Give some examples of every - my7;-+bkcfraqp qd6day vibrating objects. Which exhibit SHM, at least approximately?kqpcmqf+6b7 r;-a -yd

Is the acceleration of a simple harmonic xgbmjl2 6o n :80fkza1oscillator ever zero? If so, where?

Explain why the motion of a piston in an a h1lx: b u/kdousxu583,h rir4a cao1;utomobile engine is approximately simple u;dxshcr lou85ai4u: 1kab h r,3x1/oharmonic.

Real springs have mass. Will the true period and frequenuzp ua;9gtx(eej (w 87cy be larger or smaller than given by the equations for a mass oscillating on the end of an idealized massless spring? Exue8;ja(t7(pwz u9 x geplain.

How could you double the 79-lw7tg boa+vibzg +maximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and thenq5.ix :xk//:gme aitpcphwr06i.z -a is released. Describe the scale reading as a function of tig-0pq:ci :/r.x ae65ait/.ixw pmhzk me.

If a pendulum clock is accurate at sea level, will it gain or losew xrp, p.a9laqj u u93/h*-pspk ;)dreo-s0zl time when taken to high altqs.*kex l9rw9odpazr/3)sju- phu, - a0 l;ppitude? Why?

A tire swing hanging from a brandr:wqz;6 xmy+f x2j ;nch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of thnx; ;zxmwd+62jf: q yre branch using only a stopwatch?

Why can you make watervd3n n/au :,zr slosh back and forth in a pan only if you shake the pan at a certain frequencn/r:a vn3du, zy?

Give several everyday examples of resonan4w/ fpqv7h1(3 g hwwvo 0hfhz)ce.

Is a rattle in a car ever a resonance phenomenon? .f.wlm:pev,2fq 4pta 9we pu9Explain.

Is the frequency of a simpleq,8t0q ue+66rcxi gy8gi8mj y periodic wave equal to the frequency of its source? Why or whgy8q60g+8ymt6x qri ce8j,uiy not?

Explain the difference between the speed of*vvxlvow- .9 xj1oea,b h7vpl6f1;ju a transverse wave traveling down a cord and the speed of a tiny pie1fv9 vajl.eb*u; ,-vxj17 hpw ovol6 xce of the cord.

Why do the strings used for the lowf o(iavax0u.8jyj+x8 .hlhy; est-frequency notes on a piano normally have wire wrapped aro0 xjjohauhvl 8;iyf.+a x8.y(und them?

What kind of waves do you think will tr+cq kme45rf8 k otu 6)okw-ben uu)-w9avel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parallel to its -eufckw+)qo omb6w8) -5u 4n 9eut krklength?

Since the density of air decreases with an increase in temperature, gks ,1kr5gn +pogj07a but the bulk modulus B is nearly in 57jg+ka,n g ks1prog0dependent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease,d1re(r 2d40i dxjesm in amplitude as they travel ax2j1 dei ,r0e4dm (drsway from the source.

Two linear waves have the qxpb:ub ) lle1609tcisame amplitude and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits more energ)61:bclqlt ebx iu9p 0y? By what factor?

When a sinusoidal wave crosses the boundary betwpiil; 0r u4ki,zi6vn/een two sections of cord as in Fig. 11–33, the freqn;ii/pi 64z luvkr i,0uency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are thes0ir49-p chz kk,8-; jvjlrvg re any places you could touch it with a knife blade without d l-cs;z jjr rivh08,9kgkpv-4 isturbing the motion?

When a standing wave exists on a string, the vibrations of inciden.a;adsmy3 qvi.n/8ig t and reflected waves cancel at the nodes. Does this mean that energy was destroyed? Explain.a aygd;iis/. v3n8 mq.

If we knew that energy was being transmitted h4bg 5nx.zbq(6+ do8vjel4ikfrom one place to another, how might we determine whether the energy was being carried by particles (z b4n6hbd vek 8q +xi4(o.ljg5material bodies) or by waves?

