Give some examples of everyday vibrating objects. Which ehsd pkgz4ajv9x 6d;*t z8fh.7 tkpzwcc9p:40 xhibit SHM, at least approxihc4 96d8vwck;ts z0zfx74h *pkp. zp9gda jt: mately?

Is the acceleration of a simple harmonic oscillator ever zero? If so, where?bhevpdpjt/6e0,.x 1p

Explain why the motion of a piston in an automobile engine is approyqvjoqudh ( xctp4m3*+: oj(8ximately simph: (joo uqc +4( xqvpm*dj83ytle harmonic.

Real springs have mass. Will the true44wnlh6yx*c( h+b rlg period and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized massless spwn4h xg 4 lh6*+(cyrblring? Explain.

How could you double the maximum speed of a simple harmonic oscillahy9*e95; p9bi ivv d+9mpum nitor (SHO)?

A 5.0-kg trout is attached to thep:avzhn ( d8*zk1id;b hook of a vertical spring scale, and then is released. Describe the scale reading as vd;dp8*na zz: h kb1i(a function of time.

If a pendulum clock is accurate at sea level, will it gain or losemu.g2qmq 07mlu:a y o; time when taken to high altitqu0 u7ml2yago mq;.m: ude? Why?

A tire swing hanging 6/ bcz- w* yezgnql2h:from a branch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the brann/ 62 gbzq*ecy-lh w:zch using only a stopwatch?

Why can you make water slosh back and forth in a pan onl ifgv a 21e23p4xzn0sly if you shake the pan at a certainvs 4ag2xif 0e3np2 lz1 frequency?

Give several everyday examplesb,8j zrh 3x7:ib :yicq of resonance.

Is a rattle in a car ji bvw;46b-g dever a resonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency oqhfp (w9 oh(+ryva( u;f its source? Why or wyw q(p+a ro9; fh((uvhhy not?

Explain the difference between the speed of a tran 2hx mooo iq *5oa;elt2xjnz up7g:3)3sverse wave traveling down a cord and the speu2x*3eol:x ap5)qo7i gmooj 3n2; z thed of a tiny piece of the cord.

Why do the strings used for the lowut+ ;63 ijpmzq o.mj/)v0 cipdest-frequency notes on a piano normally have wirezdju t . ;pm/p)ico30qm6v+ ij wrapped around them?

What kind of waves do yo/c+n14z4; :u ; xobps ntni9ejl z;lawu think will travel down a horizontal metal rod if you strike its end (a) vertically from abovetezx:1z;n4b;u+9wo /ic jn p;al4nsl and (b) horizontally parallel to its length?

Since the density of air decreases with an increasj.w ljt c ,k ;b,qhw/acp* b-ow:ui ujx5+8b,ee in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vare a cj/bwt-ubl+ ,:x5o.b8c*,wwjiuj h, pq;ky with temperature?

Give two reasons why circular water waves decrease in amhok ozp/6t63*e7nmnti5gw*m plitude as they travel aw*5gt n/3 nhp6km7toe6 mi*ozway from the source.

Two linear waves have the same amplitude and speed, and othz2kc600)o; (bzs3 sklzfz mdsb. ( qekerwise are identical, except one has half the wavelength of the other. Which transmits more e06kf ke(z2zs )z.0zm(s;c q sblbkd3 onergy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of cord a i,o3 je.lmed9:;pvros in Fig. 11–33, the frequency does not chang3 m:e jdipv.o;or9el, e (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places t2hoh*;vxg-a/ f7wr k you could touch it with a knife blade without disturbing th*;rh awk/tf x7og 2h-ve motion?

When a standing wave exists on a string, the vibrations of incide pt.a9qwndrj j/e6,v+ nt and reflected wavep./, rdjetn6j + vwqa9s cancel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to another, how mmc20lg: vuk0w6 c*fp8 btd1 zaight we determine whether the energy was being carried by particles (material bodies) or by wak6m:pfzbv l 1ca t8w20g *c0duves?

