Give some examples of everyday vibrating objects. Which exhibit(z*l1h.u,xt f jyr glmg;gh 7+ SHM, at least approximateggty.jr+f(, ;l 1hxm*7 lgzhuly?

Is the acceleration of a simple harmonic oscillator ever zero? If so, i)z( rrz cl.b-where?

Explain why the motion hcdj1zvt:99 t s-ur/ aof a piston in an automobile engine is approximately simple harmonishdtrta /: u919jc zv-c.

Real springs have mass. Will the true period and frequ-2- dmmc9noe58wfki z ency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized massless spring? Explaiz 9o e2mwdf8cm5-kn- in.

How could you double the maximum speed of a simpl:j83,q 14 c xkdy:mlaz1daqhoe harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and then is mlmyzvn2s0;*j 6ybh i 08eva,re m;m 00h,2lsj v vyn8*zb6iyealeased. Describe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gaimp;70 l apng:i /3osckn or lose time when taken to high alti;kl0o7n 3c/:smp a giptude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fi qu* ,*dht5vkc/qhqpz,8aq ,yg. 11–48). How could you estimate the height of the branch using*hqvq,q a u*z8,,cp/5hytk dq only a stopwatch?

Why can you make water slosh back and for:el u+fi8w 26lpdno b4th in a pan only if you shake the pan at a certain freque2l +edo64ilu8fp w:n bncy?

Give several everyday examples of rl yr.e0m38al6 g) vao,yi 8blpesonance.

Is a rattle in a car ever a resonance x), scrg7y x 2yl)x1jsj7lw:jphenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of its sou :r se2-u-6plrb ni(eprce? Why or w-6-sebneir( l u:ppr2 hy not?

Explain the difference between the speed of a transverse wave tb,ig uj,4*nkt raveling down a cord and the speed of a tit ng j*,bk4i,uny piece of the cord.

Why do the strings used for the lowest-frequency notes on a pianop x n6b/9g3fkrz ctnb c**so;91ox2ty normally have wire wrapped aroundntg/ spc1nf29 orc9zx o*3 *6tx ykb;b them?

What kind of waves do you think pm.: i62yot nflge66bwill travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizt 2e:6l6ify . gbpno6montally parallel to its length?

Since the density of air decreases with an increase in tly7gyo k)ba5a; g:x5k emperature, but the bulk modulus B is nearly independent of temperature, how would you expect the 5ylxako yg:7bg)5k ;aspeed of sound waves in air to vary with temperature?

Give two reasons why circular waterc;md s-6hmkc b r-l2+i waves decrease in amplitude as they travel away from the sourm+r-kihcm c-6bl;2 ds ce.

Two linear waves have the same amplitude and speed, tmbbb4s+) g*aw :y ut(and otherwise are identical, except one has half the wavelengbw:u()s y4babttgm* + th of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary betweeqztlr4t9j1 v,,i(v (et ;k 3jfcwdz;y n two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Expla c4( q l vtzyjdt19jevfrz(w, t;i3,;kin why.

If a string is vibratingi iau9y/pc 0:djai;6r in three segments, are there any places you could touch it wit:ic; y6 dijiuaap0r9/ h a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incid /(e kqsd5om5went and reflected waves cancel at the5kwq/ ds5me o( nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being tran8u 8f 8 0v/ :y(g.gpnnvxpxmoyd08mp xsmitted from one place to another, how might we determine whether the energy was being carried by0 8/08.x8xuyg p8p(gyvmmdnnfo v p:x particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 mfatu9 vr osu6 k:ws67/, what is the total distance it k 6v:auo wt9sr s7/fu6travels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but is 8(n+e cri-dx .h5 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of thi(.hr nic ex-d+s elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driv n rl6 lrl7axh s5jprvu.5rl6ka.(h -9er gets into the driver’s seat. If the car goes over a bump, what will be -lv x6.r9rph7l 5(k5lu.nljsah6 r a rthe frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (a) Whsp(z(s* -xmjhat is the spring st*-j pzxs sm(h(iffness 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 Hzm 22csnp m1ew* when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg h1*pn cemsmw22 angs from it?    Hz

Construct a Table indicating the position x of the mass-j0 e bk-(-sntqefe.glm5h8n in Fig. 11–2 at times t = 0,t0-8eqsgbht-f 5n k(nj l-.m ee = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web. The web vibrates predom k:z3mxhqqit/k+,bp c: .:h oyibz3:p.m+ ch:k o,h:xiqq/ky tnately 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 vibrates 0d-na, fwmiw+ fs3a84k2ihz m with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0ai-m f+n 0imhwsf k28w,z3d4a.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 second with 28nw jy5reb)uan amplitude of 0.13 m. Detyjr)2 58 webnuermine
(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 spee1ltmje ys .r -;l+cqk9d of a SHO half the maximum valleq1 t+k -r;9ls cyj.mue?$\approx$    A

A mass attached to the end of a spring is dwx* hv fe;s3)rgo4l/6 ay ;8uncgyb9stretched 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 spuk.6os-lvx /e ring 0.315 m. If the spring is stretched an additional 0/s-o. uxve6kl.130 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attachedh1ir9bty ua+lgq9v *2oi q118 di6kau to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. Whenqo 6lib*a ahidq2 irk91uu1g+v1t 9y8 the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring ofxl0j7;zyq +i- ;oxsa c a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will tc+ i xxoa7jlys;z; q-0he ball leave the gun?    m/s

  A mass sitting on a horizontaqmp -qt:7. risdy-a)v l, frictionless surface is attached to one 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. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceler yp: vs7)rt --.diqamqation 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 = 0.45cos6c.,c zb0c (lwyf79zs c.4t where x is in meters and t is in seconds. Dete,.csb079cf zl wccy(zrmine
(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 equilib4z/xjzu2h+qo 9b k 1umf6) zsxrium is the energy of a SHO half KE and half PE? ± +/9u)1 k xu6qo sbfjh4 xzzm2z   A

  If one vibration has 7.0 times the energy of a second, but their frequm1 5,yudwfv 6bencies and masses are the same, what is the ratio of ,6wfdmu5y vb1 their amplitudes?   

  A 2.00-kg pumpkin osci8* h. fmq8 qg-erteh3 wg4ys9ellates from a vertically hanging light spring once every 0r*q. 3 ey9e88hh4-tm gsqf egw.65 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 vertical9 w:y00wcx r upgta)y:1ph7yu springs, each with spring stiffnygu yp0u7c:pat9ywr w x )01h:ess constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x is t-4m9a; vn*jz v7.kzxm p h9igin meters and t is in seconds. Determinnjv.p -gv z4*9zx7 m9t; kmihae
(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 i(/pwir*6trruqt-,+ m6l k j o7br+ qsis
(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 = 124 N/m) isy ju09umghi0 sn62tptqjoju -,2d: .c struck b9gj: u2 2jd-jip u,00cumyqtot6.s hny a hammer, which gives 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 9w s9j 9o1m9y:gdgnk iconstant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 ko91yk: d9 9nj9swggim g 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 spring stifg//zrr0.b //nh;g0pe.d fjl eube4 dofness 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 attached to a fixed horizontalog 5zhvk2v(c xcqah3:r:--f s spring whose spring stqa-:5(hhsvzf-g 2 ccxo:3kr viffness 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 bridge. After reaching hic0p;+ dajy6 cbaof* *gs lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unsp c6bc aaog;0 jyfd*+*tretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 60 s. What is r q:z q.8.oy4 lo;yxpiits
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swinnqgeq/b+ ,e0rg per second? (That is, one complete v/e+r ,0bqg eqnibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on vi+0k rxj p0e-1 yqt:sEarth. What is its period on Mars, where the acceleration of gravity is about 0.3ip vqrse yt100-x:k+ j7 that on Earth?    s

  What is the period of a k27jk . klv*d s6 xm:1ac0wbjlsimple 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 0.76 +obfbmy2,.ftp03 f chl)l fecjiv 4290 m, the pendulum bob has a mass of 365 grams, and it is released at an angfl3)oflb2+49 itfcjcy fb2m h,.e0pvle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 m. If the clock losez.zw4wwx f x9- br k wcs69d*fh, k.rumg**5dgs half a minute per day, how should you adjust the length of thebr9zw6gcw kw.x *,zgmf4 5. xwduf9-h**d rks pendulum? shortened by    mm.

Derive a formula for c,cfj5cp;qgn ug 5,b+x9cy d9the 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 at4gu.fiab p1b5 a frequency of 2.5 Hz. At it is released from rest starting at an angle of 5u a4bb1fi.gp 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 w75*rpr52 xgpo3e cu4 m2owglr ave crests pass the bow of his anchored boat every 3.0 s. He measures the distance between two crest*eg r roupxgpc2m2l4o 3w7r55s to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz24q 25szzra syfke)4c and travels with a speed of 343 m/s How far apart are the wave crests yecr5s s2 q z4fk2)z4a(compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600x,s9i-/,oyw;n2p vq us*cp m(kz:oix kHz (kilohertz) and travel witw ispn29-u/vspm,,xi* ;ox yz :okcq(h 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 ini4ur 7+v 7g/i7tnq 3dj5.zkfqqlfb2y.n2 ptl
(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 as tbi.;w-o q7v)ph w )vyphe other. In which rod will the speed of longitudinal waves be greater, and bv;owhpq i.7) ybpv) -wy what factor?   

  A cord of mass 0.65 kg is stretched between two sux), 1b qb-w xkfv1vh5vpports 28 m apart. If the tension in the-x, 5)kqfbvb x1wvv1 h cord is 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the 0l3:v,in o-gczwwn l+ckz 333j+yrvf top of a hill 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 theg wyz,+zf li333n +rockjc:3l0v-nvw 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 sidw7;y czfay,fc: fdaam((6 ax)e of his ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directlafd cy7((6 zyfc)af :axw m,;ay 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 thi1 u-q2juwei :ps difference help: p uuj-iq21ews in locating 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 caj 6sn4c*1j1 ndzkscp )n be approximated by a sinusoidal transverse wave. Assuming a frequency*sjs4 z6d)pn kccnj 11 of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensi/p run :zizfmfh7 .0ee3b-d+aties, and (b) the amplitudes, of an earthquake P wave passing through the Earth and de.m3 n7pdffz i/-:rzu bah+0eetected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquakekt 2d k id:c.qe7u88gk wave passing through the Earth is measured to be q7:kd2iutc. kg 88ed k$ 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 thro;3r uc v ;+eygsgmdw.,ugh the same portion of the Earth, but one is carrying twice the energy. What is the rat,vgr yse+m .uw;;c3g dio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, but7 f bh) s5+xhft4n.pl, guyom8(ate8bl; od3q one transports three times the power of the othg8x f p 453la)qty tebbo.+(8f,hd ;mhl7u onser. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down a total)aub+-lf7 u*nw.i n cqzt( uvb*+aec ; 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, t uc )n(b+anezqavw.+ bu-;i*uc7*lf by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each o3u a5. ej4f3weeqkn0ather. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the s u 0fkeneqe543 aw3j.atring 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 fundam5v:7x9lvlt xg ental frequency, what are the frequencies o xxl5vv9tg:l7 f the first 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 frequen*hc73 vt xpg37xsz+9ela8 q idcy will it vibrate if it is q zpxx3l avc et7*7hg9 sd+3i8fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of zgyy4:i .srk(m8 b4l./hjgyn4opd q3280 Hz. Name at least three other frequencies at whiczobg/ yy.yis 4m4kj 3h.dl:8gn4pq ( rh 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 t+bilpn44 +krm.to ru d um::h8yq6g4 frequency of standing waves is 475 Hgnhplt4uy.b + u4+ rok6i::t rmq8dm 4z, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibratnn1 e+g d-h31a xkick*vrw6ob6zw q, .;lm(f sing string are 280 Hz and 350 Hz, what is the frequency of th+wr m- 1 ekk;v hb(wnn.f6qsc6za ,o*dixg3l 1e fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance fror; u( bmj-6ywom the bridge to the support post is L = 62cm and t;u6j yb(mo-wrhe string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is measurrcjvoj0t e,v h5r4 /x-ed to vibrate at 205 Hz. By what percent should thetj /x0 ,v4crv5j ehro- 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 tohf ni x)+q 00vv7t:r7dbxbe4h vibrate at 200 Hz, but it is measured to vibrate at 20h b+q)0n xvvr0xide7hft: 47b5 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 m31bri+*)6d 9 nbmplpda .np laechanical 60-Hz vibrator. The string’s mass per unit le. 3l ir+pd1n 6n*9dl)babmppa ngth is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be adjusted by moving the pug/ u bu(pjw bfom-h)3*k*n) 9)ctg ojelley. If the hanging mass m is fixed at 0.080 kg, how many different3weu j)gp/ubt*-o)o9(n) hfgb *mjck standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth iny ahutv 3erxj,:/hlnz-/hl 87 a tub at just the right frequency, the x r/,y/hu3v8-lljt en:h ha7zwater alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s s,/.) x8won1 tt l;rkj3fbyygmtrikes a boundary within the Earth between two kinds ol)1 3;oj/t8,yb rx.k ntyf mgwf material. If it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the o,itiuce* /j0f)*g kb velocity changes from 2.8 m/s to 2.1 m/s0)uboeki/jt * ,*gifc If the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is travelig u* c6oba 5vq.xn7fu,//oggt ux 0y3ung in warm air when it hits a layer of cold, dense air. If the sound wave hits the cold air intou,av.uu6xg/q0gy7n f/g* otu53 cx berface 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 stri.(as6 ms.s -c5dq/1no qxg x dqaerp7)kes a boundary between two types of rock at a 3q .s(d 7 /p.x6o)5c-qaqnmr1dsg esxa8 $^{\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. A+f 4ec7th2)-pawfk rsccording to the user’s manual, the dish has to be pointed in the direction of the satellite, but aawp- cht) +s4fke 2r7fn 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 acr:x3 -okwgif**whb-+9su gbifoss 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 warning, people have died during tsunamis, some of them att39kwb- gsbgo+ wi hfi:-* uxf*racted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 55 ztt/9mqr .ha00 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.] a/. 9zttq 0mhr    m

  A 65-kg person jumps from a 5-pjjzrc) 7sd7ak wp-g*qjt 6window to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behav7pzaw)tj q7 d5gjpc-jk s6-r*es 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. qa5mgr2u, gs m-jr:zl6 8 h+vdThe mass then falls 33 cm before it stops and -r8,s mlhgu a 6+z m:r2vgqj5dbegins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge sprw fi67km50a9 9rmkkt )du4 in ilxm4d2ing at a speed of 22 m/s (Fig. 11–54), compressing the spring 5. xm9il4m d2 )k ri9kwi06fa4u75tmkdn0 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 (dia( sj+ fb-vu*0 vnl-kdih nkb/*meter 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 (Fig. 11–55). Estimate the speed of waves in0v/bi--+b*k hvkj*ln f(sndu the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the c)vm6o+ 0z-qen.szm7b+yc m ie enter of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be6ezvz.+cy +sobmm -7) 0imnqe the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x1ckio3i0hdeo a/l *w/ is in meters and t in s0el 31woi /k*ach/ oideconds. 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. What is :qpx:-er9tcn8wy ( l89ne ro+jxoy k0its frequency if it accelerates at 0.50g (a)e +:89njln8r 9cqyo:r-xk0ot e( xw py upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on b4p 0hgd ,azy,the raft, it sinks 4.0 cm deepz0pbd,g, h 4yaer 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 d0 s 4n/k qsy24lqidr1instrument are tuned to play at 392 Hz (G) and 440 Hz (ys2rsdlq /ki10 qn 4d4A).
(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 stretcheg q)dfdj kr(ziazm h5 n08/q35d two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy secqha3/0dfqrz j8izk )(5ng5 mdtion 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 a frequency of 264 Hz, and the tip of each pronga3k oadj wm91v5j e.w: moves 1.8 mm to either side m j5wo 9ka1 dj:.avew3of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion 4v k5l kktlkz( 9+vv1rof frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order thvt(5v49 +kkkl kl1rvz at a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “+ p*g re+k)h8b( xctbzfree” end if that 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 string with one end fixed and the othergt kbhz*8x+c erbp)+( free.

  A “seconds” pendulum ha, eq9u17r;asziws1zxs a period of exactly 2.000 s — each one-way swing takes 1.000r1 1axz s;,i9u qs7zew 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 vertical diah pz r*/g ;6uqje; (ntpd89nprection or can swing as a pendulum of small amplitude e9qn(;tp6h/ zp p*rua;n dg8j, 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 stre2pr 5yede i a)xrom8b-e 5mj-1tched under 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 will the two pulses first meet -r-or2 y1i85eejm pex) adbm5?    m

A block of mass M is suspended from a ceiling by a spring with/ye*r agv4/p3o. qgfs spring stiffness constant k. A penny of mass m is placed on top of the block. What / 3 /ogv yars4pg*e.qfis the maximum 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 t2h;c9*rz e) :ffidoia) fwsz)he junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Ref)dzi;i9 fo c)s:2r* zwhafe )fer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. / ) yhkv7jtkqg+ay)7e 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back j7 +yv eqth a)/)kk7ygand 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