Give some examples of everyday vibrating objects. Which exhibit.m4zuboa( + vt SHM, at least approximatelvt4za.m+ob(u y?

Is the acceleration of a simple harmonic oscillator ever zero? apd (h;ky0qn f4:g 7ljIf so, where?

Explain why the motion of a pi. 5io27c;qm yku qmv 9h3iltu:ston in an automobile engine is approximately simpleu ;iuohm q vk25 cl7:.qym93ti harmonic.

Real springs have mass. Will t* kzmz fit j)9f 9tswk+4l*ho+he true period and frequency be larger or smaller than given by the equations for a mass osk+m9z*jwois+k)t9 f4 f*lth zcillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillat /npy. 4jys(gjti amb76wt.o8or (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and then iss yui 7m3jz7odw,/ov; z9vkh( released. Describe the scale ryko sm7z7v/zjd;( ,vuw39o ih eading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose 0:zo:6nccz k mt 8xb6ztime when taken to nkzt:xcbco86m0z6z: high altitude? Why?

A tire swing hanging from a branch reaches nearly t byg2fj9c45smmdxg7krm* i5)o the ground (Fig. 11–48). How could you estimate the height of the branch using only a stopwatcsjd5 mgf 25rk i 9)x47bmyg*mch?

Why can you make water slosh back and forth in a ptt(wpv6an k d4*h-f 3yan only if you shake the pan at an64wv tdpftay(k*h3 - certain frequency?

Give several everyday examples ofhi8 w/:gcs 6s yeg1wogn uh/(6cn)+el resonance.

Is a rattle in a car ever a resonance phe c-/.8oo a7p: m0o,d 58youokwdltyq onomenon? Explain.

Is the frequency of a simple periodic wave equal to (qow/f 9 2 3qjn:wud ex6 mr8q1i 4usdbhyt1s2the frequency of its source? Why oruos :d1njemtbwr1h(8 q w sx293dq64f/q u2yi why not?

Explain the difference 0au .i rqekq5/between the speed of a transverse wave traveling down a cord and the sp5aq rq/ ki0.ueeed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano norlym,ks sy6.3t, /wly o fuea9se30gz;mally have wire wrapwyzeo,ayk/,u3g l9 sle s;sf m.0y3t6ped around them?

What kind of waves do yn3n v658:q3u (e*6npqnufwk rda),drsj zb- hou think will travel down a horizontal metal rod if you strike its end (a) vertically from above drnq(-)nez fds: 6pvrnujq6w*u3na5k 3bh,8 and (b) horizontally parallel to its length?

Since the density of air decreases with x1r o4prwfz8f;lvz,b9ah9; y an increase in temperature, but the bulk moduhlx rpy9b 1vw9;f4ra ;,oz8f zlus B is nearly independent 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 in k*+tcdhjp o+wyju;*6.d o 1oz5dl -gm amplitude as they travel awayu 1dod.dj6 jkhw tl*+pgc; 5o*+o-zmy from the source.

Two linear waves have the sam bkm yh6wr3;,5gc(mpfe amplitude and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits more energy? By what f ,fg wr5mk ypc(36;mbhactor?

When a sinusoidal wave crosses the boundary between two sectig/dj; 0jh9 u(ez)xwvsoz(;q jons of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Explain whse (hd)q/jjzj;guw z;9 v 0(oxy.

If a string is vibrating in three segments, are there any places k74:n)2 td j kwpzgl/3 rlsgn1you could touch it with a knife blade without disturbing 27nngps:t jk/lkrdl3z g1w 4)the motion?

When a standing wave exists on a strinnd w211qxfd+*fry, pto l+ l8bg, the vibrations of incident and reflected waves cancel at the nodes. Does this mean that energy was destroyed? Explain. x*d tdb2 ,w np11+fylr+8lfqo

If we knew that energy w vji0kzj*mh;sdu q65t o 3+ss:as being transmitted from one place to another, how might we determine whether the energy was being carried by paj z* 6sjs53o +t hk:q;d0msvuirticles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, z7kn9n+ g/iptwhat is the total distance it travels in p/ nnzik7+g t9one period?    m

  An elastic cord is 65 cm long +8nl/ jgz02nzv uocg9 fz2f0cwhen 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 elastic cord?n+fv/9u zn j02f 0gzcg lcz2o8    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver gets into;go0 1wsrj z,a4.asx o the driver’s seat. If the ar0j ssow4 ox.gz1;a,car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangtw7v+zzgowbqp *:0j+ fm5li k 5(msh1s from it. (a) What is the spring stiffness const5i0bj ktvzq+(+*m:ow p lz fmgh5w1s7 ant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mass of 0.60 kg is hue77.inc )bxy kng fromkny) .cxbe7 7i it. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 118z;) (xdapzeb–2 at times t 8xdea(b); zz p= 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 predomx z, lsizfyuz78/h/;u pfml2t21 je5jinately w yuilfe/mfh8tpjz2js;z 5 z1/x2 u, 7lith 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 freq5 hn o4 goy/s:zz/skvi z7:z9cuency of 0.88 Hz. When an additional 680-g mass is addedn z :5gvokczs ys/74o:ziz/h9 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 go e-2syvx1 -cspring vibrates 3.0 times per second with an amplitude of 0.13 m. D-g yso1- e2vcxetermine
(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 Sy-3io zzb k6udv50/fxhjd28 jHO half the maximum valu6-x /kdf 3dh0vyzb ojju82i5ze?$\approx$    A

A mass attached to the end of a spring ij(lg1:2huo 9ewmvwq 3s 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. ew 1v(j.vzbku*m mf l39gb,s5 If the spring is stretched an additional 0.130 m and 91s5 .,l kbj*uz(f vmegbvm w3released, how long 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 stiffne)hu*crowh nn:05+ hthss constant u+nw)0:5rth h*on chhk = 280 N/m 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 pop,.)2,p swjz do6ttjyegun 0.200 m to “load” a 0.180-kg ball. With what speed witt es,j2.6,wjo)yp dz ll the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attacw)s jme p1.wa s-8v:1-nxtrmyhed 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 )jve ay1 n-txs8mm-ww:pr 1s.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 vibra xu/)qju71qs (gl h*n1.aki8) g fwcjptes according to the equation x = 0.45cos6.4t where x is in mkq wx (n8p11l j*quu )h7a/ifgc.gj)seters 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 isa+ p anioglnzk .xs7f0m *e/o;fo(g;. the energy of a SHO half KE and half PEk*x ns o/z.i;opm7 lfnaf+o; (0.a gge? ±    A

  If one vibration has 7.0 times the energy of a second, but their freque3awiq51hrvs syjnf 0)vit 1* :ncies and masses are the same, what is the ratfr3vnw1*)as :shit1y iv5 0qjio of their amplitudes?   

  A 2.00-kg pumpkin oscillatyb/zkej,0) ,xkd .qzges from a vertically hanging light spring once every 0.65 s. z yq)g,.z0/ , bkkjexd
(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 vz/v u,ulunk1qp7 9(wk3b/ spm ertical springs, each 9nuv1quw, up 7/sl3mpk /k(bz with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equat63 ga7skmer3iion x = 0.38sin6.5t where x is in meters and t is in seconds. Determine 3gir36eksm 7a
(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 o6l0ib/ 5fb ypof 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 on the end of a hor*aiuna rxommc/l 6l t+ )x33g5izontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an inmu3a x/ ci*xgm)at6l 53r+ nloitial 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 s 8aaan n9m3-urtiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.28anu -mrna a3960 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 spring stiffness chtadq8 kde-/ 1onstants $k_1$ 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 attacpxyvu2* 88o/yyf xc 3yv:h .ached to a fixed horizontal spring whose spring stipuvf8vyaxy :cych2/yox 8*.3 ffness constant 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 hisz2mop d0t)dt+ 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 oz02tdm pd )t+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 60 s. Wuowbzu:p /s jlt, -s56hat is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pmas hkf);g1rahsl48v0si +0 tendulum be if it is to make exactly one swing per second? (That is, one complete vibration t0v0;i)mh 1t 4f+gr8 s alsskahakes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period h3 du3:yyp-ond:-a xo/ qk4js on Mars, where the acceleration of gn3 3j/sy-o: po 4q:ax u-dhykdravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80;v92sozvk chs y0p1j 0 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 m, the pendulum bob has a mass7c2l; 8 l)d mkngv;ayc8lqqj ; of 365 grams, dlq)8c2yjl 7lmvc;g; n8 a;qkand 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. If the clock loses b0:pvoxno2j:7:px+ 4vy -qju n9 yywphalf a minute per day, how should y -0ppvpb:+97wouvyq x:4oyjy 2j:xn nou adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum speedx7q *5a9bbj o45v,o.f ebzso w $v_{max}$ 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.( htzkv1l qxvr x:i0 )*wa78hf5 Hz. At it is released from rest starting at an angle of 1 0 xvztaqhl7)*virw fk(x 1h:85 ${}^{\circ }$ 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 2: 9 ewabv8*ytj qr3nethe bow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the waves traveaqr*2:bjtv 89y3 ee wnling?    m/s

  A sound wave in air has a frequency of 262 Hz algo71epof6oae /wr u5n7 q6p.nd travels with a speed of 343 m/s How far apart are the wave crests (compre76r fg1qnpel5ooew o7/ap6 .ussions)?    m

  (a) AM radio signals have frequencies between 550 kHz andjxir* obdsfbw+pw8(,/ ;ux(m 1600 kHz (kilohertz) and travel with a s,(djr;ib( u/m* 8wfx bpw +soxpeed 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 longitudsa/oz38x)la/rs(zu5 t8 d jmminal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same el442bljeie 0 ikastic modulus, but one is twice as dense as the other. In which rod will the spi4 elib 0jk4e2eed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched tlpyieh0x+ 3 v ;tr(r4between two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a ph4r3vtt erxlip+0 y;(ulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a s*,qu6 uf+x gerteel 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 observed that it took 16 s for the pulse to reture x,gu qfur+6*n.
(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 belo2 y 6 0gca,xy rkwb +,i*ik,hd 8vb6lpv.ag+vhw the surface of the sea. He hears the cbgy , ,k rx2 vpdhwlkvi0a +.gv68a+*bi6,yhecho of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and the;(;4fd psqbqrot( gp q+v:ge1 7x 1pgis difference helps in locating the earthquake “epicenter” (where t4:g; e qgq ;1+7qpfpvs(x p edorbgt1(he 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 be approximated by a sn4bnzwpz+ dqk * e7lb1 tv)o(4inusoidal transverse wave. Assuming a frequency of 0.50 (+4zvk4 1lwezbdo)qt7n*n pbHz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, ad0 .7j1 gp6ostuf i;h:bya zq8nd (b) the amplitudes, of an earthquake P wave passing through th:1g dfj7zp 0;uaos86bqyit. he Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is meapled*9f(, ps isured to be iesp, *fp(dl 9$2\times {10}^{6}J/m^2$ 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 59hmjuf* u.ees 1rv2v travel through the same portion of the Earth, but one is carrying twice *h s. efmuvu5rvj2e91 the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretchedqe;fk2*)a k3+f,ixsbxl i bt ny b/1w8 string have the same frequency, but one tran2;)w /a1et bx3il b,+qkiny 8sfkx fb*sports 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 move up and down a totaf9v w/72d9 -/hs v hatwwhctg5( nzd;pl vertical distance of 6.0; 2g(tawwzws-pvcvd h9th/5/7fd n h 9 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. e k:y08ud5s ai11–52 are moving toward each other. (a) Sketch the shaped: u5sy 8aike0 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 has happened to the energy at this moment?

  If a violin string vibrates at 440 Hzgpv+4ixg5 l( ha7 f,9mw3 iz +rhylhd-8ojnd8 as its fundamental frequency, what are the frequencies of the f l 4yw(+o rgh hdgvi,8ah dj5+8p-7xlf i9m3znirst four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3$ =    Hz $f_4$=    Hz

  A violin string vibrates at 294 Hz when un56zv wzhb-2wifingered. At what frequency will it vibrate if it is fingered one-third of thvz wib52wh6z- e way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops a6 i;z 9i.vaybvt a frequency of 280 Hz. Name at leastibi9.zvy ;a6v three 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 the frequency of standing waves 3jes1jsr2kyz +e 6uha;i, mh gt7/;znisk2e1;s ;mhgrin3/ju,hj szte76ayz+ 475 Hz, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 c81nhz5fbz ka v-tr+3o.fin is5n6:oHz, what is the fre- 6k5n 1. t35oairvciof+bz8hn z:ns fquency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g.tv/gx r8rh8:s 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 the fundamental and first t /h8g:xvrt s8rwo overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is measurzjflf): 7u3o(dkb wf8ed to vibrate at 205 Hz. By what percl )f z dj8ouwff3b:k(7ent 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 sum :18x qj74 -gwsvm)o4qcw ybupposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension )j1 -: q4bo7u4cy8vw msmxgqwin the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is pr- l*o0sx3g4in+ :oonby/dnattached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass per unit le+*dxp 3:l/ nr0byoon-4gnosingth 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 tht ad3w :+ c t 3e;s;5a8d3jij pvh4yf0i:qnjcee pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varyinj0in5c;j3+d;s:hvt it 8yp3dj a a3ew ef4:qcg L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a w4p(n 2wdo :)dd;9m cvtkq ldf+hr;z1tub at just the right frequency, the water alternately rises and falls at each end, remainingt1fkc:wndhod ( 2p4drmvwz9;l )q +; d 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 wxnb.;rigx 4y2*z tz bm8id .w8ithin the Earth between rtbm8y;iw z2.ng4zd.b*xi 8xtwo 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” where the velocity changes fro/b hi9/tc lzik;7*qf9ei s:vjm 2.8 m/s to 2.1 m/sv7;9ljht / zc bii /:qekis9*f 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 when it hits a layer of cold,f-psvd. a10b80ekci+0 na umy dense air. If the sound wave hits the cold .v0ykmb1n ec8ua p 0-diasf0+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 si- xzbr 4qzf;1trikes a boundary between two types of rock at a -zxb;ifqz14r 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. A km9 ,8ppx gerg:se.3xccording to the user’s manual, the dish has to be pointed 9pxx ,.ek 3mgsr8g pe: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 xuh r mac:m pdad(l)2h7,rsn2ppx2z9k df;92 velocity 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 h97(a2padrcrs22 z xlmk2hdump hx n );,df9 p:ave died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has axe1hrud:- .bbbrp5tex 4,h -p spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500- te4pp 5d:ux , .br1re-xbhbh kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18whdf o+ 9l0:vh m below, which stretches the net 1.1 m. Assume that the net behaves like ow0+f9 vl :hhda 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 freeey70epwrhmuy g4hd*(/il4 8zly hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the freqhyi0 /4rdw*p87ueeyg lz(h m4uency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), co :0x7dpkdck q3gk+h /jb iut(/mpressing the spritk hkug3xc/d7idkbq0 + (/j p:ng 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 coffee (di)cnqmvzn b5 m8cm2d 6.:ckch;ameter 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 wave2n)v bchdm 5ccqc.;mmk6n8z: s in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the cen yrovt0n 9xn3.oj2 cg5ter of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sound jr 0 tc2xgnv5y3.noo9emitted?    Hz

  A 2.00-kg mass vibrate )( zrcbb4rwc0s according to the equation x=0.650cos7.40t where x is in meters and c0z(bb rc4) wrt 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 frequenm -sg+4 al*gee/xju0 rcy if it accelerates at 0.50g (a) upxe 4 ejg0/+r-m*suagl ward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raft,h1+uplb 9l t48ll*v mw it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for a whhl84m1lub*l9p+ v tlwile.
(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 tune;u,by jd)sbx(5ryv+ jd to play at 392 Hz (G) and 440 Hz (Absj,yur) +;jx5d( bvy).
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stretched two-part cord 2 7rx zcgp4i-5j shpk-of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavcxpps75- -jg4i2r zhky 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, and the tip of /akgz yx;( y8ceach prong moves 1.8/yx(a gk;czy8 mm to either side 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 frequency 1.*his w (z 0o/.sfz9idt5 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 t9s /os0d.(hit*z zwfi he board during the oscillation?

A string can have a “free” eu ,gciu7wvbkrz:8+ v8nd if that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the reson7kvzruc+ wb: u8vg,i8 ant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period ofd4ojgo6.yl5 s8/k 0 qqgqqx:f exactly 2.000 s — each one-way swing takes 1.000 s.85 gk o q/l6d 0qj4yqf:xosqg.
(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 oscilur+1 ilw3jos 1 6dcof3late in the vertical 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 t3+swj163iouf o1rldc he 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 $\left(\begin{array}{c}k=130\mathrm{N}/\mathrm{m}\end{array}\right)$ 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 da:3ay *xl rf9255 N. A pulse is generated at one end, and 20.0 ms l xr*9daf: ay3later 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 a spring with spril.c(v x srrx);ng stiffness constant k. A penny of mass m is placed on top xxrc ;(rl)v.s 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 sto6o i ;luerfr41f/q a2(b qu8weel crane cable is 22 m long and has a diamet(qi eqflarf6b28uu/ 1;o r4 woer 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 (oe94rl.( xge9 ims d+xwhich also gives the dimensions 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 (Sedlr o9m+eg(e 9 .sxxi4ction 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz