Give some examples of everyday vibrating objects. Which exhibit Sg2 buongsgpi9*xj; 6kvo7 ; j8HM, at least apo;nu xk7pj*og9;ig 6s2v gj8 bproximately?

Is the acceleration of a simple harmonic oscin-h 0p ceu ys+4re33ipllator ever zero? If so, where?

Explain why the motion of a pisto:nztb 658mx,v,b fvmzn in an automobile engine is approximately simple 5fmbnvb6,zmz:xt v,8 harmonic.

Real springs have mass. Will the true period and frequency be larger or smaller l b: 8oeh8 9nhufkiv2,(f3sf;c iyn(vthan given by the equations for a mass oscillating on the end of an idealized masslyk9f:f (,he8ov2i;bcvnsi 8l 3uhn (fess spring? Explain.

How could you double the malv+i7 *:f z8o3xgeq0ovv ykknjh,r49ximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the ho7mwkp6 l(aa b uk/1h1eok of a vertical spring scale, and then is released. Describe the aw17b (ukla 1m6/ phekscale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose tp72m ,3h l39jx5 l vgzwkr 6y51vmhmyx70mcqvime when taken to hihw, 9vr50j77m 3zl mp52hm36xvy vlmykcq 1 xggh altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–4x9(bbcd eikd :ykh- +r)w9/ mv8). How could you estimate(d+edymvbih99 rc kwk )- bx/: the height of the branch using only a stopwatch?

Why can you make water slosh back 3u2dz 6q-nhss and forth in a pan only if you shake the pan at a certain frequencszsnhqd32 6-u y?

Give several everyda/sniomvb,( hha89j- y y examples of resonance.

Is a rattle in a carnw p:v1 q )h:ej pgrb20-;enm9 l6fw)ook3kkr ever a resonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal tow4. mbliyjunusz )4r /+10v il the frequency of its source? Why or wi4b s/4izry +10 jul) lnvm.wuhy not?

Explain the difference between the speed of a transverse wave traveli umd)9myg/xu) si *rt+ng down a cord and the speed of a tiny piece of the corrum yiut* sx)dmg/ )9+d.

Why do the strings used for the lowest-frequency notes on a piano normally havep,)6np)4pf9utp a4l gcfg5d/hqs0f u wire /udp5 n 0lp ghtu,pg )pf6fs)af94q4cwrapped around them?

What kind of waves do you think will travel down a horiqesm1y*s cn04iay0q 8zontal metal rod if you strike its end (a) verticy q1mia400 s e*y8sqncally from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase )/lh6el +fz3dfs* ew din temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound w*f zd/wd ehse+ll)3 f6aves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as they y wbnw9 1vz8 fbu6y ycb2ajy:33- no4dtravel away from thea nfzwb13y9o84b6jw32y v-ucdyy b:n source.

Two linear waves have the same amplitude and speed, and otherwis ol xlkgp5loh)(z i(-,8tk tl-e are identical, except one has half the wavelength of the other. Which tratk g-lhl)i(5okl8topz x, - l(nsmits more energy? By what factor?

When a sinusoidal wave crosses the boundary ben d seyagf2zvo:*15av42z4ohtween two sections of cord as in Fig. 11–33, the frequency does not change (although the waveazov: gy52 hev1*4s 2 o4danfzlength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places y/vx6*u/ aikafg;s 6n u6ov1tdrne /4dou could touch it with a knife blade withoutk6s*f;1 n 6dgai t/uxdvvuo 4/a/e6rn disturbing the motion?

When a standing wave exists on a string, jd) b;t-34fj34*yu e:h0mqayskuugo the vibrations of incident and reflected waves cancqa eutgyj4-ok bm; h4u)ufys3 :3j0 *del at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from 7 ( eonsn;(ymcfvb uyg(mny ).2s+a( pone place to another, how might we detersy)2 7y; vau(pgn+(yfcm.obmnn ( e (smine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergo0depnpq**e2 /xvy+t d es SHM with amplitude 0.18 m, what is the total distance it travels in one perv e **2detxynp0dp+/qiod?    m

  An elastic cord is 65 c4l 0 d6yytjoj1m long when a weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this t1 j4jl6 0ydyoelastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg dz2 cf+7akrm-,c qp+qf river gets into the driver’s seat. If the car goes over a bump, what will be thapck7+,+zr f-2f mqqce frequency of vibrations?$\approx$    Hz

  A fisherman’s scale strc j)y.(ld e/mxb nvzq8j14im6etches 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffnes.vj8y 4/d()zmq1m c6i j xblens 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 cjzu (v):j lw.x:kja :a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency ifvkxw: :j):(jzla. cj u only 0.38 kg hangs from it?    Hz