  If a particle undergoes SHM with amplitude 0.18 m, whawnka7 g j dqd*1mf(;k,-szs/h ;/ ewsat is the total distance it*s;zd 1/(-/a;w,q mw ksgn7ef adjshk travels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs f xu2qrf: +x u;9yz-ruirom it but is 85 cm long:-2f xx+y rzuuqir9u ; 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-kg driver gets iy0afvzboz4 t qv-wq9;17e)n xnto the driver’s seat. If the car goes over a bump, what will be yf e q9z xb71z0q v)tavow4n-;the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (a) What h7i91 5-sa9 crbyvbq ca1+ 4mtgurj n3is 1ca hbyjir +utqnb7csrg4 9va-913m5 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 frequency of 3.0 Hz when a mass of 0.60 5qr z-g mmdfmzk049x ehk08: kkg is hung from it. What is mmezfk0q m:k8r0 4xdz9g5h k- its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of tiq zrox)t8b,9q zp6- xk0p7zche mass in Fig. 11–2 at times t = 0ckro 76zt, xp -9qibx0p) qzz8,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caughtul4 ; 8hbfy2vu in a spider’s web. The web vibrates predominate;hb2uyuf8 l 4vly with a frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vib +tn f7e:ulqu1rates with a frequency of 0.88 Hz. When an additional 680-lu:nut+ q7e f1g mass is added to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per secon9ky odzof1l 9.3d gmu+hrrqv:fq5h:5j*stb 7 d with an amplitude or ou5q.gkd7s*5:zhlj 9t hbyfq3 +9m:d1forvf 0.13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equbgrqw2 nrt g43(/m2 loilibrium is the speed of a SHO half the maximum valumog 2qr2 w/3rlbn 4t(ge?$\approx$    A

A mass attached to the end of a spr zulj01 1ie) ,xfxv*xeing is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. If the spring is stjwr /: 86 vzvoy-okx6qretched an additional 0.130 m and released, how long does it take to reach the (new) 6 zoxryv/wj8-k6 q:vo equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with 6 fqw5v9;l wrmkt 59tospring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m fr 5 owqwrftmvkt6995l;om 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 of a toy popgun 0.200 m to ) n1ntlf7 jsy9cjv g2s49iqc7,sp/s c “load” a 0.180-kg ball. With what g42pfi1 nvc,9sssl t9 j)7ycs7j/ qncspeed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to on l)s4lbsgc r p)exd 0cr5hrv2d) ,5(sne end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. 2 b p))lv5en (0scrs d)x,dshcr5lgr4 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 = 0.45cos6.4t where x is in i od 1r4quboe1*x 8hka0)xss2 meters and t is in seconds. Deta02 )d*1xq1ho rsiox8sebuk 4ermine
(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 thepqma 2j rox9;;h a0k7e energy of a SHO half KE and half PE? jka72hraeq;0 ;x9mpo ±    A

  If one vibration has 7.0 times the energy of a second, but their frequencies anyzb4n s7a+k. wh er mc 4q2(tq*0tsj2nd masses are the same, what is the ratio of their amplkjsbwzaq h qstt0 n4m e2rc472.*yn(+ itudes?   

  A 2.00-kg pumpkin oscillates from a vejz) ,h jfhe(*kn4+e5n9lp wak rtically hanging light spring once every 0.65 s. p4kkeel nwjna+j,z)9 (*f h5h
(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 sumn b 80t4 hw(*twgga,1n-x ksgv ln;/upported by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–gnv(mgl/a ts nb,4 h g*01;t-uwwxk8n 49). What will be the frequency of vibration?

  A 300-g mass vibratess .+( p v3+ sk(uzu2j1ttxl*3odszedz according to the equation x = 0.38sin6.5t where x is in meters and t is in seconds. Dzxd3u o s(jkuldz32.1sp *zvst +e(t+etermine
(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,pk:z 7rily ii5.gr71c 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 horizontal n;sr+c 0fsh zihs3+(u spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed 0c h+(hzsr+i su ;s3fnof 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 Nhi(mmjv2o f -;/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 velocityfm ; m-h2voi(j 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 u gski0zdyk r8y8 69u6to two springs, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block bylm9gb05. h iattached to a fixed horizontal spring whose spring stiffne hl5b0my .9bigss 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 l j1bykp-z23 jkg 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 bejl-3 zb1k2yj plow 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 exacgeb2p/ 0n q cnie78quow,jw - xd;uk,5tly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swing j1+ ykyy2l ,ma );qk,psdrih6 per second? (That is, one complet)jirylyds +apk2yhq,k16, m ; e vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its perioaadcn /-w-jj1 d on Mars, where the acceleration of gravity is about 0.3n jac/--j 1wad7 that on Earth?    s

  What is the period of a simple pendulum 80p+d 6phno)r36 bom ,yc cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is.l 30 eetpnx+ub jfulf98 wem.(s d9l36+npua 0.760 m, the pendulum bob has a mass of 365 grams, andalx9+tb0lum6sn puejdn + u. 9 ef(ewpl 833.f 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 p4k qx311s//f*w l mt c*1 rpv5jfpnerm. If the clock loses half a minute per day, how should you adjust the length of the pendulum? sh5 /wpftp/ j f rqnsp3*k clxv1*rm114eortened by    mm.

Derive a formula for tr vl mw(v1xbdq tn3r0f5z.c+hv b /.b4he 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 from /lj7j s3szg;hyn 6w: ;jq7wdzrest starting at an angle of / wzj;l3s;g7zh y:jq6snjd 7w 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 boat every 3.j)n k3)ps hhsvs-8s7y0 s. He measures the distance between two crests to be 6.5 m. How fastv ph 8yh )kjn)7sss3s- are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a spe. 7 v(zqhz wz,5d;dicoed of 343 m/s How far apart are the waczv .q7wzh d(5odi,;z ve crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kiloherghn6pey9vp,gx0. 1h jiq o,q 5tz) and trgh qi, 5qve hp0oj.xyg1np, 69avel 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 lon ea.8 g: qqm zb/rb.(d58bzffngitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as dense asls.lw a5 rq +-gqpvi4p pdr2;hp ,c,4v the other. In which rod will the speed of longitudinal waves be greater, and by,lhsrwiap 4,2 lpv.cdrp qg4 -qv+p;5 what factor?   

  A cord of mass 0.65 kg is st1 x9*krie)zvxnoxt.x11 6k zp+j+ grgretched between two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one support to the1vx 1kpnrx+xzr*xz ie9 6o +1tkgj.g) other?    s

  A ski gondola is connected to the top of a hill by a steel cable of lengl/q7 x:ekcsi1 qa po8pz97 :wvth 620 m andleoqi 9q7k/pv8 :7 sx:wc 1pza 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 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 hi.u)620t5 fcft x8vbzrdvnl/ eps -f:zs ship just below the surface of the sea. He hears the echo of the wave refler 6f.d 5/:2bzufpxts0fe 8vvl) tnc-zcted from the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different sput. r)x 7r* n,lzi1rpweeds, and this difference helps in locating the earthquake “epicenter” (where the disturbance toi*7rzrrx ,u .twln1p) ok 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 sinrn 98 xnsptf4/usoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, whix4npt /f98 srnch actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of an6+ g/slc hhxv1 earthquake P wave passing through the Earth and detected at two points 10 km /shhg x1+vl c6and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through tha, pyz9z qgyx87 nu(5ee Earth is measured to be y uy 57e9aqzzxpn8g,($ 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 th0w:n8 o 7roj;w9vzigwqu+e(jrough the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of the two waves? ; +njwrqu9ew zo g7i0(vj o:8w  

