Give some examples of everyday vibrating objects. Which exhibit SHM, at least ap55mhkl87 r02zu gn9kxqzw.jiprox2i5 98kzm 5xhnjzlrkg.7 0 wuqimately?

Is the acceleration of a simple harmonic oscillator ever znvpd+;b; 3o emzp4us9 ero? If so, where?

Explain why the motion of a piston in a v iq24p4+h6kjt+3jrp ejp:pmy1e;uen automobile engine is approximately simple harmo6+mu3h pq44p:r jje kej21y vi+;tpp enic.

Real springs have mass. Will the tedyufoy vqx2.1g0y: dmd(7 :nrue period and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized massless spring? on 1fyvyqxm(ud7yg : e:dd.02Explain.

How could you double the maximum speed of a -:4lls :kqvrrsimple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the8 mcbkk l u;u.l+s.)mm hook of a vertical spring scale, and then is released. Describl8+ mm) k um;..cbkslue the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will ith.2ynr- zd yd6uc fy/* gain or lose time when taken to high altitude r*d-c.u6yf/z hdny2y ? Why?

A tire swing hanging from a branch reaches nearly to the gr7qivs) a9 4rahound (Fig. 11–48). How could you estimat4aha9svq i7)r e the height of the branch using only a stopwatch?

Why can you make water slosh 2 nn;+pvydf uq, x8wj.back and forth in a pan only if you shake the pan at.+f;vwxy d j82, qpunn a certain frequency?

Give several everyday examples of resg8mxk+: ph9f bt1g/eob,jfu9 onance.

Is a rattle in a car ever a resonance ph15mmbguid,h 4c7 yz0o enomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of itr5,marp0zgpg 49o6r xx/ p+dl s source? Why or zp mp0rd,rr/p 5 go9+xa64 lgxwhy not?

Explain the difference between the speed of a transverse wave traveling dngh 71b+)txokw j2, +b tu8fcbown a cord and tt )ob+uwjk b b+7gfx,2n8hc1the speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano norm55i xur dot24z ,p6-:mkxyzhyally have wire wrapped around tyixtxu4o2z ,5hr -d:56m zkp yhem?

What kind of waves do you think will travel down a horizontal metal rod if6d y9mia(kh09ir8 - ungwr. fw you strike its end (a) vertically from above( 0udf99.awr w8r i-gkym nih6 and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature, but the2 z5x6 sp)oacg0 t4/oknf, uta bulk modulus B is nearly independent of temperature, how would you expectto6 ua n5 g pfo/k0x,st)2zac4 the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as they travel a35z;k5wb ,fdfej + 7ojryl h n7zo0l0pway from ; wnj00e+zlf,ol5kz f7hd73 pryjob5 the source.

Two linear waves have the same amplitude and 4 q w uyh;(uf127qejaps1n+jn9 nap4rspeed, and otherwise are identical, except one has half the wavelen+nu; ajnuawp 4sj14n yh92pr7(eq1qfgth of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boun1k*ke9ok*on kdary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wav*ekko kno19*k elength and velocity do change). Explain why.

If a string is vibrating in three segmentqu-yglu.qr*vx 3 7(vsxf t f(/s, are there any places you could touch is (vqruf-tuq3y lfx. 7vg/(*x t with a knife blade without disturbing the motion?

When a standing wave exists on a string, tc 8ki,sb7f anrt cu06/he vibrations of incident and reflected waves cancel at the nodesb fiat6rn0, ckcu/87s . Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place 8r qrvh(go: a rds3yqb67n7(vto another, how might we determine whether the energy was being carried by particles (material rhrqq7n d 3 rvo8ya7(6v :g(sbbodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total distance 7hsjnieft 3-4 it tra4- jn fhi3t7sevels in one period?    m

  An elastic cord is 65 cm lj io3 4 ,8oa21xjnqyezong when a weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs frome ojo2, n x48yqizj13a it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg dri16 * lvn capyjb 9mv.bq7s9zq+ver gets into the driver’s seat. If the car ca* 1vyb6lvq9.b mnq 97j sp+zgoes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale st0asyvokjaum--u4:+(w fl1aznq s /9 p retches 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the qaa9 + l:zn0sy-sk/w-(f1mo j uaup4v spring stiffness 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 4dhnnay uot-1 vi8 1l4mass of 0.60 kg is hung from it. What is its frequenca iolh41ud4 v8-nyn1ty if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x*1wb iyb)3 oto of the mass in Fig. 11–2 at times t = 0,t = * 1y ioowb3b)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 predom4 *szw8lc qq ,b5aug/h7ll: ominatecuz4lmql/ h,gl :awq o7bs85* ly with 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 freb,r) cn0yn :bs 2a2whequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequen0wbeya2 sn ,nr2 c):bhcy 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 se 1:r4dgnq4j ukqtq al;ymg 510cond with an amplitude of 0.13 m. Determine qt41drm;a0g1 q q:ln4gyuj k5
(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 fhvw. vd x7q;1 5a 7gfml*xrpp;rom equilibrium is the speed of a SHO half the maximum valla xfv;hr5v7. q;m*gx dw7p p1ue?$\approx$    A

A mass attached to the end of a spring is stretched a ytre9ta-c1;(g w6cyg distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. If the spring i q.h: tz4vgwn)s stretched an additional 0.130 m and released, how long does it take to reach the (new) hw: nv.gt4)zq equilibrium position again?    s

  An object with mass 3.0 kg is s3doo 18wau, c:yz5b+ 4k gz(jxhp*qoattached to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is s hz8 (cwzkg oj3 4o* qx:by,1udoap5+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 s, p j4prfypfho78*b+ezidj *0pring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ballh4,j*8pdzr+ f 0i*pfbyo 7p je leave the gun?    m/s

  A mass sitting on a horizontal, frictip.8.o6 :rijesa /xts eonless 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 spring by 0.12 m. If the mass is released from rest with txop t:s 68ea.ijr/s. ehe spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x = 0.45cos6.4t where x istzn .vcca; zwp,vb) 26-h 7oej in meters and t is in seconds. Determinejve- )znv .c;htw b6 p7c2oaz,
(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 equilibri 5kyxkzrh;4j8n1oc w q+x5za 9um is the energy of a SHO half KE and half PE98hky w5c;n4o x5rx zazq1j+k? ±    A

  If one vibration has 7.0 times the energy of a second, but their freqzb20 pu e1,8 s 8jawy,n)hjyuabbx/z0uencies and masses are the same, what is the ratio of the82 8b0hyajn b0su /,u z bjy,ewxz1)apir amplitudes?   

  A 2.00-kg pumpkin oscillates from ahj,mdq*l )dg886yy auk xn( 3d vertically hanging light spring once every 0.65 dx8 ,ld)*j(nyy68dgk3 hmq a us.
(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 verticf, j2mn63zvxts0t a z-al springs, each with spring stiffness consta2x z3tjn tvsz0,-amf 6nt k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates acc6bap35m l )qudording to the equation x = 0.38sin6.5t where x is in meters anm5 la6pbuq)3 dd t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and B. For each, what)ag ,2d3 sdqjps 0lf(z 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 horizontal spring (k = 124 N/m) is stj2 xibksn2vd-/) g a.yruck by a hammer, which gives the maxaj2yn/ -kg2sb. div)ss 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,+qeqx ,m47 sdk80pps -o frco with an amplitude of 28.0 cm when 0.260 kg ,4q8o eor-7 pcfsx0mqs d+pk, 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 sprignr .zi bw;6z c4;xmm9ngs, 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 horizonn -+h/3oj ly) tbyz5eatal spring whose spring stiffness constant iso 3tj/eb+-lzn 5 )ayyh $ 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 mva4c ;a8dil0aass 65.0 kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the brici al;4aa v08ddge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 60 s. What is it 98jtnc ;bu2gg4aw ep.s
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exacon*m 6+10 kaqhvxt/fncky fw b*r)7h0tly one swing per second? (That is, one complete vibratiyq0*wkfotrvxb*+hfmh 6c1 n7na)k /0 on takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, wher ay;k )7d qgzy8l+-ixje thez-8 lqy+xjid)ag7yk; acceleration of gravity is about 0.37 that on Earth?    s

  What is the period of a sim7:)cszc . djaxa(k3adr,k su +ple pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulum bob has a 0u (kw*ms1aodmass of 365 gra wou( adks1*m0ms, and 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 t07d5pzlv2 1ji t9ci6pnri .y jl)r dk9he clock loses half a minute per day, how should you adjust the length of the pendulum5 n)i j2djydr7lc.9zp9p1vki6 irt l 0? shortened by    mm.

Derive a formula for the pyq:mjw-q nd1wc:xult59 z8 8maximum 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 freque b (k:/h+r5ts; msayimncy of 2.5 Hz. At it is released from rest starting at an angletrbs/h m:a myi5+( k;s of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchore :x4+0pa,w m x9vuwzizd boat every 3.0 s. He measures the distance between two crzx40 : ix v+wupw,zam9ests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels w;tcd t2)dlha,.url 9pith a speed of 343 m/s How far apart are the wave crestslt2 9rt); d c,adhu.lp (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilohertf7 )3)ack 7o/g ej-ta 7*bp1nmdp rdvzz) and travel witfmga7zdp eoa7bvr)pdc3 k1 n)t*/- 7jh a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of ldytf3uwbz0e(4 m u5: eongitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same el4zk;n gw ujtj(xz1-v0c (f*i4ijoi; wx-dvd0astic modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves b4xizo*xu 0w04; iwkdjjfgj(cnvz1t; id- ( v-e greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. Iz wuc1tnl3y/; )1hn *ec(znqnzp0b )nf the tension in the cord is 150 N, how long will it take a pulse to travel from one support to the otherhzt lnnn0nw)e )qyz/3u;cb*zc( 11 np?    s

  A ski gondola is connected to thu.e1yb) sou ydu66*wqe 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 py6suuw)6 u.eqbo y*d 1ulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side) rw3x:.s3q,ewrv43u uoew vs of his ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this poin.e33wes: rq3urv,x4) w vowu st?    m

