formula for 0ekz(0b re5vgthe 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 is released fromgcyuo 9/,y a.-td;w lwps 7u.z rest starting at an anglyw a,tgup lc/9d..wou-s y7;ze of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchored bo .lu27 poacanj92ej qij1s2.vat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast aaa2.j21 njj 72u9q cespl. viore the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed of ) liy8h,4nn ydyp5s/dfoup ,v1x4ly ;343 m/s Howod)fn;4yyl 8iu1vly5xn ph, / p,dsy4 far apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 8mqhb6ie8 1n qkHz and 1600 kHz (kilohertz) and e6qi1n 8q 8mbhtravel 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 lonzau dy 7n :nr+(34xdq0rrk.mbsef:z1 gitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but ongw,z3ztrsiv v;(n6 yig1fs - -e is twice as dense as the other.- gw1ii,vf vgzy; t3s(rz6sn- In which rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If th6f kupzv4*t, te tension in the cord is 150 N, how long will it take a pulse to travel from up *zkvt4 tf,6one support to the other?    s

  A ski gondola is connected to the top of a hill by a ste f 7z-bqy,q2u.vwby5 fel 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 observed7f5 u.q,f2vbwzyb -y q 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 su ;lqmpr avry j9jeak);z /7,c3rface of the sea. He hears a9rr7lm;a;z3 k ,/)e vqpjjyc the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an eag qw9z:i8qg f0tqj;)x rthquake travel at different speeds, and this difference helps in locating the earthquake “epicenter” (where the dis8z 9w:ij)g0qqg qft; xturbance 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 approximattfjbci (,v-jv2d 29pwfe t*.ted by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what fjf v(ett b-29p*wtdic j v,2.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 ampli.cg- hqw.73x zlani) a9u p0m.8nevvntudes, of an earthquake P wave passing through thn. p0mixna.wu 8g-av 7v9) .zlehq3cne Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthqua oiif8s;9+:1f*yv mqddq. pqe ke wave passing through the Earth is measured to be v:1q i;dd peq8q.sfm9*y of+i$ 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 portio9 se (, d -cw*,3jakme8mqqf0tvlo6kmn of thesmqkf ,9a6 md8 cqe k (jovl,m0-wt*3e Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string hxap9op3i45b l ave the same frequency, but one transports three times the power of the oth4ppx9l3b ao5 ier. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move n n b7jf6 /de+c .pxo8ia:+hjdup and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KEaf 8ox/ nb idjd+h:j6+ep7c.n change?   

The two pulses shown in Fig. 11–52 are u.:x6vp dee4ke*acm8ftu0g 2moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of thegma ue e:2 fu0tc4ke v*dp.x86 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 vibrate3w*vm/+r tz,)1kkcuh .sugmt -fg5w ts at 440 Hz as its fundamental frequency, what are the fkt / tf ur3z+*w 1.c5mmtkusg,gwvh -)requencies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 2 ev,mne xb1)y80eh *2jem/o cf94 Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrateso,2x1 ef)e0nme yh cve8mj/*b as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz. Name at.otkmjj ow;+5c-ld ).kn zr7v least three other frequencies at which it will ;k 7jz+5 kt-ol.nocvm.r )djwresonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of wave,lq7q. ,nybch;-lflcs on a string is 92m/s If the frequency of standing waves is 475 Hz, how far apart are twohq.-,cq;yc ,l ln 7lfb adjacent nodes?   m

  If two successive overtones of a vibrating s3tod row/0vax6ube-vk 91hvbn-.7d ltring are 280 Hz and 350 Hz, what is the freq6-x ev 7tol.wbr nboh0kv3 9d1-v ad/uuency of the fundamental?    Hz

  A guitar string is 90 cm lon ho 0ej6;ou 324fiy8czu-rum lg and has a mass 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. uez ; fhumojic-6lr3 yuo 4280What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it i se+nlqedc+3hr2xb o1i6lb/ 7s measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correctbx/+ein3qdrb o2el 7+ 1 chls6 the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to6u7v78tjtbs- i uu-9ih3c ej s vibrate at 200 Hz, but it is measured to vibrate at 2ji7b9hvs e3 u-ju8itc7 u6s-t05 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mech,8g7qorkm z3; mfi*mg,k 7osv anical 60-Hz vibrator. The string’s mass,k3g*rvos,8; gif 7km7m mo zq 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 adjuyee/n pg l)21(-to lxfsted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standto)e1p/e - y(2llnf gxing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the watervx -50ot5eqwl back and forth 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 Heo5q-x5w t vl0z. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes ac.sdcj*in/lp yz/30 gh)hc .l boundary within the Earth between two kinds of material. If it approaches the boundary at a/chd p chi0.jgs.)l3cnlz /y*n incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where th p;hvj );x9zwpruw35ne velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests mak;pj3wz;hv 5pn9rux w)e a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hjoybkh9:ark 0p8q 3e 9its a layer of cold, dense air. If the sound wave hits the cold karj938hqkbp yeo :9 0air 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 siu. c3tgvf/m8)oe dd n. 04naltrikes a boundary between two types of rock at a 38o4ean.8t/ ug3 d fmndilc)0.v $^{\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’uvg1v w n9k;;ks manual, the dish has to be pointed in the direction of thev1 nkv;w ;gu9k 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 73c) m6ek eq;qn50 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and n 6qe;m)qk3ecwarning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper1.dc vuf zvf u*/5p3rh has a spring stiffness constant 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 u*hdfrp/3 uvf. c1zv5 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 tqaszz 61f7exr9 *8m 9hjw/b aeqeq 5)ohe net 1.1 m. Assume that the net behave* )bwh9s aej9817a rq/mz eq6zx5eqfo s like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hanging spring. The mass*gemt2rrl)o6 5 a8wjkxv7 d7c then falls 33 cm before it stops and begins to rise. What is the frequency of the oscillation? 8v g)k72mcoj5t le*6wr7ax dr    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 1utp*9 cpa *b,vf0klm+ 1–54), compressing the spring 5. t0bv9*mp+,uka*lc pf 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 (dhlghoa0c5, q6 um0)cwiameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starqha 5hu, om)g060wcc lts 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 fwfsu*. a1h+h/wj u5z h (jmgx7la9t;rrom the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequencyl/h1uzw5 mr(hh+a xa wg*.f 7 tsj;9ju of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t w, zdmgui9e8lj88. qqr //7 :pgzeuioehere x is in meters and t in seconds. Determinei.g9p/mu8req8jle e87d/: o,g zqu zi
(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 :yvdq6xks :lo 29b )zlf. What is its frequency if it accelerates adx 2yb6s:olvlk : z9)qt 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raft /)q9zag3bjmmy. gi(xs14 hbw ; c)vfu, it sinks 4.0 cm deepeqv4u cx.b) i f ygzj/bh1w)a mg;ms(39r into the water. When he steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrumd tfq4*yz l8p2r5rk) aent are tuned to play at 392 Hz (G) and 440 Hz (A)rt a*4fdy 2zk)5 pr8ql.
(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. knwlbg0ej6e9 0 /n;kc9a ;rlxDetermine 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 ewlj0;;le/rc0ka b xn gnk699 sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 H1xhs ;w(yr:n0ybm/vmkc *p/ 4b s) dqqz, and the tip of each prong moves 1.8 mm to bnyk*4/cm mv pdyh;x r /wq(qsb 0s)1: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 mo5 5/w*fyci ;gb0qdvsn1jl 7sqtion 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 nfq/15isl5q;b0 7vy*n swd j gcot lose contact with the board during the oscillation?

A string can have a “free” end if tnqrz*rzk1 z 2a2tkd62hat end is attached 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 s*n a1rz zkd2kq 2z6r2ttring with one end fixed and the other free.

  A “seconds” pendulum has a pew ag nbg):r0h6wd4u v1riod of exactly 2.000 s — each one-way swing takes 1.001vggw)adu: 0 wbhn64r0 s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the verti a2 0iuo2vmwa/cal direction or can swing as a pendulum of small ao vim0w2u/a2 amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: 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 tensionn3q*l7y3 okw*ei45 z /fwjlcvs ;as/k of 255 N. A pulse is generated at one end, and 20.0 ms la3 lf* ;v*i 3wywso4ca ns/jq5kel 7/zkter a second pulse is 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 with dn4mfdy: w h z;2;+f5g1 gayotspring 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 penny tod wh:15gnzg fy42o;;df+tay m just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cable is k40b.) qa2gllim e5vptn51fj 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncingn1lj0 lbite. f2 gk)mq54a 5pv 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 a plate as shown in Fit(qwxa.x ib2k3ocl 3)yml :v9g. 11–58 (which also gives the dimensions of the block). You push it siy923tmol x .x(c3vaw: qbkl)ideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz