Give some examples of everydayvxn:7u+m8k dw vibrating objects. Which exhibit SHM, at least approximately?dx:+u 87nvk wm

Is the acceleration of a simple harmonic oscillator ever zez2gdkox 9 :ku+ro? If so, where?

Explain why the motion opk6v,css6(ahu,qu 7u1;nqwv f a piston in an automobile engine is approximately simple harmonicv(u1kpn,; uhs u 67w6aqv,sqc.

Real springs have mass. Will the true tpx;rwr;rcgti7f+hy o61qe.zwn 8 +1 period and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized massless spring? z. w gr7e +x8rchw;f;op yrtt11+6inqExplain.

How could you double the maximum speed o( pnl:m4)swf)j nxj1 qf a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical s abf/ ( lma30tebn(u1 1,aungkpring scale, and then is released. Describe the scale reading as a fu/ u ga(a nbna3(m1f0etlk,1bunction of time.

If a pendulum clock is it rkk*ksxjxq2)/pmor)d6 .8accurate at sea level, will it gain or lose time when taken to hi p*jdtim/k q 6k8rr)s).2xokxgh altitude? Why?

A tire swing hanging from a branch ts ys (sa,h-;8b(/6 cyl dgvrqreaches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch using only a stopwatch ( 8/sybar yl6hd vq-tgcs;s,(?

Why can you make water slosh back and forth inubd lk 42xg27-gxr 5ko a pan only if you shake the pan at a certain 4xo- lx7u rg bd2k52kgfrequency?

Give several everyday examples of:: dvb b7z59ych4 vcbl resonance.

Is a rattle in a car ever a reson lx ztrab6*;;he xwb)may(*my2hpz5. ance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequetb;ml nck4*b few5ljr* a- 5x0ncy of its source? Why oracxjtl-l0 5 *frwb4m; bnek5* why not?

Explain the difference between the speed e. ylroch1 (+ff5xpi:of a transverse wave traveling down a cord and the speed of a tiny piece of the cofep+( x:yl ocrih51f. rd.

Why do the strings used for the lowest-frequency no6z-t-c) s,rw2ljd wdetes on a piano normally have wire wrappe rs2d-wj)z,dt-w6 elcd around them?

What kind of waves do you think will travel down a horizontal metal rod i0yfef8/myn4bk40 f(1 iccnzff you strike its end (a) vertically from 40fc(nf/0 fyief4 c yzm n1b8kabove and (b) horizontally parallel to its length?

Since the density of air decreases with an innp9.rv b sz n;tebo;:-i. pvk,crease in temperature, but the bulk modul p;svi,n-.:kopn9r bb.te ;zvus 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 dh 4aivg1 0mbp.)ykgaak2 e- +in amplitude as they travel away frak+a yd4i-gpb0m .ahe 2kgv)1om the source.

Two linear waves have the same amplitudw;hbsd0m7 cz lj. e.n2e and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits more energy? By wh 7m znd.w2jh0.celsb;at factor?

When a sinusoidal wave crosses the boun7 srkx bu7xjj8fyk005dary between two sections of cord as in Fig. 11–33, the frequency does not changekuj0 78kf0xjx5s by7r (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are bm*3b+n em/n-fxn7 yothere any places you could touch it with a knife blade without disturbing the /b3 mxben*7+-f nnmo ymotion?

When a standing wave exists on a string, the vibrations of incident anmc1q. e) 9yqjf 9pwe-jzxzo( :d reflected waves cancel at m:zxjco-e.pj wqf9q 1( eyz9)the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was be9wab5bd 0iq me.eqg/q j7 c9+ving transmitted from one place to another, how might we determine whether the energacimq b.qd59qb/ gew0 +v 9je7y was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total distance9)pk y8;cyyfwv,; vew;b qt1f it travels in one period?fwyy8;p k t;9,1ybwv; )fq evc    m

  An elastic cord is 65 cm long when a weight of 75 N hang -vvwzr7.w9g0 q qbjv5s from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this ezwqv jgv0v57-r wqb. 9lastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when itstdqb.s8f(d s(.c -*pl a9silrnn/yn9 68-kg driver gets into the dris(*.9q/ydblpid9csnftran sln( 8 - .ver’s seat. If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 c4vb0 +iq vi- js6c+r+okvv7qfm when a 2.7-kg fish hangs from it. (a) What is the spring stiffness constan k70v-o +fvq qc+ rbi6i4+svjvt $\approx$    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 frfhgsv rdd0-9 +lz/iua -mh(j.equency of 3.0 Hz when a mass of 0.60 kg is hung fro dvrilshjf ha0gdu/.z-(m +9 -m 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 timb:n 0azdzz9 e :t wni*/kqw3-des t = 0,t9z :ez/dd0q*3n-btwi kwazn : = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 vibratqxy:9b8 kv93 d/wv )wtzy3tlt,j jqe1 es predominately with a frequency of 4.0 k 9jwvq : t8 yy,dxzev 1qw/339tlbt)jHz.
(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 frequd.;- mms dtt0nvrb+ 3uency of 0.88 Hz. When an addir m-dt .vst ndu;0+bm3tional 680-g mass is added to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times g23om z ;aznuis-91 onper second with an ampl 1gn3uo z-;mzios9an2itude of 0.13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed of a SHO half dd8ug ,9v*cobdwv rdd .bd 636the maximum value?v.gb83 r d6 dd6c,owdd9* vbud$\approx$    A

A mass attached to the end of a spring is stretebf7sg ,kfq p1wlh0 /6ched 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 stretc(rvd3ewm b0; la fobaq. ,h0m(hes a vertical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it hldw rb; 0oe(3v,mmb a0qaf (.take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached nnaqfz.vda- 0oi24x .s/w+j k to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the o2i+ d4fajw.q o 0kz/avsxn-.n bject 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 spb6 zm2uai(s8 dring of a toy popgun 0.200 m to “loadd8szb ia2(6m u” a 0.180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface uo 8q.5c m2q.e8 5beq-kzyzaris 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 the spring compressed, the mass experiences a maximum acceleration ofz8u-ebq.q ceky .qaoz25r85 m 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 = 0.457j-tzt7.skx4 gz fm pcn0.o y0cos6.4t where x is in meters and tgz70 x oymkf7p 04s. .-jctztn 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 hptl)9g(bp*(1 y-m: i :lc nba7qnumw from equilibrium is the energy of a SHO half KE and half PE? ±ltn)p1uip*b: bnmgha(yw97 -q:c( ml    A

  If one vibration has 7.0 times the energy of a second, bu 7y bo*9sncnu:5 oj9fht their frequencies and massj 7 fn:9yhsnuc o*5b9oes are the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hangabps poc, 5h5+.kv42.v)gxsczko ;cq ing light spring once every 0.655oakc sp4sh k) 2z.x5c;cvvb,gop+ .q s.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallel vertical99href;a.p wx 2e3y+gocwkvozj p69o; o6n -q springs, each with spring stiffness constant k (Fig. fx-;g9+o9or2o 9ejcnke3 y.;6qpvow za6hwp11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the e*c+ao5(iv5nd c cvu t*quation x = 0.38sin6.5t where x is in meters and t is in seconds. Determn+ *c* (co5dt c5vvauiine
(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,pb x;7 jznd7o53ioq:mocz7 /cpvnb) 2 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 horizonta(nouoc8k ju6 ,l spring (k = 124 N/m) is struck by a h(uon8 6oc kj,uammer, which gives the mass an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305 8k)hq mr bv9 .8iiuny;N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) witni8) ;9qmb h8yriu.vk h 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 springcwerb qqn3 qo 8.fe5+y/5:lles, 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 t44 g 5:jp70enmn.d e5vfwicsto a fixed horizontal spring whose spring stiffe.wvji0cfnmteg5np 45: d4 s7ness 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 mass 65.0 kg jumps from a high bridge. After re;1z *db tnsv,6rea; q-xoq nx)2pg2wyaching 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 brid * pyx 2t,sg;enq;aw2-bq) nxv16rz odge. 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 i( + rw.s;cg)z:kv hucmn exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to makef/jp 1nq4opdhtr0 9o6plom g0w3 -v4r exactly one swing per second? (That is, one complete vibration takes exactly 2.0 s.) ph rodjpftr 34pq1 4nm/0- 6vo9 gwl0o   m

  A pendulum has a period of 0.80 s on Earth. What is its period onq-40 bz g6(7m3tiumzweu 0f4 dwf9tda Mars, where the acceleration of gravity is about 0f9z 0f6uq me w3407di4at-dmztbwg (u.37 that on Earth?    s

  What is the period of a simple pendulum 80a ,r3)hnp; 5v y)+ pxsbo5fntv 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, thhffyev8atq ;5z f4d7l8t0g9de pendulum bob has a mass of 365 grams, and it is released at an 5a9fyfqg87vzh;lf4 0 ddtt8 eangle 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 0u*l l o.3 kyikcv2*ykof 0.9930 m. If the clock loses half a minute per day, how should you adjust the lengt kuvkkl* . ic2l03yy*oh of the pendulum? shortened by    mm.

Derive a formula for the maximum sp il 4mrmvtzimgz*)nu 5a8x 9-8eed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscilv jh22:lwg ld(m 5ag/rlates at a frequency of 2.5 Hz. At it is released from restgw:g(2jv lr2/ 5l dhma starting at an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchored boat e3 wzo3 g-5 kaaew,q6verj* l4vvery 3.0 s. He measures the distance betweene5*4a w j6ra,- 3vgo3zkwqvel two crests 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 v) zs18svj(a0x z9omg travels with a speed of 343 m/s How far apart are the wave c)g 09o v s8(zjxm1zvsarests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilohertz)3 t c0*u0e;ibq7v dfgj and ttf*cie 7q0 v0;jdb3ug ravel with 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 longitudimf x.qqi-.bw 8nal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one i) h+glw;nvtipty 25- js twice as dense as the other.2 ;-wn5vypthgl ti j)+ In which rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between twrs ur.u-kidhz,zk;b1 no::d1o supports 28 m apart. If the tension in the cord is 150 N, how long will it t.h iknkz:1u-o,: zd rsbrd1 u;ake a pulse to travel from one support to the other?    s

  A ski gondola is connectedtp np 6c,xu8isc*lp26 to the top of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return. ti2 nc ,p8uxcl*p p66s
(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 be3o8uc(p(hn(sgg kb v- low the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How o c-b(k3 sp(n(hg ug8vdeep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and this dg/3/us 6 peagvifference helps in locating the ear/e3a g6 gu/vspthquake “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 approx40e8j xi.q kniimated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what ampli8 iixq0jenk .4tude 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, and (b) thecs/c4 xug/ l45kal rjk:c3vu3k2ix -f amplitudes, of an earthquake P wave passing through the Earth anuf3 4j kx4xki s l gu5vc2r/ckca3/:-ld detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquakedd u8 q9c*vqz0 wave passing through the Earth is measured to be u8d*0 vdzqq9 c$ 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 through the same portion of th 8 rr ejhp1y-6ht20t-k0 bmirje Earth, but one is carrying twice the energy. What is the ratio of the amplitudhrbri p r8-206tje1- ht0jkmyes of the two waves?   

  Two waves traveling along a stretched st.ml(d0 lx4o yfring have the same frequency, but one transports three times the power of the other. What is the ratio of the amplitudes (l4.y m xlofd0of the two waves?   

  A bug on the surface of a pond vn:c.1i8t eoa lh ,bz2is observed to move up and down a total vertical distance of 6.0 cm, from t:b 21ln8tceh.azvo,ihe 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. 11–52 are 7-okvhg;yl/q .az;pgmoving 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 the pulses pass each other, the stringqz.go- k;;hp/yal7g v is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundw: (xwiieak 0).(qjgfamental frequency, what are the freqkiwe(0 w i x:fg.q)aj(uencies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingere 6ciwag*pfub 6s68zq4d. At what frequency will it vibrate if it is fingered one-third of the way down from tu*cbw6ia fp 64sg 8q6zhe end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in c1d3f;- cpz zwfour loops at a frequency of 280 Hz. Name at least three other freq3czdw1pc-f ;z uencies 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 frequen7q unrw n,/)hxcy of standing waves is 475 Hz, q)x /hnw7unr, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrcxc7accyg5 ngd rcf.9,:j 8v2 ating string are 280 Hz and 350 Hz, what is the frequency of the funda 8x5c:c.cj gvrgd, 7ccnaf9y2 mental?    Hz