  Two waves traveling along a stretched string have the j+phdqhi r7*nq51j ekoz*u3* same frequency, but one transports three times the power of the other. What is the z 1jrnhjd *upo7e3q+qik*h5* ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and doxkuuxc,1 ql ;4wn a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease tkl4xux, q;1cuo 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. +vr*,retwythl* hq6iei fxf1. biv+1y *y ,+j11–52 are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pasr+ ef yqbif.i,vtj r+e,*1y*hvh+x y itl *w16s each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as i tqaw*exb)9 ) 1:d*se1toitx ots fundamental frequency, what are the frequencies of the first 1o1xsdxow *tbea )9tt:e) i q*four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what io5/t0cxmdqwzg+m o sp; 0+8w frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a st0;+i8z ps5g+ m/0w c qodwxmtoanding wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz. Nam w3b *;scebnsor 6c (b mhj+379v8xsoxe at least three other n9s6*x7b(oje;xch3rmbs wc8sb+ v3 ofrequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of stw98xqd q(: k wajpt8jw*v28xwanding waves is 475 Hz, ho:kd*wqpx jj qw9v(2wax8tw8 8 w far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, wfy*242u1p u vl/uj7h ob,)raw awoi5.blb mz4hat is the frequency of the funp o.b u2 bbz5/ m,aoru472w4livy *jalfu1w )hdamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The di- ip,frtf b*1gstance from the bridge to the support post is L = 62cm and the string is under a*bt,r1g f-fpi tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar str-gkj7d 75 bswfing is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 7 7sjfdkgw5 -bHz. By what percent should the tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200bz r o3syym 0p:41s9tk Hz, but it is measured to vibrate at 205 Hz. By b0tzy9y3: k o14rsmpswhat 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 mechanicalf gmj* 9adj s2d3+iby: 60-Hz vibrator. The string’s mass per *a3bjfyji9d :mg 2+dsunit 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 m z,p4yeqos 73of the string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many y,37q pmoes z4different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the right frequency, tz2 tbn *7p mzi28trld4he water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the ndm 84t2 z*zp2lbtr7 ifrequency 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 km6s qd e1wpq.t2 b dyh(z2de46tud/ wf:/s strikes a boundary within the Earth between two kinds of material. If it approaches the boundary at an i ewye64 :dhqwdf6pd(s2.d 2u 1b/qz ttncident 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 undes/rgsy6z kzz/idw c5x+() fh4rwater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests z4) 5 x w+i/rdz( 6fhgk/yszcsmake a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm a o 0q umvr xppo)msb:w*z 9r1y689e i+.p:fythir when it hits a layer of cold, dense air. If the sound wave hits the cold air interface pe0:rxf)9p 6tiymr: .ou 1 hmwqypbv*9o+8zsat 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 tyahw8;/qrkcn :pes of rock at a 38 8/hrk;aq c nw:$^{\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 0.5g,efd hk9li0q3 cry8d(q +dp,u68tij m in diameter. According to the user’s manual, the dish has to be pointed in the direction of thdq,lr0 t p3i8 f gi(h,u8qyj9+dc6k dee 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 t2q:l to /yqn.ek.m4;atf.xoPacific 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./e:qlo.2ta4omx .tq;nfk t y? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spr3o*ai sq1q+ de b 3:fhu4dww3ring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall atuq3fqowde3s4* +d1: whbira3 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 thu,2st6s 1a 8a kcqtawh)3nd c3e net 1.1 m. Assume that the net beh68 adahq 3ct su,k w)t1n32casaves 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 zv3n s asage nx70fl7*jd9z-2hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of the o7j7lvgnnd z-a0*feaz3s x29sscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), comprempyxmvb h,0v7wa4;a i9*x p6pssing the spring 5.0 mxaipwphv x9b0 p4*m a;7, mvy6. (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 (diac,a, : e)apoji u.vhr0meter 8 cm) at just the right pace of about 1 step per second, the coffee sloh.)v:j ua p rci0,,oaeshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of aiy:3e f qt8zqyp5u l+7 33-rpm phonograph record have a wavelength of 1l qf5z :+yui3p78 tyqe.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates ac*4fd e1t9)i +k nqo,-*uvutcdu+m dw ycording to the equation x=0.650cos7.40t where x is in meters and t -*tw+u1t,u q) odeyd+u i*vdfnkc9 m4 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 f. c3;2e ;myrmsd*wp3 vj What is its frequency if it accelerates ats*d mr;we3j pv3;mcy2 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(34hn;nbvwr o9s v3qx raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for ;9xh 3(vw rqnn4obvs3a 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 playv rh yhfy38ya9x5wv (: at 392 Hz (G) and 440 Hz (A)9(rv w85ahy: vhyyf3x .
(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-partmp p,h 4g*xwc3lk41/ cmfk/ pd cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy sectionc/g kmcwp fhp14l *kx34pm d/, versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at awguh*9901zlfl) x k;vii;7xbes vbl 1 frequency of 264 Hz, and the tip of each prong moves 1.8 mm to either side of center. Calcuv w;lsbk 1l zv991xui); hb*l7gi fe0xlate
(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 f2-y qs1t x0)ryq6hr*m.+sc / oiqs dhharmonic 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 contact with the board durin /ds hcqys fq i*- x2r+6t)q1hos0r.ymg the oscillation?

A string can have a “free” end if that end is attached to a m5rgfb:(u3, - s bosndring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one5r -ugmf dsn(:b b,3os end fixed and the other free.

  A “seconds” pendulum has x:q2- vz9ccvz a period of exactly 2.000 s — each one-way swing takes czc:x -2qvv 9z1.000 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 d rx/9x3j +na6p r6lcaspring can oscillate in the vertical direction or can swing as a pendulum of small amplitude, butr/pxan3l+ drja6 69xc 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 un, by-ewx2t(b pder a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where willxpby b-(tw 2,e the two pulses first meet?    m

A block of mass M is suspended from a ceiling -s4rmib,*n8a xkfux44btqt7 ic6y r- by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maxitnfi- , uq 4xi 7-8tr mbb4*y64ackxsrmum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane c;l( 0a/7o: fdeb2j dj3vux qokable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car o(e dkjo jv/0buf7d :a x;2ql3bouncing 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 onawnn-sre)yzgf jc+- 5*3q )al a plate as shown in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as showcjn sy 5)narf)+wze3g-- lqa*n, 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