  P and S waves from an earthquake travel at different speeds, and this differ,wj9wae0x rlzp 38q 1rence helps,rrqe 38 90 walwjzpx1 in locating the earthquake “epicenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated by a sinusoidal tjn6b ljq6 .2mqransverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of fm 2j66jbqq .nlrequencies), 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) themeifo+xkf 3kayg 0*:1 intensities, and (b) the amplitudes, of an earthquake P wave passing through the E ka xf0:1mof*ye+g ki3arth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earct*qrvk+ v/s) ggwz-b-v d) q*thquake wave passing through the Earth is measured to be z qsrvg+c )wvktv q*gb -d)/-*$ 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 travel sm)hsco x.a. dv. .u4vthrough the same portion of the Earth, but one is carryio.dm..4vh )s. uxacsvng twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, b:dtudp u ;is pet4q)37ut one transports threetp34supu )i dt:de7; q 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 obsero 4uj .o.pj ep ts7 a70yqe:vnmz(je;0ved to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a(:0p0a.jz v4te yeej smu7.jq7no;o p wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving4 u -hcuwf(a h.jq41cn 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 momen4 h(u-cqau hwj1.ncf4t 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 frequency, what are the v8 (lx-bthc pfmx3;m 0qu8,yn frequencies of the first four harm c 8xh;8qpmfv-0m ln x,b(3uytonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what f(qjmn/m /ws f1requency will it vimn1 msq(//fjwbrate if it is fingered one-third of the 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 at a frequen.yn +w* j+dmvpcy of 280 Hz. Name at least three other frequendm pjw.v* +yn+cies 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 e.8pm8ybwgx 1jas 3r-hpf 8h*a 7u7fsfrequency of standing waves is 47e1aup88rwh ymx* 7 sb37.h8gff psj a-5 Hz, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 35m)/(dwqt 9z6 f/zmmbn 0 Hz, what is the frequency of t 9mm z/ 6fdtnmb(zq/)whe fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The dis r(t1rfpbppv 67 v5dd:tance from the bridge to the support pord 5b(ppp7 v:t1r v6fdst is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it isio9 1tm;b)ptly1/amx measured to vibrate at 205 Hz. By what percent should the tension in the string b1mob;9 1ptlxiy tm/a)e changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed tj by-(f 5vq lx+jtvu6:o vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be chauf+j- (: 5xtyv 6bqljvnged to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplid od3olvyzxf+7 312 jqtude mechanical 60-Hz vibrator. The string’s mass per unit vf237dqlo+djz 31 yxolength 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,i ;r/ zf*w*lkoqymb2t l22gb of the string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many dig2q,/w; yi mtfbbkrl2*2z*lofferent 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 righ *2iwrcs*d2 t8bn u2g dvb:0rkt frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the fre8t2 kubv rbgc :w0d* nsd2i2*rquency 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 traveli/9b(-+ dsg2hlq9d,bm vbg jjnng at k.0 km/s strikes a boundary within the Earth between two kinmbj/9vq-2hdggn 9+ (jsbb dl,ds 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 dv83(rx.wktz hi06 kg0ej0ok underwater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the inci exh0vgk0ojk(i6w k tz0d38r.dent wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is travelingvut8i-f9fxe,0o b ny0xlg) j0 in warm air when it hits a layer of cold, dense air. If the sound w)8ogfb0j,-x uvi0x nl0 9yfe tave 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 waqttx(-usrl jk/q.5 i 2f1+tc-k8yy49 gus gnive strikes a boundary between two types of rock at a 38uq kr ti ggsqyy.jct1-9 tl i/-f5k+ ns4ux28( $^{\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 ec 8dd0tgf heduok;/+;x cu ai4y/z m (0xj.r)user’s manual, the dish has to be pointed in the direction of the satele4x/h tre8+oy/dg.mcu f)k 0;ddxz ijacu 0(;lite, 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 trzmc .cf-de:osd9r80i avels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in rmz0co9c8i f de-: .dsthe 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 a spring stiffness constant ork,ljga : fm:.1w4vp z2:hoxpf 550 kN/m Find the maximum compression of the bump:lhg.4:2, xp1 : vz wrkpofjmaer if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from y ln +3j4 jvs0or-f;(t5yy4 ,mr zsugaa window to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a sim zy- orl;4yvgjjfs(+3r 5u,4snt 0amyple 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 the8nn7*h s1thj+xctzz mnr 6-1y end of a freely hanging spring. The mass then falls z8yxh-jn r7n+* nsh mt16zct133 cm before it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig.v ac q5e 1*ms(ie3x5bz 11–54), compressing the spring 5.0 m. (a) What is the3 (5b5a i1ms*zevcq xe 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 cia8b: y92nu3gbio tn .m) 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 spbu2 g9ib:a.3nn ti8oyeed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the centn*ro y+n4shta+ mf ),ter of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be *hrsmn,y an)t4 of+t+the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0eidirq6*vb6 j7,g, -iip-snqms *z3 i.650cos7.40t where x is in me q,-j i-i6bn6s iqv*sgz7r,*diei pm3ters 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 f47 ;awj(by vz+ps2s. lf29or adfbay/requency if it accely rla/b fv+pobz(a2waj d s4fs2 ;7.y9erates at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kr 2mr c18nobvfxu43 740txha,qlr0j ig man stands on the raft, it sinfbr uqrj24n3thrm,8i0xvx 7 c1al40o ks 4.0 cm deeper into the water. 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 a cr*b+dx)oahw r+.(dgt 392 Hz (G) and 440 Hz (Aaxdo(.)hdr+cw*br g+ ).
(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 of Fig. 11–ha*rtz-2 phrm h-9t/,hs.d y p33. 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 ttpztsrmh -r h. ya29hd*h-p/,he 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 hxi 6x- p+ jlemc*a-2ttip of each prong moves 1.8 mm to either jmptx*+ic a2xl -e6h- 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 sigde9i,am5urs/mqgl36*u ,l hp* /fm nmple harmonic motion of 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 duri,g36su /qmpd5m9lh*m r/f agleu,n *ing the oscillation?

A string can have a “free” end if that end is attaov vce1zq9yilw,1w/nz nuh lot.2;86ched to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of9iu,henz6nv1czq 2t8;/v l.wo 1 yowl such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each lmmk+d 7 1c7flone-way swing takes 1.0l17mcl kdm+7 f00 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 c zfx8-xy y-tq+an oscillate in the vertical direction or can swing as axz xy-+tfqy -8 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: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched under a tension n5 maqu q*p7 a0f/pe;sof 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is g;aupnpq07*/ aqe m f5senerated 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*4 g+e7kw b.r*t t(wu5;tlmt zk7dbzl with spring stiffness constant k. A penn5ke b7*dtz7mbk w +gu;l t.w* zr(l4tty 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)kvpqy6;r( bb 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 oy; b6bvrq)p( kf 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 ()xvzm6cz- b(8nz 4xbz h( (ffjwhich also gives the dimensions of the block)jh)(-zc8b nz4fzmv x6x( b( fz. You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz