Give some examples of everyday vibrating obje lbnunmxwamxy-p;3m4ke 4 5 c. ,-dgt/cts. Which exhibit SHM, at least approx ,3 .4ktm mmxa/gcn;y4-xw-nde pb5ulimately?

Is the acceleration of a simple harmonic oscill0k gg.xearyei3 .u v4)2yci 6lator ever zero? If so, where?

Explain why the motion r8l ekp jvz-gasy2:ua;1nwv whw*6 ;2of a piston in an automobile engine is approximately simpl g8rk;aw:-lsh 6*pu1 v2awjz;vwy e n2e harmonic.

Real springs have mass. (istc3ve3y9e+nrc9 fWill the true period and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized massless spring? rc +ci tey3fs(9ve3n9 Explain.

How could you double the maximum speed of a simple harmonic oscilla*y- z anmf(v 7oda s8b8cnkn65tor (SHO)?

A 5.0-kg trout is attached to the hook o ;n0kfk :aqaf8lv*.: yyknleb) 8j ux.f a vertical spring scale, and then is released. Describe the scale reading as a function of timvj8 n yk:n)0y8kl:u ;fx* fqe.aa. bkle.

If a pendulum clock is accurate at sea level, will it gain or lose f96*i q 9pmwic6rasu- time when taken to high a ai9 u *prmqc6iw-fs69ltitude? Why?

A tire swing hanging from a branch reachenikg*;az ,f a4s nearly to the ground (Fig. 11–48). How could you estimatezk g*an,a;i4f the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if ypu,ld 71 kw:,q ,of mswz6l6fpou shake the pan at wp 16lsod7,k ,wzf:q6,fp lmua certain frequency?

Give several everydaynqzseo7 4h *f7 examples of resonance.

Is a rattle in a car 6p 4g3kcci ek 8kxbi:8ever a resonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequrap5 o mxszi.j+8qz/n 1l0 3juency of its source? Why or w x.i5no+z8mu0j3/1lrpz aq s jhy not?

Explain the difference between the speed of a transverse wave traveling doc 8pvr2,ad.y 0t -vppav ,yyg9wn a cord and the speed of a tinyvv.yypdatg8vyp c0r 9 p2,,- a piece of the cord.

Why do the strings used for thed9zw1qtp;a6l/;lv l( . eqbjc lowest-frequency notes on a piano normally have jd/ ;ql b lt96vl(1awz;qp.cewire wrapped around them?

What kind of waves do you think wil *o2s76qj8ufkgp )fz4u8uv.1hj m azal travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally paravz mh.ja88 fksu1az )fp o426u7qugj *llel to its length?

Since the density of air decreases with an increase in temperature, buhf,:p3an qd*i -/rmtlt the bulk modulus B is nearly in/a qrt,-:*l pfmd3hindependent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water was *:x3 pg3rrcuves decrease in amplitude as they travel away x s* urr:3p3gcfrom the source.

Two linear waves have the same2d/o ru44c 8jx 2u5m eovqfzqql*)r)b amplitude and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits more energy? Bj)ud4)ebo2qo 4r2 / ql 8uq rmxz*c5vfy what factor?

When a sinusoidal watpso 70)k 4j wh-xns+lve crosses the boundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do c-jxt+)o ns40k whl7 sphange). Explain why.

If a string is vibrating in three segments, are thepp:s u.opr0r- pdg, j7re any places you could touch it with a knife blade without disturbing the mot d0orp,pg: rpj. sp-7uion?

When a standing wave existgqdb 4cs0-xs5 dlj3a /s on a string, the vibrations of incident and reflected waves cancel at the nodes. Does this mean t-qgls 0a3xjs/ cb 5dd4hat energy was destroyed? Explain.

If we knew that energe nssx*;d2 ii6y was being transmitted from one place to another, how might we determine whether the energy was being carried by particles e;62 i di*nxss(material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what imj.57 ; z:9oox-kfji2pgq; ocs w 9lubs the total distance it travels in one pejm.-op l;ukqo995 i:cobs 7x gw;fj z2riod?    m