  If a particle undergoes SHM with az*bj0o +:oqkpy/-bx amplitude 0.18 m, what is the total distance it travelb/ykj:o +azpx o-0b*q s in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from )r/t/z9 u k;cjojgv0y it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” cons9; gj0r uo)z/kvj /ycttant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68/rqk d (;tc *.e:tsm -e b-+pyw(gnpbg-kg driver gets into the driver’s seat. If the car goes over a bump, whate t yqc* rp.gk-(pn -mbdw(sb: /ge+;t 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. (vg e)eiq8resw d +hp o6sk*vo-ax4 /07a) What is the spring stiffness constant 0viod*g6sk vae)- rwxho p/ +8q7se4e $\approx$    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.rvts72 4 m pyhtbn7z6 8woq(f)60 kg is hung from it. What is its frequency if only 0.38 kg hang6syro 2vm 47phwnf8z b)t(7qt s from it?    Hz

Construct a Table indicating the position x of the mass in Fig.buxv2xf6 5s5nkjx8e- 11–2 at times t =v 68fbxusknj x5xe-2 5 0,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 caught in a spider’s web. The web vibrates predomy,*- bhwfr e-uinately wiue-h* f -byrw,th 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 with a frequency of 0.88 Hz. Whex5qtqkeyy (v1a 18h7w n an additional 680-g mass is added to m, the frequeny(1 ty7hqwev8ak5 1qx cy 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 second w:12iw9 .xydd y/zkfanith an amplitude of 0.13 m. Determi/k. 9y xw2ay :dz1dnifne
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed of a SHO half the maxcu y4 p6l*p;q9cuts6yimum valuepuc9yplcuys*64q ;6 t?$\approx$    A

A mass attached to the end of a sprij9j7tvf3sn :)yws w zydl4+2fng 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 spricewmz1nlz92 nyh84 f;u 3x*mang is stretched an additional 0.130 m and released, how 2w8ef34 1 h9c; axnunz*lzmmylong does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffness cu6be5 wa9bbe 9onstant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its eb 99e6bwb5ea uquilibrium 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 0.200py-d f41q,418tyh z2a hm esfo m to “load” a 0.180-kg ball. With what speed wi yhqhy18 ,psm ed-2f1z 4af4otll the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is i g u3y:atz 05zdsotk f)j n:+.dejy,9attached 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 fromzt:yt. e5uf:sg+o ) kj9ya0,djzdi 3n 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 ip+v :ib,wur0meters an:iwb+ur p ,i0vd 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 energy of a SHO half KE179qd1yfn 5j/q+ )swa: liru; z pppzp and half PE? :pwpy z;/as 11p59lijfq) nr7p qud+ z±    A

  If one vibration has 7.0 times the ua xh/z68aheu+ spa r.tn4.xwd9/1 df energy of a second, but their frequencies and masses are the same, what is the ratio of e14z /usart6 h+9fhd/d.uawx8p.xan their amplitudes?   

  A 2.00-kg pumpkin oscillates fro01b q+ 2hev ;;+qiqamp) gztulm a vertically hanging light spring once every 0.65 s.mih+ +b)q 0av; zept;g21qlu q
(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 suphoyvkz c2 *-4w*9yb x03ppsyfu6ogb 0ported by two identical parallel vertical springs, each cy*w b*y xh3-4z2ofsgp9 0kob 6vpu 0ywith spring stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation xg -z.-o toe 9*hf)uss*zr/:y/3m6 hoewpv yzn = 0.38sin6.5t where x is in meters and t is in seconds.ehey6 . 3 z **oy/nopo)wz/zhsv--u9sf:mg tr Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, jws4 : qc +pf +i**vcgdynd( )b9/ujknlabeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the enva0fxo;:0 tb ne,ajv73fc)ed d of a horizontal spring (k = 124 N/m) is struck by a hammer, which g0) jeo: f3b0 xcefd,7;n tvaavives 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 stiffnessl4u9 9cqjsaa- mw/+ilr )p 4zf constant 305 N/m vibrates with an amplituzja paf4/r+u)qm4sll9 -ci9 w de of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, wit vc2w2eg),1m p def,ufh 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 attached to a fixed horizontal s+ )y-i8hqurp2 xx/p ggz0a p(zpring whose 0yg ph/-a)xpuq+rxzp8(z g2ispring stiffness 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 bridt-alh/,h.g1mfg* kyo7 o2ruige. 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 stiffness cons-go.fgku/rimhyo h* 7la1 2, ttant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 60 s. What is iruk5.klqee ct.pyk6 e2923o kts
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one bst)f-2ca) wuadqykyo4 tf7j2c 4:x:u3bz +y swing per second? (That is, one complete vitb daoy4jb2s74afw)3 2k:z:cfy qyx+ t uuc)-bration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. ws) vfw7efklw:ir., 7What is its period on Mars, where the acceleratio eifwww7.7r klvs:,f)n of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulr;lf7t(z .1no .ep sbuwqj.j + csyps za;i-22um 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum isrfv )bt)o6qtq7.b eji-kc88(e qpaw . 0.760 m, the pendulum bob has a mass of 365 grams, and it is released at an angle ofwbqof r..t(ecv)8k8- tjbp a7q q)6ie 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 ofy+lerbu7.u -r+ uh 8z 3gblqz6 0.9930 m. If the clock loses half a minute 8h7+3 g+zlbqzr b.-u6 uluyerper day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum sy+ hdqg7 7t tl.a xieyc509i1speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscill qg39rji( y/ kgo-whx0ates at a frequency of 2.5 Hz. At it is released from r(y-0kxg 9 h/qowijgr3 est starting at an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchored boat eveua n.e2zeyb5+e-* xlkry 3.0 s. He measures the distance between two crests to be 6.+z b.k2eeyeux5-aln*5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travs-,lvc q- f(w zb:zgmmf7ml7w ,2.dwlels with a speed of 343 m/s How far apart are the wave crests (compressvfzmwdl72b,(w: c,ml7 mlf- z- w.gqsions)?    m

  (a) AM radio signals hxw-2e ) 6nbujxave frequencies between 550 kHz and 1600 kHz (kilohertz) and travel with a speed ofuj )w6nx2b x-e $ 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 ofw;npz k4l p6v( longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same y88pke):4gck qk pjk8o.1sdxelastic modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal wavekg.kd )e48sp 8kqjypo :8x c1ks be greater, and by what factor?   

  A cord of mass 0.65 kg is str9mmp 5pl bu09imop++zwnl 3d5etched between two supports 28 m apart. If the tension in the cord is 150 N, how long wilip539nmdzp0o5l uwb+p m9+mll it take a pulse to travel from one support to the other?    s

  A ski gondola is connected tok 3t2:mon9bj y the 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 ttj3k2b:9om yn he terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below tpusp62m;dtn/ e:g u 4che surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this ptdc6 2;umsu4: gpnep /oint?    m

  P and S waves from an earthquake travel at different speeds, and thi b,lz ift:. ln-kef tab;u8v+5s difference helps itt kv;:bfabf 85.z, ue-ln+lin 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 wav +0fjvig.rqq0e can be approximated by a sinusoidal transverse wave. Assuming a frequency 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 the0q fjq+r0v.gi acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) t- ujx mgu3g14lhe amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 k1x3mugg l4 u-jm from the source?(a)    (b)   

  The intensity of an earthquake wavwsew7*8t 7 iti9 ryb9x4gza,ze passing through the Earth is measured to be 8ia x99g bs,4rz7wt tye7wi* z$ 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 tr1pm 1 s1hj27xxv9 iokbavel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of th xvj 1ix921h17pos kmbe amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, but one tryt5 k lkbplaz20)5; eoansports three times the powl50;bzop5 t ke2)kayler of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is o(g*,nhkzlc+r q vfb(1 bserved to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum n(g ckzfr,+qv1( l h*bKE change?   

The two pulses shown in Fig. 11–52 are moving tl-9 xjlsq d1xx qm* npm9o,;.p ia59aioward 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 pass each other, the string is straight. What 5qaxnpp1*-,xi9s x oqd. l9 mai9mj;lhas happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamentp4c,:zk3 sjdnmy49u dal frequency, what are the frequencies of the first four hajyp,sc4d9 k:udn4m3z rmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates hrphz2 k g3f0ap*ndo*/o s ,/sat 294 Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down fro/,k 2 /spf*ds 0ah3ho ronpgz*m the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string re9+bokig m, w 2gl;re*usonates in four loops at a frequency of 280 Hz. Name at least three other frequencies at which it will resonuwlb+ g,k2e *r9 g;oimate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If them6 wp pt9l3ez. frequency of standing waves is 475 Hz, how far apart are two adjacent e3mz w6p9 .ltpnodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, wjr ; dd3va6hl6hat is the frequency of l6rdhd;vj a 36the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. T0aa,ftm 57v kshe distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two o kva7sft ,5a0mvertones?    Hz

  A particular guitar string is supposed to venmho7m f-877vv 50t.ng olbdibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correebvt f 7 d0 77nm.8lhov-mo5ngct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is suppos)7h7c tdqnd heemj(7m5/h fz gr4ud12ed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension 51hd)42m entgj zmequ/77(r ch dhfd7in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a sfo2 rlc ae6+y -f1uh(/ a*clfkmall-amplitude mechanical 60-Hz vibrator. The string’s mass per unit 6a+/f-l f(yuhc *alrcek1o2 f 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 len v-qbxbcs3,;y gth of the string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L betwee;sbqbc vy,-3x n 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub a pws5u2q(kue) p)krs/t just the right frequency, the water alternately rpk)2s uuw5()rp /s ekqises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary within the Eart mf,o)xepxp4vv6-m hk mc(34mh between two kinds of math4,mp)m6epv( m ckxx 4o3f mv-erial. 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 velocity c ft./y cemnsg9 0:ah fbvdl-fini0xp dy2(1.3hanges from 2.8 m/s to 2.1 m/s If the incident wave 0 ydfitef-3abgs1 2dn/(0c xmp.y vhn.9il:fcrests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm ais-g)pjowf8n:.ptma *n 4ihd9 r when it hits a layer of cold, dense air. If the sound wave hha: )nds9ifgopp wj4.n*8mt-its the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundr* 3 ls7a49 i,t1ldprmcono 8eary between two types of rock at a 3tmpn9ro 8olis7*ec ,da1l4r 38 $^{\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. A2rxn00mmw /r480uzhln* qv92pjxjmq ccording to the user’s manual, the dish has to be ux4/ vj rx 0p9mznm0hqq*r j8nw2l02mpointed in the direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and 3 5 -vko:nzgm0kpti*bvelocity 750 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 warning, people have died during tsunamis, some of them attracted to thk3*bn05go mzki v:p t-e shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness colevqq rcvx;/d, vos us* )9-zj-j)8qxd40 hlcnstant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.v9ev- dhl)r)zj ,-8cj/qls4ux0*c dqvq sx o;]    m

  A 65-kg person jumps from a window to a fire net nf 6u,j9e qarn;*k2xp/irv 7(i1qxizm fa,p 218 m below, which stretches the net 1.1 m. Assume that the net behaves like a simple siq2 zfu;e im prn1p6 q2if(/jrxn9xk ,a,7 *avpring, 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 free*a4ld9t+ hmy.b ne8skly hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of the oscillatioyme8 l*k+at 4s.nbh 9dn?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s7y.cm q b7d1qd (Fig. 11–54), compressing td7cq qymb 7.1dhe spring 5.0 m. (a) What is the spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of cofmrn ,a+92mpp afee (diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee. p , mpr+ama29n   cm/s

  The ripples in a certain groove 10.8 , hwjc( 80fgvw lw-5umcm from the center of a 33-rpm phonograph record hav hluf 5wj-(0gw8 ,cmwve a wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equary nuc u+b9q,-d3c(tvtion x=0.650cos7.40t where x is in meters acy urtd( 3cb,9n qv+u-nd t 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 oscillaszym01 , 8xj enljuui -hzv2)4i)iu 6ites with frequency f. What is its frequency if it accelerates at 0.50g (a) upward, ) ujji6xhyz iilzi-mu4,ns21v 80 e)u   f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the ra:0trup esm 8q r ptk8:0ppv7v3ft, it sinks 4.0 cm deeper into the water. When he steps off k8vm pt v0:e7:r tusppp0r38q, 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 instrun nd- 5pjkug182 nf ,.ekf;yxhment are tuned to play at 392 Hz (G) and 440 Hz (A).81jpxfegh, ;n5ydn2-n.kfku
(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 stve raxes*ybs (g1 6(t4retched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heav4evxy(( b*t sres6ag1y section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, an*s kt3(j opali02sj3nd the tip of each prong moves 1.8 mm to either sidej s3*n2l 03oi(tsjapk of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of frequenq8ctrnfn8 5x6 h9u,.muf.qs ncy 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 (rn8.n. nx6c f5,q9qsu8m hu tfFig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a ring that can h6w t2p;jvhj/nm32yl3ul9 jt slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibratiohn2jlhwtm yp3jt/u 9j3 v26l ;ns of such a string with one end fixed and the other free.

  A “seconds” pendulum has aonvvtn o5 vpt3n)lnytj ,3k/i9.81 ke period of exactly 2.000 s — each one-way swing takes 1.000 s.nkev/ vi k3y1j)t nton9o plv.nt5,83
(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 oscjdzkb m4gu7* .illate in the vertical direction or can swing as a pendulum of small amplitude, but not both at thek mdju*bg47.z 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 tension o1k8r : gvc0nwke6u8jvf 255 N. A pulse is generated at one enk8wuj1g: ck e06rv8v nd, and 20.0 ms later 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 c*kj41xeeh.x .tb uyt+eiling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top oyjute. 41h*. xxk+tebf the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cabz2u2( wd chkhjx s3 2 3 .gv(frf+m32qsec1yzyle 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 peri3( k w r 2s3+vjuhy.yf2cm2qe1xsh3(zfcgd2zod of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests oeh jks)s v)h+ae+ ;rr7n a plate as shown in Fig. 11–58 (which also gives the dimensionsar)s)h ; ek s+rehv7+j of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this 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