Construct a Table inbz(s845bl * 0qv ileijdicating the position x of the mass in Fig. 11–2 at times t = b 0i jqi(5e s*8z4lblv0,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 caug9h9 kv 2mnu c g7(z50+crdgpheht in a spider’s web. The web vibrates predominately wi+k0 h dr95v9umg2pge( zhcn 7cth 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 frequen (4wmcmd4h *jucy of 0.88 Hz. When an additional 680-g mass is m w4dhm* (4jcuadded to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per s5fig 03x 6ltz7s x h8aky4mlw0wh.m8gecond with an amplitude of 0.13 m. Determineyxms 0g a5tzi848h37x 6lfh wwm0.kgl
(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 equilib5n yq,hk*x.my/ s wu-okfs-a+,dx u 0trium is the speed of a SHO half the maximum valuet kmd uau-qyhsk -x5x*,y/owfs.n, 0 +?$\approx$    A

A mass attached to the end of a sprin0j8mrcb0w 5t p;:;* xehjn jieg 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 fu qaycncbq3ci *yg1ep7yswu525 ylsm6 ,99 ; spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach ys u9p7c 3y*25cy9,qcwey1;fbunia6 mgls q 5the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffnes jb 3gi -0wfj3* tuyb8twl7a+is constant k = 280 N/m and is execjj3 3 78awib0*gtfi l-wytb+ uuting 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 compress6naa vp2e t cuz)mi c4+j8q)6d the spring of a toy popgun 0.200 m to “load” a 0. e z6a+na46j d2uvc8qmp))cit 180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictr,k wef :op lk iqu1-rsa.l,58ionless 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 sar8luo- kf.e5ps,k iq w1,rl: pring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x = lrz :drf34w uiyo(f2vk7:3 u z(mc kru:k3gf; 0.45cos6.4t where x is in metersu4z(( y: fukl2g7c3o:vrfzuik :d f3;krr3 mw and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the z3+k3+ssv eduenergy of a SHO half KE and half PE? ±k +s3sdvuze+3    A

  If one vibration has 7.0 times the energy of a second, but their frequenciesynw7f 8w69: gyu xkyu3 and masses are the 9yu7kw3 nw yy86g:uf xsame, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hangind(g) 6v6l7d jd4 5e yg3zlxbwyg light spring once every 0.65 s. 6(z)bd4ld 5xg6g7wel jvd y3y
(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 sprin5t1 h)tsbb-or gs, each with spring stiffness constabst 5ht1br o-)nt k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t whewdxp9;zp*se1m fx+n0re x is in meters and t is in seconds. Determinx+*; zp 9sed0fn x1mpwe
(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 x2w ip exptwo.vkxx96 .35dy4of 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 uct9 aa;v g.q-*5md z2 vshy1con the end of a horizontal spring (k = 124 N/m) is struck by a hammer, wh . 15zuhdy*v-mva;2gc9s c taqich 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 constant 305 N/m vibrates wit7 z0bd.mm+qhgi5scf/ h an amplitude of 28.0 cm when 0.260 kg hangs from it. i7m h/mzqds bf5c.0+gThe 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 stiffness consnts .j)2hm oi;tants $k_1$ 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. f g/oz;p:e+gs600-kg block attached to a fixed horizontal spring whose spring stiffness cong:zpo+ge f;/s stant is $7.7\times {10}^3$ 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 hish- f jn9fdsl zt 81* 1y)iwbpnb(d/c)i 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 unstretched length of theyc9*hd(blw )1- b /n8i)tijzfp1 ndfs 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 its xx30+n *buil9a2 9xa/xoa mho
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pen4 ,xzk4 (prs 6fyr+qwfdulum be if it is to make exactly one swing per second? (That is, one complete vibrationf( r,4kp+frxw4y6sq z takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, i )pc l;uqu 73zshk(erog eu:4(ll.s;where the acceleration of uskugo ;e ls4l: (e.) ir pch37zq;lu(gravity is about 0.37 that on Earth?    s

  What is the period of jk 3i*qbzvyp;s hn00; a simple pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.ro8s/ 8ngu) yy760 m, the pendulum bob has a mass of 365 grams, and yyg o8u8sn) /rit 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 0.993 ;n sckh;yp*3b0 m. If the clock loses half a minute per day, how should you adjust the length of the pendulum? sho chpy3; ;n*sbkrtened by    mm.

Derive a formula for the maxim vx4n6:7 vt)*falsevz4 2u oajum speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing ${\theta }_0$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At it is released wo9a8 tczq ;pm4ynh/xymr* .xg4)u 4v from rest staruo4.mv9yxtx4 ;/* ycarh)nq 4wpm 8gz ting 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 7 mqslm9 8e0 y*:sfvgnx/ /dlfof his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the wavesvq/ 0s :7gf 8d9*xeynmmlls/f traveling?    m/s

  A sound wave in air has a frequency o r itzwiex((,7av 6m;lf 262 Hz and travels with a speed of 343 m/s How far apa rx6,(7evmatw(i; ilz rt are the wave crests (compressions)?    m

  (a) AM radio signals have frequencivgx.0 jcfxl0* hil2w5es between 550 kHz and 1600 kHz (kilohertz) and travel wlw0 52i .hg*jvx c0xflith a speed of $3\times {10}^8$ 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 longitudinalbn g blvi302rtz9a3 d2 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 amr3 amb7.boxw:q/p.ks the other. In which rod will the speed of longitudinal waves be3.p o/w:b 7ax.k rmmqb greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If 37qmoy1n5b xt;;w gsm the tension in the cord is 150g 1n;mt7qso;wyb53m x N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected t0nby o mim7(g1o 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 the terminal and sends a wave pulse along the cable. It is observed0g7n y(bi mmo1 that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the surface of the sea. He heauhq.jazj n bh1 5mg-1(rs the echo of the wave reflected from the ocean .j 51j1h (-ghnq abzmufloor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and thfhl-ypvdj n:i4r v5 ;h,g 59qyis difference helps in locating the earthvn -pdgy 4,i5rj 9:qfh5y;vlhquake “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 can c1sj-7ef r 13t c7ks.vfpkpy, be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes,1,tvc r.ef syps j7fp3-ckk71 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 intens i6p,jp(a pr52aak 1ym(pzn0j ities, and (b) the amplitudes, of an earthquake P wave passing thrapr2a,jk ma 0zji5n pyp(p(16 ough the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an eaizl9ia 8 v6:qgrthquake wave passing through the Earth is measured to be a6qi gv8iz:9 l$2\times {10}^{6}J/m^2$ 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)$\approx$    $\times {10}^{9}W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $\times {10}^{10}W$

  Two earthquake waves of the same frequency travel through the same portion of tir5 sz m:*;qxfhe Earth, but one is carrying twice the energy. What is the ratio of the amplitude5iz xs:rmf;q*s of the two waves?   

  Two waves traveling along a stretched string have the -mu;esxexnfyt 71 f (2same frequency, but one trans f(-fx my;7uts2ex ne1ports 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 px:76(,i f ri v0g9u*04wmyglxvaf an cond is observed to move up and down a total vertical distance ofnv(a rgx,flcfm igyi 4 vu*a0w90 7x:6 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 KE change?   

The two pulses shown in Fig. v c6gz 7vmv y( 15;2u:6jf4eo8uhjbcz0xlcnq11–52 are moving toward each other. (a) Sketch the shape 2 ejmc1 b(j574uuog08 yvq f6cznvlh 6;zvc:xof 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 has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental/0zwj 9m)1i (du8tbjwb ymrok3( zwy2 frequency, what are the frequencies of the first four ha 2w0w( ri/bwumtz9y3 1djb y(o)8kj zmrmonics?$f_1$ =    Hz $f_2$=    Hz $f_3$ =    Hz $f_4$=    Hz

  A violin string vibrates at 294 Hz when unv 1)6i91haauj0-e s kzncs2 :mipkl*ufingered. At what frequency will it vibrate if it is fingered one-third of the way down fro6 cz01e i* )km:u2klpj-isnva 9u 1ahsm the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a1cjv. 5f 5vt2sor 0cyu frequency of 280 Hz. Name at least t5v1fyv2o 0utcsc.j 5rhree other frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  The velocity of waves on a string is 92m/s If th5x/um7io4gt ew*ll5mm 0aig4 e frequency of standing waves is 475 Hz, how far apart are 704 x otlwmi*gml 5g/ea5miu 4two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, what isqd, pv5f 91qev4+9qp) lo wdvc the frequenc df +9qpe,q)vpv4v1cdwq 5ol9y of the fundamental?    Hz

  A guitar string is 90 cm long and has a mmxiaml70;t b5m8blx 2ass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of thebxm2 l;bi xa8l7t0mm5 fundamental and first two overtones?    Hz

  A particular guitar 2:) m all7 csrx,nxta1string is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what pem2sc1)ta x , nlrxa7:lrcent should the tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hzmudvhn :f3w19 lze /u1, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be 3/z9u dhm uwnev:1lf1 changed to correct the frequency? decreased by    %

  One end of a horizontal string is attach-pt js uq 7g1j1wk6jk5ed to a small-amplitude mechanical 60-Hz vibrator. The str suq6tg -j1k 5pkjj1w7ing’s mass per unit length is $3.9\times {10}^{-4}$ 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 pulley. Ib((5x8vv nu,qurkrkh ((6 cnwf the hanging mass m is fixed at 0.080 kg, how ma5vk n(c vuuq(,(6w br8rkn(hxny different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the right fkx)z)b49ffz a requency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speb) zxaf94f) zked of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s su-w342q, 16n scm.rb yqvl9bxsc )ts wtrikes a boundary within the Earth between two kinds of material. If it approaches the boundary at an inciu6tm3r2 1wsn4,s. cb wby )sxcvlq -9qdent 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 r l6n03ucaozg .+z 6xybgf-7yr/3 swo changes from 2.8 m/s to 2.1 m/s 3 .xznrz o/0 3rg67uyy6l fo-+abcgswIf the incident wave crests make a 34${}^{\circ }$ angle with the shelf, what will be the angle of refraction?    ${}^{\circ }$

  A sound wave is travelem. ((m)g.nh5b(o0 sdptz xvzing in warm air when it hits a layer of cold, dense air. If the sound wa 5x (sme.)(z gz(npvohtm.db 0ve hits 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 strikeu/t76c8ufzd)kco0hiw ss r4 /s a boundary between two types of rock at a 34 oc/0iskrs/zuc6d f)h7u 8tw8 ${}^{\circ }$ 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 diametelx,r 0a jkb(c6r. According to the user’s manual, the dish , c (ak0jb6xlrhas to be pointed 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 velocity 750 km/h travels 00xu 0nfxtxj 7ows)s0across the Pacific Ocean. As it approaches Hawaiin0x0o fj0 xu0) wtss7x, 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 and boats.)    min

  An energy-absorbing car bumper has ;.t59g h zejura 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 consezg.e5 r9hu;jtrvation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which stretches thecr :9nvz; mv6b net 1.1 m. Assume that the net behaves nczv9 v6;:mrb 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 freela j5q (5u ij,4gormd8xy hanging spring. The mass then falls 33 cm before it stops an4o,mg5(a 8j5q ujrxdid begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed vey 1n)wc3ujut *d7qb54q r)rof 22 m/s (Fig. 11–54), compressing the spring 5.0 m. ( er y 3ur7t jcq5ub14*vnwd))qa) 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 the right jv(;pberu(z * pace of about 1 step per second, the coffee sloshes r (vb;(ejp uz*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 centel6:m)f gm ve8c+1t zy2ap3ggbr of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will bz8e 6b1clp3v2af +tm )my:ggge the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates4rr,id;vr.e-llaipy-n* z 4j according to the equation x=0.650cos7.40t where x is in meters anr p--ye ;l4.*,zri alnridj4vd 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 oscillates with fp3z,n4wzisx5 requency f. What is its frequency if it accelerates at 0.50g (a) upwar4nx5w,3 izpzs d,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands omg:qy47 fftv -e3mom1o8hdd7 n the raft, it sinks 4.0 cm deeper into the wa7h1oe3mdg74-:ym8 vofmt qf dter. 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 instrument are tuned to play at 392 Hz (G) and 440 Hz (fll3+b1u.b ba9p z*un b*bbzl1nau9ul +p 3f. A).
(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 tra 3g76e0vikr+mp.d wljveling down the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of ikmlw.je6+ g r03vdp7cord or the lighter?

  A tuning fork vibrates at a frequency of 2 kn3i*ru74xkr */;j1e shh frx64 Hz, and the tip of each prong moves 1.8 mm to either side of center.*xj urnx1ik3*7fh e;r /k4rsh 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 oli7bczk6jd8 1h .mx- lf frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscill- izbdm l6xl 7k.hjc18ation?

A string can have a “free” end if that end is attached towo ufm+ 8i.yim10q)f c a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths ofi 8 u1qcmiym+f.w) 0of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000syy,j qg96 /k ,fiwji) s — each one-way swing takes 1.000 s s ,/wf,q9gyijkj )iy6.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793{\mathrm{m}/\mathrm{s}}^2$    m
(b) If the pendulum is moved to Paris, where $g=9.809{\mathrm{m}/\mathrm{s}}^2$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62{\mathrm{m}/\mathrm{s}}^2$    m

A mass hanging from a spring can oscillate in the vertica mbjccc ca:k c,ys4g+*8:cf ;gl direction 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 oscillations or the period of the horizontal swings, and by what amount? [Hint:cbc*c8may+ ks jg;:fg:c4c,c 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 $\left(\begin{array}{c}k=130\mathrm{N}/\mathrm{m}\end{array}\right)$ 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 of 255 N. A pulsdl 1gsuvt*r- +(qpcw0 3cq 6fue is generated at one end, and 20.0 ms later a second pulse is ge+utcdg c630r-pu v*qq fs1lw (nerated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiatas c i)x..qt:k2+duling by a spring with spring stiffness constant k. A pennyqic kt:tsda. )u 2+a.x 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 of the block? (Assume $m\ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cable 25dq cm y*7ez0a dnirjile:/2is 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: Refer to diie:rc*z2eaq7m5j02 nd /yl Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which also givcsd*rah) bs-0)q xn6u es the dimensions of the block). You push it sideways as shownsuxqdsr)c0- )b nh*a6, 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