  An elastic cord is 65 cm long when a weight of 75 N ha xsxhpup6a*2 7y,tm/f t-kl0gngs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” 0,k2 xtp7tsp fy/*ahulx g6m-constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm wh v4/e9,h ifq soo-vldf kiw025en its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frvq,s5i4i-loof/ h0e f2d kv w9equency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when7aidiqbq.+cjp+ / iz9 a 2.7-kg fish hangs from it. (a) What is the spring stiffness constantb7dp+c ii+q/q9aj. iz $\approx$    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 pod );dn-arn)6pgp m;mass of 0.60 kg is hung from it. What is its frequedn);go- ;pnr6)a ppd mncy if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the sq :(+tg,nfzw mass in Fig. 11–2 at times t = q ,znwsft:g+(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 i ,r,oxj d3b9x2qdu8ukjuk( f(n a spider’s web. The web vibrates predominately with , (kdd,k2qjrx ojux93u8(buf 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 0.8f(pzlajc*+e( 7 q+lqc8 Hz. When an additional 680-g mass is add+(qcf le+z 7clja p*(qed 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 timesx1p(jo-* 5mhyq8ahd l per second with an amplitude -a1lpqj(m doh 8x5h*y of 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 equilibrium 6f +kifok..f+ rae)qoe hg4g: is the speed of a SHO half the maximum val64eo k.fg.ghf+qio+ke )ar:f ue?$\approx$    A

A mass attached to the d;mb-k5eu :rg2n0fr +quc 7 tvd,/ iskend of a spring 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 stretj1,iat bd)ld ,c3d6 biched an additional 0.130 m and released, how long does it take to reac3 b,jc)i6,d dt 1ibadlh the (new) equilibrium position again?    s

  An object with mass 3.0 dx /0epgluv9jif* 1av. wib8(kg is attached to a spring with spring stiffness constant k = 280 N/bi.alvxdj 8/*wge f 90(1ivupm and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a toy popgun 0;vgbll5s)h) i.200 m to “load”igls 5);h vlb) a 0.180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to o1gwmq2 r 98iqrne 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 fromiq2rgm r9q81 w 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 inwb+x3 6ndfecp)m o(1-ti eu*z meters and t is ien3m+z-w*px6u(t ef 1b) o cidn 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 equilibrin/qfu v(2j8 zrum is the energy of a SHO half KE and half PE?rn28zf/q uv(j ±    A

  If one vibration has 7.0 times the ec v.tvsmtbs6ys 6p7*ac 0sq/+nergy of a second, but their frequencies and masses are the same, what* q+a7m.sc6p/ 6bvyssc v0tst is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillatwgb: 1xhia m54es from a vertically hanging light spring once every 0 ma51hx4wig:b.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 vertical springs, each+nr0c g90rqe/f*0eeyra he7,rjw ;j j with springj ree/;eq yr9*erw rn7 0gj0ca,h0f+ j stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equa0rigw b f+aoz0jlg66 hu17,6d x3hjhrtion x = 0.38sin6.5t where x is in meters anhhojg+ ,06l juixzbrf3wd 0gh76 a 16rd t is in seconds. 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 v p9qv8j51:mi0mzbzl of SHM, labeled 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 odr:lg+vt3wcqr5lxa fg ;qic 821p l(,n the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an 5i 8(dxq c clla2l,rwgp+1g t:rf; qv3initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305 N/x iv-p 3kp ypd3yrt++4m vibrates with an amplitude of 28.0 cmrptpi 3xy-p4dvy+ 3 k+ 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, with ,l5df: d+ sgz+hhp5y;upvn;w 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 +)dx goheer( yb +m7u b y97:nd j7-x8yeop;jfa 0.600-kg block attached to a fixed horizontal spring whose spring stiffness coo 9b x+7 rxgdnf uy;ey- 8ybjjho(+ee7m7d):pnstant 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 withoe7 qhg4wf6 teld( 01. bvcy*v mass 65.0 kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hittcqd4ylh 6w e*7g1ve bv0t.fo( ing 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 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 6nrg+ vxcgh i6)gx,k660 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pevcc:i+3 pbgm1iydggl5af11 6 t88 jaundulum be if it is to make exactly one swing per secondp3+:fg5 b tvmacic agu yld18611i jg8? (That is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period ofyj 6/2ui2up zw 0.80 s on Earth. What is its period on Mars, where the acceleration of gravity is ai2 zpju/w2y6u bout 0.37 that on Earth?    s

  What is the period of a sim4t)dhnp7 v m;:f0vusbple pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 mj:malx 5c:x jl /6f0ez, the pendulum bob has a mass of 365 grams, /a: jc zxef6lm jx:05land 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 m. r(y- mvqvm0v.j2a(c dIf the clock loses half a minute per day, how should you adjust the length of a(0. mvvv2 c(qydjrm-the pendulum? shortened by    mm.

Derive a formula for the maximum speed zc lwf4ht*6 4 bf.fpo0)gbq*/v+wfsa $v_{max}$ 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 freque p8+lidx*kq.4(hi +iq x vpu+hncy of 2.5 Hz. At it is released from rest startinkuixq+dp+ix4ipl (8*h .hv +qg 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 crestcll-ssrf*7e87 t kb k0s pass the bow of his anchored boat every 3.0 s. He measures the distance betwc -lfkk *rt0e8l7bs7s een two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency o2em6jm::;coe pokyet+c 8n d8f 262 Hz and travels with a speed of 343 m/s How far aparte :j no c8e2 o68cd;emtykm:p+ are the wave crests (compressions)?    m

  (a) AM radio signals have frequenc* i*nwi4vidis 3d6s3h q3py,vies between 550 kHz and 1600 kHz (kilohertz) and travel wit ii i3p** ss,hdqyv3w43n6v dih 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 longitv y wbk1z.yt +-13z n ti+ult.db4+ihwudinal 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 m;8jf8u fm8n gye9qked5g:x b- .j)glas the oth8eqbnj;f5juy-d.gl:gkf9 x8 8gmm e )er. In which rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If *p k a 3glujp)johcq3 +5.tvxl(te*s9 the tension in the cord is 150 N, ho*o p.3qusj *lh k+5(xvte)t93lagjcpw long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of length 620 :j(8 )drnb x9b8:cekip jc- t.mf +cosm and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cablom8es8.ib+xd:9 kcfnc t ():jj-crb pe. 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 h23+ 5nqy 6mazt*rgj gyun0 1blis ship just below the 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 oceagz3u+5tq2y jn *01bagl6 yrmnn at this point?    m

  P and S waves from an earthquake travel at differcvc 4i/zq5 9f9u 21tqivqr5q nent speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbqz 9r c2iq9v5cvu nit1f4q/ q5ance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated by a sinusoidal traj3c 87 - lhi:*u-qizl2r1xg;ypnseym nsverse 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 n m7-ye:;rghc -2q * i8lix3yspj ulz1the acceleration a>g]    m

  What is the ratio of (a) theoyu,1 ojnz3:i l+;zdo intensities, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected znd ; ,+:o z3yoji1uolat two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through t4ks. oj-ac8 kne n+j(the Earth is measured to be t4j-nnj+es.o k8 a(kc$ 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 txuig6*)sqce(t w 72t9axcr k0he same frequency travel through the same portion of the Earth, but one is carrying twice the energy. What is69(kcu qe2rx gw*tx7iast c )0 the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same (apm:4z aaj(enn to 4fp9xa+ j4yv s,7frequency, but one transportvj,fxt44n (n a9p ymop(aa7z e:+4sajs three times the power of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to xso /2p9pn3yib w a)xn0c-:lymove up and down a total vertical distance of 6.0 cm, from the lowest to the highestn/lxox3p pb 92):yay i cnw-s0 point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are syb4t m:cz 4v)f:0lcjmoving 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.0y4bm z:jc ):cstf vl4 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 4zrg.tn nj1t+940 Hz as its fundamental frequency, what are the frequencies of the first four har+ttz 91ng jrn.monics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when u)m/1ul 8bo:pd4 embatnfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a sta):bapu /me4o8lmt d1b nding wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz.lcbk s.fa 7)6 fo9:ro- lu3rxvdw;b0y Name at least three other frequencies f; ly.bdo ur bc o9)-3r:vfsl 7x06kwaat 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 frequenctkwya+*0ui. u y of standing waves is 475 Hz, how far apart are two adjacent nodes?y0 tui w.u+ka*   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, what xno ifvi3.7 1b-js g7osci h-w1z+w 1xis the frequency of the fundw+71cj vh x-o w.-iig3ozs 7 1b1insxfamental?    Hz

  A guitar string is 90 cm;+p1fyytup k; long and has a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string isfu+;tp;y y1p k 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 vibu8zu 1h2 h.zk frqmvs)23r / 8q.zrymsrate at 200 Hz, but it is measured to k/2s32r m)sufqrmzrq .h .vz1yh8 z8 uvibrate at 205 Hz. 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 s)8)/ks u yv2ilz cd7nttring is supposed to vibrate at 200 Hz, but it is measured to vibrate adsk /izuv)ny7t8l2 c )t 205 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 p)en1 ::;bqr3y ,y1z (zzmvdsrx ud )sifdn+ /mechanical 60-Hz vibrator. The string’s mass per:s zfp)z:3 () m;i +evxzdqddy,y ubns/nrr1 1 unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the n +lhmq-i4 tgqy/(eg4 string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many dif+gq gnqle(4h4 m/ yt-iferent standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth indwj5v3gc hmg k2-t (*ip+q0 vslzl 0u( a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at theugl5lvm+ws-vzi 2( hqp*kc30 0d jg(t 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 withinnin+sj 3k( d gele ,/h8+gvm)1h lm8+c,ajw ei the Earth bet8)n ji/l g,ae+,v+(m13hke w isg+c8dhmlje n ween two kinds of 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” wherol,r nszl.g02 e the velocity changes from 2.8 m/s 2. znos,rl0glto 2.1 m/s 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 traveling in warm air wheq ljbz1q18r(ln it hits a layer of cold, dense air. If the sound wave hits the cold ai (qbljz11q rl8r 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 boundary betwe7vod4jja4*irv ffm3 )en two types of rock at a 38 v )dj4*m 4vjoaf7ri3 f$^{\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. Ae/ ,u z:: nug;+ojne z47acnyiccording to the user’s manual, the dish has to be pointed in ty4 7anze:nue,:zo+/ igj c;n uhe direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 km/h tra;dmb;ium:6y3 - jpb4;mu qpc avels 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 the shore to see stranded fishes qb ;jp yu;i-mpb3umcd;m :4a6 and boats.)    min

  An energy-absorbing car bumper ha 69rf x:fm h 2i(p.,hd6bcydpis a spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use cohd9 d 2ipy 6:c,fxpmb (6.ihfrnservation of energy.]    m

  A 65-kg person jumps from a windo q+-kfb3r hn/t0jd /12tc chtm,zaab5w to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net be1t+hb/c amn5/0 k-br2zc3th,q d jafthaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hanging spring. The mass then /yf 5st x/c9(tnnn8 bdwc2 (ogfalls 33 cm before it stops (cy/n2/5wnbsf ttx9(o8 ncgd and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring a to9r;rpz q32zt a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 zz9;2p3rr qtom. (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 (diameter 8 cm) at just thsdx4kl tsnx0ujjl5;l e5 8 q86e right pace of about 1 step per sx 64d 0xk5qtslsl njj8 5e;8luecond, 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.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-rpm phonograp:*wagi wv5 fa9h record have a wavelength of 1.70 mm. What will be the frequency of the soun 9:*5awa vfgiwd emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x is i2spi tzja5ya g666:hl 4+g zimn meters and tya 4amihzj s6g25 6g+il:t6pz 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. What is its frequency ovfe65es/ -cbif it accelerates at 0.50g (a) upwar o5ecsf/eb6 -vd,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stankp nl+f,soxuq9 5j.: ids on the raft, it sinks 4.0 cm deeper into the water. Wheno.9p+:k,xul j 5sfiq n 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 instrument are tuned to play at 392yh0b(2cn lw7x Hz (G) and 440 Hz (A). 2 x0(lbhnwc y7
(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 s.mqt,cf9q*o m 7k2xybz3i5b stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy sect *2q y,kfs 9qb.7btmoicz53xmion 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 prong movo jp0p9mzzn 3z40 q+bjkg4 0imi77fwyes 1.8 mm to either side of+g74ofwj0mz73p0jpqin9izym 4b 0z k 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 frequency 1ymn.p wgy.*i /g(q3n1l6o d:up;wmo l.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed / *q1noguywp.w:(o;ngy p6mim 3dl.l there (Fig. 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 t.zbs o n51yd5.qz4wesw z -p-dhat can slide wis-dez1bd .5q ynop .5w4 z-zwsthout 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 other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-sdcgvrk73f5u n )3b:(c tky *lway swing takes 1.000 v*(uy:r c7tk sd b 5kf3)ng3cls.
(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 direca )e jlx+5; u ftuu-om85alu3stion or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillation3xl 5f+ 5juuuaot-ls) eam8u;s 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 mk-iw+d 9g*fzhass 123 g is stretched under a tension of 255 N. A pulse is generated at o+ i-d*9hgfz wkne end, 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 ceiling by kb.h9 5o zr8iwa spring with spring stiffness constant k. A penny of mass m is placed on topwh k8b9i5oz .r of the block. What is 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 the junkyard. T50 yymz o+rux;e*cny,w3tv( qdhq v-/he steel crane cable is 22 m uvwnho5e ;,rdxv30 (tyc/+m- yq yq* zlong 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: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which also c es,0gyy1d b8qhy 4/qr +vd7ugives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins tc/uy 0s,dhe r7q q+8vybd4y1 go 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