  A guitar string is 90 cm long and has a mass of 3scx7w6wvlm h(v0:+jl .6 g. The distance from the bridge to the support post is L = 62cm and the string is usw0c7lhv6xm(wv lj :+nder a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string isy oz6hd-nw* -f supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in thzw- hfn*doy6-e string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it iidbo h 5 4n1o c3h,vy150v6 vz2vygwexs measured to vibrate at 205 Hz. By wha60,2wv 5d1x45y obz c1n3vh eiohv vgyt percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached u5vm/jt:hyb 4 6j qq3he/u. qdhr;/bp to a small-amplitude mechanical 60-Hz vibrator. The string: .;vhbte5q/qup /j3j64q/hrm bd hy u’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 string may be 6c1rgj i 62ub(. iiumiadjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, hom b 6uu .iirg6ici1(2jw many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water 0*q ; p oc)e2jbirxy)cback and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relativec0)iop b;qxyj*c) re 2ly 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 within 4d0zcb 5 1k vn(f.5 mw8h:r hlk-yxtlvthe Earth between two kinds of material. h5z (vhlxl8kdcm -bn.015t v:wfkyr4 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 t v4qlzt*c e5hzcd*m0+he velocity changes from 2.8 m/s to dv+ct0 z z*c 5elmhq*42.1 m/s If the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is trave vomk8)mc+n+ oling in warm air when it hits a layer of cold, dense air. If the sound +o)n v8moc k+mwave 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 a boundary betwehb7 rfupuve*tn5 g4- :en two types of rock at atnr*peb-7fg4uv5 : hu 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. According to the2bd q:ebidkg2zf x;- t+c9(ak user’s manual, the dish has to+e- dz9q(;x d2:kg bibakft2c be pointed in the direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 25 fmp p(lo8,1tfy7db n(sz: u8e.)wlcd0 km and 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 have died during tsunamis, some of them attrasopcf,u .(el8 dp7:d( tf 18ywmz)lbncted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness4r11ej a/gmpafgz.;q constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1azea .4gj1 1;m/rf gqp500 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 18 mubo.r(1ani mx d 2o) m:gkc+6v below, which stretches the net 1.1 m. Assume that the neo+vdn6:ik cra1gbxmmo 2u ).(t 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 freebe ki25lgeb99i ,f) xuly hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency ofbk e29eub )f5li9gix, the oscillation?    Hz

  A 950-kg car strikes a huge v8p zgmw1bh4cyk*zc s6 - .0tyspring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0hy-vpck g8tmby4s wz.1c0 *6 z 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 (diameter 8 cm) at just zq:cwx a3)qd-ku +s(nthe right pace of about 1 step per second, the coffee sloshes more and mores :q awxq)d+n3 ckz-(u until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a cert 6pcy5 jn:c8dgain groove 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency o5cpdj6ygcn: 8 f the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t whkhr:cr7fwl(-b vmp 4 6ere x is in meters al(6hbmvrwr-7:4 cfk pnd 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 frequeno.v2 tzn u(o xiek0x(.cy if it accelerat .zniooxk20evx(.(tu es at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raft, it sa51yqa by, ewaj7i v ,++3gcb20lzpp sinqz0y1,+ elavpi, bp+wbc5aa73gjs2 yks 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 at 392 Hz (G) and 440 yv6zdad :7ab8Hz (8dd:va6z b7a yA).
(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 travelisor5i;qn/to ;q2 *pf lay* ds)ng down the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in ** 2;fpl)5nod qiy ros;staq/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 m*2ot l(ej jg6o qa84hof 264 Hz, and the tip of each prong moves 1.8 mm to either6jl4taje*mooqh(2 8 g 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 fred srw pf2z/gh.tj fhr5bl9c5 0;+a 5wkj 9acs7quency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble plal/s2g kar 9wbd0jjpf9t fz75;s wr.+ hh 5ac5cced there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that f-kv*2w*r6n 5uwdx;/llto9r mksueixb 5j 73end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonanwr*j 23l xwxs7ktnu*fb;ukre il d5/9o5m 6-vt vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of efkgp y0c3 ctf m; en,v8nq08vq.0;oss xactly 2.000 s — each one-way swing takes 1oe;qycfk. g0c ,pfv3 m0n8 tqsn0 v8s;.000 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 sy7o1duxwy /v6wing 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 ydvow y 71u6x/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 2xqv6hp vcd:0 y.9d1shkt/plmass 123 g is stretched under a tension of 255 N. A pulse is generated xl1hv9 vdk h60d:tpp2 s/cy .qat one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a dym t5a5c ff/;r q ,cz)9l*(ljk eltx,spring with spring stiffness constant k. A penny 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?td l/qcz*(f5x,)9 mle lf,tyj;5 rkac (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junk0ug .a( c4pbmx8vb;gz yard. 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: Refer to Table 9–1.]z8;mxgcga0pb u4 v .(b    s

  A block of jello rests on a plate as shown in bxr53nq6 k n9gFig. 11–58 (which 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 vibratir3ng 65xbk9nqng 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