Give some examples of bs- +p2 emf1v ;;ehvoqeveryday vibrating objects. Which exhibit SHM, at least approximately?f+e;-; o2q emh svbvp1

Is the acceleration of a simple harmxlr 3o8tjty( b2qsu 76*j7rf, 9h-ov y/wt vsmonic oscillator ever zero? If so, where?

Explain why the motion of a piston i fpt5i+ ntp-v7uaaq1s y,42nmn an automobile engine is approximately simple harmoni+qtvn4yfu1n- 5 pma7tps2 ,aic.

Real springs have mass. Will the true period and frequency be larger on;wzo 1cvanu*zt2i: ah0 v5g1r smaller than given by the equations for a mass oscillating on the end of an idealized mass i5 2z1cohaatu; wnn1 *g:0zvvless spring? Explain.

How could you double the maximum speed of a simple harmocn fcj0l8h)gd2.fg)nnic oscillator (SHO)?

A 5.0-kg trout is attached to 9fsdy-uq: y60qmim l +the hook of a vertical spring scale, and then is released. Descq:9y usily-mmq06+df ribe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose time rs tk6vj qu*kn0 8d6x1when taken to high1uvtkj 06q8s6 drkn* x altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–48)7td.jwk-0 1,1 qi1zlo zfc ofkaiv33g . How could you estimate the height of thlckf1j3o go-1tdq01i f a.z iv,w 7kz3e branch using only a stopwatch?

Why can you make watem h++s; *gzrpbr slosh back and forth in a pan only if you shake the pan at pzb;rm *g++sh a certain frequency?

Give several everyday examples of resonan 4m4c fzq(o-0kt6gyy6ga k)ufw zxmb,.3nfv4ce.

Is a rattle in a car ever a resonance phenomenon7e: auv se,,cq? Explain.

Is the frequency of a simple periodic wave equal to thkpak86vh *ki sl*c-)p e frequency of its source?6 vphki kcal8s*)-*pk Why or why not?

Explain the difference between the speed of a transverse wave tpessa)d sga):0s x h*qd*p +-traveling down a cord aps-)qdd **xaes hp )tg+ass: 0nd the speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes0v.yb0e7nr3x ikjsndm, 0 ed 7.)mmca on a piano normally have wire wrapped aroundn7smx0 7 ekdrjmcab0d,m.3 y)e 0.v in them?

What kind of waves do you think will travel ddy60w6vhs/fr4gj(c5eunw z ;own a horizontal metal rod if you stwhcdg5ef/y4 v wu(jr6 s60n; zrike its end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase e 9).3al.metm)f4zg lbahp(k7tr as5in temperature, but the bulk modulus B is nearly independent of temperature, how would you 7lmape(za 4a f9 )t.skhg)mrt 5 b3l.eexpect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water wav;3 6v csqe62djintu2res decrease in amplitude as they travel away from thei;26s2t vdeq 3rcju6n source.

Two linear waves have the same afalyog.kv iz5- ,oec4vz40; p.hr , urmplitude and speed, and otherwise are identical, except one has half the wavelengthz4rp 0ok,vczai4f v.; , y.roe5-hlug of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of coro2skv zx s0 ;jkfld*;2d as in Fig. 11–33, the frequency does not change (although the wavelength and velocid0s;lzjks* of2;k v2xty do change). Explain why.

If a string is vibrating in three segments, are there any places youl yw;olr/ l h6,k5 3zhkc;k qboq/-lv5 could touch it with a knife blade w lz;/ko5kk-qvlwhy5q/ 6 b, l rc;lh3oithout disturbing the motion?

When a standing wave exists on a string, the vibrationh548es +oz 7ya hq,kiq9cf5 9e/qmtkys of incident and reflected waves cancel at the nodes. Does this mean that energy was deqheif7k 85 +q9o ekstz 5cayyh/94 qm,stroyed? Explain.

If we knew that energakh 4mza3x/vt/-kct:vc,t z/ y was being transmitted from one place to another, how might we determine whether the ec:3,tka takzx- /4vv/ /mchz tnergy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitunfrq-f5s :r2:w 3q tcqo/tp5s de 0.18 m, what is the total distance it qsf 5wrcrnsq-t /35tqf o2:p: travels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs fro*f lvq (xfln+2m it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of thxlfl *+fnv2(qis elastic cord?    N/m

  The springs of a 1500-k/.hmdw5c+gemomq :: j(ri m 2yg car compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car /de gwmij y.:c o2q:hrm+m5m(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 f :8uf(ez fih.fish hangs from it. (a) What is the spring s. z:f(iuh8 feftiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mass oiw015it t+p 2 i5m 1x78j;cknmatbm gof 0.60 kg is hungm0it+ jc5pa ;t1x2gn 7 8tm ibok5m1wi from 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. 11–2 at times*u10 jgjic) 2a arjr6t t = 0,t crgij0)j*ta j62au1r = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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+ 0d xgjf evds(9in(k1 in a spider’s web. The web vibrates predominately with a frej dxv k9 df+ins(10ge(quency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency of 0.88 Hz. When an3 rl x 5f;w9j gh,0jm)difi8ew additional 680-g mass is a elhj,iw8j9gf ri0x f3d;m5w)dded 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 vix m/t d 8ma0j941qksrcbrates 3.0 times per second with an amplitude of smr q1adk0 48mj9xtc/ 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 is the speed of a SHO6 x-hwuyg: t3;: ltovv half the maximum value?l :-:v 3oxtth;u6 ywvg$\approx$    A

A mass attached to the end of a spridpih cf 5avwkn 2)w3k,:u(t l7ng 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 spr-aaop 6r 1.erping is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibriupprr6a.oe-a 1m position again?    s

  An object with mass 3.0 kg is attached z. zy*omob )t0bsop69to a spring with spring stiffness constant k = 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 .0sbompzy z* tboo6 )9of 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 802yyi bsvux fc:ac+)ewk /::f* .0 N to compress the spring of a toy popgun 0.200 m to “load” a 0.asi:w bu+fkexcvf:c )y: y*2/180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one end of a. 8s:zjnlpjau- jb6x,u8a n a. spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, tnu8l-u pn,b8 :a. a6.jsj zjaxhe 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* m0g 9j qqio(7aywr4s = 0.45cos6.4t where x is in meters and t is in secondm q0*(j49iwysr ogqa7 s. 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 enerno emad)g5sqo.) 2ot8gy of a SHO half KE and half PE?d52.on8 ae)moos tg)q ±    A

  If one vibration has 7.0 times the enerno mswu k17kv.o-p), wgy of a second, but their frequencies and masses are the same, what is the ratio of their a kowwuk v.7 )m,1nop-smplitudes?   

  A 2.00-kg pumpkin oscilp0p*qyu g 8)ydlates from a vertically hanging light spring once every 0.6p)80 upyygq*d 5 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 identicahuj- xmir(7ae: t/g:zl parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of ( mau-txe:hg7 j:z/r ivibration?

  A 300-g mass vibrates accor .ut+ vk2boe.jb ev:ch6cok*9ding to the equation x = 0.38sin6.5t where x is in meters and ..+buvkvtbhoc :*eokcj2 e 69t 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 pk4im,zpmlx4++ -y1xijpj * rof 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 mdma0 vpf)jxr2.mv8 7 rest on the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 28 ).amvvmjx fdpm 0r72.96m/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 vibratlqdh*ujcla2 +-*8qh kes with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the eq8l udh qk 2j*hlca-*+quilibrium 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 tw j 9ng,oydcz d/jmamk0 ,p r-)zhd9:9lo springs, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed horizonv* yo .5.d-*j1qctc1rubve yatal spring w-q1trcyjv. ca*e.udy * v15obhose spring stiffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with)rg84 9mgsa cxvfz,n2 mass 65.0 kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point ei,)4 gva2z8 fn9mgrcxs ght 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 v-q7 nj, ngg/ ;tg1imcuibrations in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simpl) 6f 6)lhy f.a6gkdrgme pendulum be if it is to make exactly one swing per second? (That is, one complete vibration ).l6ag yd ghrf)km66f takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its hsl,z1w pbe -.period on Mars, where the acceleratl,bseph1- w z.ion of gravity is about 0.37 that on Earth?    s

  What is the period of a simple -r e001 lb) q;sriuengpendulum 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 m, the pendulum bob has a mass of 3-,bupej2.3r,ip c-u:a; p lhmyc e+sc 65 grams, and ite2 .r-yacpb-sjlip;cm:uep c, h,3u+ 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 pendul8f2s1 zbi4mxl um has a length of 0.9930 m. If the clock loses half a minute pe4 ms8lx1 zbi2fr day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maxc0r-z4*1vb w ) j gyk4(m.pp:m rxkfoximum 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 from tu3kwnvezt3p sm/mg 1,ux2j; f.b) 4erest starting at angv x4u ;1 3p e/ws,mmjtf2u.zb3e kn)t 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 u01 1:z9 kthuvf zrv8vcrests pass the 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 travelingvt 0v:rv9u1z8uk1h zf?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with et36mj pofh0xe,* ji+g efgqc 96ei.q*r+h9da speed of 343 m/s How far apart are the wave crests (compression xeff ,9.j*o e q+6mee9jhirgditgchp+q603 *s)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kha 9f/fi 9 +lvgjz)e(dilohertz) and travel with lh/d)gfe+fj z9 va9(ia speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal waves inss0c e7g,2 ; v-fluwahs3c 3tk
(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+ b(jm/ cei dkfw+h e8v0uf11k as the other. In f( evhbkcj8u+me/10idf k+w1 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. It+iv lcox,sbopy :*mid rg:5n t2:396l -sgobf the tension in the cord is 150 N, how long will it take a pulse to travel*p gi6sx::9:t+ nclgoo btsm5- o ryv, l3db2i from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable it+ xmy4qr88n 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 retur+4yx88qir ntmn.
(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 bem kv ;eo**kv2dlow 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 ocean at this p m;2o*dkkv* veoint?    m

  P and S waves from an eg*wgg cd5il9ix+;b w7ngt 7:rz ;in+rarthquake travel at different speeds, and this difference helps in locating the earthquakectn+ wbx77;g;i: n z9 g*il+id grrg5w “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 be al lnc2)(*du6., vp.inmmwmfhpproximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set mwm.lm d(*lf n. nv2)u h,pi6cthe acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of an earza)sqw 91he3vthquake P wave passing through the Earth and detected at two points 10 km and 20 km from the sourewh) s1q9za v3ce?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth isltdpyu6-6601 psb(dr pzeq ,q measured to be yqp 1rl6d 6,uzb0t-(se q p6pd$ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency t, 2efq1ha5 oxvde6 r:ee2t5)gu*mnl bravel through the same portion of the Ebe*6gveh tamxqo1 re2f,und5 52l )e: arth, but one is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the sarkxd,c6 cou :/me frequency, but one transports three times the power of the other. What is the ratio of the amplitudes of the two wave:o /xdckcr6, us?   

  A bug on the surface n . invo42 d.;fp7qe+sfutrrxdsm/7y7e,i c0 of a pond is observed to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripple+;rv4 oud. nyesi,fdx02./iqe pft 7cn7s7m rs decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown inc+/ hutwm)k 9.nmr2pl Fig. 11–52 are moving 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. 11–36a, at the moment thnckm )./hrw+m9tpl u 2e 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 frequency, what /ddf cgrbcc,f,.i)f9 are the ,i,br/g .cfdcd )c9fffrequencies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 H)p8i.ulu(l/knl f 7vdz when unfingered. 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 strind)v8 nll7u . if/lup(kg vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequencrvc63 fg.0d eky of 280 Hz. Name at least three other frequencies at which it wi60 rckf.vdge 3ll 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 standing9p wb e(q-hey74zdrl0r*1dxbm3 3hen waves is 475 Hz, how far apart are two adjace( bpen*3qwdbh1 9hd34mex 70-yerlzrnt nodes?   m

  If two successive overtones of a vibratings,z ,3 cdysu7urgs.. w string are 280 Hz and 350 Hz, what is the frequency of the funda,7z w3sc..sygu sdr, umental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance from the brq(fj edp/z +k;idge to the support post is L = 62cm and the string is under a tension of 5+/z qpjd ;kef(20 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 2:wna7-0 t1oqj 8 nuhqw(m89(iviky u y00 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequencies ak uw7a ni0t(myv9:(y -w1qj8o iuhn8q re,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar str*q-dn *moyu 9tlp z0if:3 w cw.4;ymnying is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency? decrease-q *c n.nt:iumym ow3y ylfz; w90dp4*d by    %

  One end of a horizontal string is attachedbt+u tag3jg,3l vq4kof: rpz 6,b7h9k to a small-amplitude mechanical 60-Hz vibrator. Thet k 3v+ 9 jp gogqbk,,h63u:47tzlfabr string’s mass per 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 8f),va / mm y fu zwvgfj8o27i/y:i)(meaca4 istring may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achiemf4m)j82a, gv(/a:uciiefy io ) z /a v8yfmw7ved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at jusbeq.*6le .c gpt the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a sta eg*qelc.pb.6 nding 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 withi -vxa/lk hy,+hn the Earth between two kinds of material. If it approaches the boundary at an incident angle of 4h av xhykl+,-/7 $^{\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 fro4ssz5 trs,rl( m 2.8 m/s to 2.1 m/s If the incident wave cr rrl4( s,tzs5sests 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,12euj 8lpje 4l dense air. If the e2u8llp e 14jjsound wave 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 strikes ajg.t e**biijbn.f:) t,zfi0 d boundary between two types of rock at a 3tn bii.0)d**f.f:,ztjejbgi 8 $^{\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. According to the user’s manual,v x/:fs8is xju.o v4 4u*0b f.fvbfoo, the dish has to be pointed in the direction of t4f*v,.vif x/0 xb8.jus4ou:vo fs ofb he 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 velomm.,d3c uztifb)y/9r )hf dv)city 750 km/h travels across the Pacific Ocean zfvyb))3/d .i u9 t)c,fmmhrd. 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 and boats.)    min

  An energy-absorbing car b n /7301 qi59zn azjvulvhhee5umper has 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 2.2h35el z50a ije/ z7 9n1hvnvuq m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fi( oc16ldw5lymu t+1e ere net 18 m below, which stretches the net y c+1wt5( ml1e u6oedl1.1 m. Assume that the net behaves 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 ma1 1wkgri - h9h*.wf3elfk2 bqrss then falls 33 cm before it stops and begins to rise.qhrkwhef*g11. l-2kw9ib3 f r What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a h8okq6 qj 1rdf/w)dl -speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stilq)6j h/w1odr- qfd k8ffness 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 jumtueb*wb 1 wbv 4 .47/pssn,kzdh6.xtst the right pace of about 1 step per second, the coffee sloshes more and more until eventu 7tsmkn6 4hbuw*z1b w/4d t,svp. e.bxally 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 ofoa1vd-n0 eq mb*b 9b yu9o9*t6a g6zmx a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequ bnoq6e1zmda a*m-b 0byv x9 699ot*guency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to thoh18qcspo vvqo(c, w7oy5:uew0m* 6h e equation x=0.650cos7.40t where x is in meoq7wooq8 1 , s6hh0c 5uv:m( epowycv*ters and 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 frequency f. What is its frequencyn)x7 iv ah0bk5 +hwgv80)clz(d fwiqwn,) xh, if it accelerates at h(nfwizv85x, ihc)wl)0d q,hk 7+awx v )bg0n0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a pi(d. em+en(dz)s/ ( qq:h wzblake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for a whilmqz (i zne((qe+. s/wdb :ph)de.
(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 playop yb+b2wy*7 -nrhnddli:.n9 at 392 Hz (G) and 440 Hz (7o2:ydnb*yh+. -dnw rli 9p nbA).
(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 stpsf s93g y8f,1kxha.fretched 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 cord o9fsa 3f 8s,x g1p.fhkyr the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of each prong movy gl/v24p wj+h5dp,nues 1.8 mm to either side of center. Ca/p+4 h gunw, ypdl2jv5lculate
(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 harmonic5dw+lm x5ptr)w/ u(e/ qbga p, motion of frequency 1.5 cycles per second. Wht(wdm5,wluq/5 p r+ex /ab)gpat 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 oscillation?

A string can have a “free” end if that end is attachew 1p* gc+s*ucod to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths o u+wg*ccp1* sof 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 — 8x0e98bh rzya zivj63, n:1iqz ctuh+each one-way swing takes 1.00cjr:hi+ b9tauz ih60,nzeq8zy1 83vx 0 s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertical direction or can d9+k, ,u. gy6 jy)igcy df pfia/8;adrswing 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 si ua;)pydi c6,d9 ,+fjry/d8.gkgafy wings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

  A block with mass $M=5.0\mathrm{kg}$ rests on a frictionless table and is attached by a horizontal spring $\begin{pmatrix}k=130\mathrm{N/m}\end{pmatrix}$ to a wall. A second block, of mass $m=1.25\mathrm{kg}$ rests on top of M. The coefficient of static friction between the two blocks is 0.30. What is the maximum possible amplitude of oscillation such that m will not slip off M?    m

  A 10.0-m-long wire of mass 123 g is stretched un 4 qk3lvl6;sowder a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite so3v64ll wk;qend. Where will the two pulses first meet?    m

A block of mass M is suspt/pa2,8j u v6u ,ifrttended from a ceiling by a spring with spring stiffness constant k. A penny of mass m is placed on topu8tpt,a r i/tfj v62u, 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 (x qimk7(*e6 rb t,bnjcar at the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Referjbt,7( *bqe 6rn mx(ki to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (4 c kn1wkwz)a2which 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, e kzw)wan21k4c stimate 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