Give some examples of eves/4 :v(xzqb oou by.t1ryday vibrating objects. Which exhibit SHM, at least approximately?o/t.( s:1ubbo 4xyzv q

Is the acceleration of a simple w a + h)vire 4q5pn-eilk/e:-9tf1qroharmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approximakw( 5nt3gzuht. k9nj:q5i p4ntely simple harmohj (t:95nw tpikg3 5.4nuk znqnic.

Real springs have mass. Will the true periody2 n 3w6nh5 9fudoxhk7a k6i.d and frequency be larger or smaller than given by the equations for a mass oscillating on the ehyf7ku 6aixd.2o95h nkndw 63 nd of an idealized massless spring? Explain.

How could you double the maximum spfe w0 exk1i:.eu+fzr1 eed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a verticald-s5bev 5 +;ed-scpe u spring scale, and then is released. Describe the scale re+p;d s5es eec5d-b- vuading as a function of time.

If a pendulum clock is accurate a0 dwh .c)4fjpft sea level, will it gain or lose time when taken to high altitude? Why?pjd4fc f).hw 0

A tire swing hanging from a branch reaches nearly to the ground (Fig. db01ok*t: +wkk)st-xdvvc. w 11–48). How could you estimat*-kobtvkdtc:k.w x)d 0v ws+ 1e the height of the branch using only a stopwatch?

Why can you make water slosh gg n- :z,wr9mnback and forth in a pan only if you shake the pan at a certain,9g-nz:grmw n frequency?

Give several everyday examples od,whsk xl:e 1*f resonance.

Is a rattle in a car ever a resonance phenomenpo75 7mgkio u3/v g(xuon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of its 0 m4po)mhw4y. ,l/uhn t jhsi,source? Why or why nhw)s ,/ .04 ,iohmhljmtp4uynot?

Explain the difference between the speed of a transverse wave traveling down a6nmv ds7ub7s+ava;ap3slp 6 2 cord and the speed 6pad;a p372vlnsvsu 6s+7abm of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano.3taeuz. xqm 4 normally have wire wrapped aroua.qe x3t.mu4znd them?

What kind of waves do yofs jl2ef4h 6u.u think will travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parallel to 26uejh f s.l4fits length?

Since the density of air decreases with an increase s4r0mdqwm ouu* 0*m2b in temperature, but the bulkbd2 4uum0 w orq*m0m*s modulus 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 yesgk);,qtqk24ta 6xrd d hy9,z e6k( waves decrease in amplitude as they travel away fromqxq 6 ,t,);yyz gd9ekk2h r6adte4 ks( the source.

Two linear waves have the same amplitude and speed, and 651d/-( chjxsmd wcniotherwise are identical, except one has half the wavelength of the other. Which tr j(d6n 1m -x5dscwih/cansmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of*i3uop:q)u yj:vjnv/( dtd(xl0f z b1 cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do0z:nxu1il)vt:j udqf 3p(dv/(b yj*o change). Explain why.

If a string is vibrating in three segments, are there any places you could tok-p5xm0 1 mteuuch it with a knif-p0x mekt1mu5e blade without disturbing the motion?

When a standing wave exists on a string, the vibratio mm1uiuog( gry. 8/tg6ns of incident and reflected waves cancel at the nodes. Does this mean that energy war y . /(uotmgm81ug6gis destroyed? Explain.

If we knew that energy was being transmitteqek9f o7 lrhs+-xw*aq ,5 axd*d from one place to another, how might we determine whether the energy was being carried by particles (material bodiesf*akx+*hlqoq-5 wadrex9 s,7 ) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total dm ) ux8p,cv+ycistance it travel cmu,+8 )vyxcps in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but o20hrlfogvc5al5 3g :is 85 cm long when a weoa0c2f l:gl ghorv3 55ight of 180 N hangs from 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 rb- a0x7 b d q9m*+.i1.6qvnfws tofsnits 68-kg driver gets into the driver’s se fw+d7bqoq6vnixmf01 s.br.s a n- 9t*at. If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (a) What kn vd/ b5(bds m,f(8(aijpdcis8uj31is the spring stiffnesss1a up53c( /isn(m8bjfid8j,k( dvbd 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 b)isfeyeo61 - a mass of 0.60 kg is hung from it. Whibf-) e6e1s oyat is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the poswoy5zgdct cf0 x3w(;*nk3wu+n1s b6 bition x of the mass in Fig. 11–2 at times t = 0gk+(xs3 wn3b61zcyt05 w fdu* ;bowcn,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 wa9. n*. qoy5hj ar)d,jaq(sgseb vibrates predominately withr asho(qs aayq*)jjn5,.g. d9 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 spri0-6 v6x yv84zly (jql3u(op :sis 6im0nklzkpng vibrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz.vkyvlij3siu4m 6:s0(6n- (zlpx0qopy68l zk What is the value of m?    kg

  A 0.60-kg mass at the endx,2 ngn8jl0c6u wi*p eq5 owz- of a spring vibrates 3.0 times per second with an amplitudei ,c0njg5l8uxwpwq n2*z o6-e 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 SHjgd bt ir,/*06zrl:m/ilv 3klO half the maximum value?6l 0ll*vb/dm ij3/it rz,r :gk$\approx$    A

A mass attached to the end of a spring is stretched a disthyam24-whnw qnn.c:/fu. b7o: u-uf xance $x_0$ 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 springs0*daw2 - 7skqtj -qgwrv-1is is stretched an additional 0.130 m and released, how long i1-j ksaqw gs-d 2rvw7q0-t*sdoes it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attacheb. ddc9frdz/8 d to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020cf zd8d/d.r9 b 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.( on)o kz4hhng q;et./,1dvwn zu,bv00 N to compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will 1(kz0o).,w nzuv nt/ ;h,gd nq eho4bvthe ball leave the gun?    m/s

  A mass sitting on a horizontk6ay;oiwy16 g al, frictionless 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 the spring compressed, the mass experiences a maxi66iywo ;y1gakmum 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 = 0.45copoi;t2zp 4lh()rfhr1:jfn , ys6.4t where x is in meters and t is itif1(phf r) y:nh jzl4orp,;2n seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equinyx6u4 i/ta (axix ,l5(bj;qtlibrium is the energy of a SHO half KE and half PE? (i/ui(5yba atjn l,xx6tx 4;q ±    A

  If one vibration has 7.0 times the energy of a second czbo 2n*ttf7dbw;:8m , but their frequencies and mb8t2nd w;oftb7 *:z cmasses are the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin os9 ;n;gxebkl 2dh:u:v,vy 6u cicillates from a vertically hanging light spring once every 0.65ub;6e;vi:hdn29u k:vyc x g l, 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 identiyzombpjq -getp ;.vhx19e4u6s1x33h cal parallel vertical springs, each with spring stiffness constant k (Fig. 11–4.yj m3 hz v3;b41uoqeext p1xgps- 6h99). What will be the frequency of vibration?

  A 300-g mass vibrates accord+-k; qwasdzj, stw/ m5ing to the equation x = 0.38sin6.5t where x is in meters and t is s zk-twjaq ;+ws /,5dmin 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 is ;0k2 gm xrczh6+sykqvd: r0d:
(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) i1zdrlrv (i:og *o8ooac 1 )3lzs struck by o :go za r*l3(z1 )vd1ciol8roa hammer, 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 springvaw uu6-pv* )y9f) z6 evks.ez stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes throug* v 66e)9ywvskvfup-).zuaezh the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring stiffness constanu+r vbkl+1kw)auq;4z ew z. *gts $k_1$ 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 horizi:5 nck ys -ola 7o1l*i e/,rh43pzaunontal spring whose spring ancr/,iaok n lys4p uz75h:- oi31* lestiffness 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 ju;9q9i,m ombgpmps 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 bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord. bi9,pq 9mgom;
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 iudmyn2 )s(uns87(jj ds its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exac z 8 78fwgqabr:x+x0ictly one swing per second? (Thabaf08zc7 qiw+gr :8 xxt is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.r0 dq9nmt(i n580 s on Earth. What is its period on Mars, where the acceleration of gra9m(t qn5nr0divity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm lotm; :syct8s q0ng
(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 4udmq 95 :63rsgrpsor mass of 365 grams, and mor5srqdrug4p9s 6 :3 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. Ifbgg94i zrc ab 0b-x8qd*qp-v) the clock loses half a minute per day, how should you adjust the length of the pz8q4) *9p-qvdg i gbb0b-xra cendulum? shortened by    mm.

Derive a formula for the maximum speo se(xx4 s-d1eed $v_{max}$ 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. Atoon (fa784 90 * o4h0 1qouqcdidy :dwu-pzqvb it is released from rest starting aopdo*07(fozwd4hyo84q qdcvqb 9 n- i:u0u a1 t 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 fu1:enksqs tw/ v1:ju;/r,q2 vjg8if his anchored boat every 3.0 s. He measures the distance between two crests to f:1v /frvw n1qu ,g/ei:jksu; qsj2t8be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travelst tj klbfp+ci0ja. twj3i5zo3m8 (w3 7 with a speed of 343 m/s How far apart are the wave crests (c3ttzwmj8(0 ji3b+op k5ta3.iw7l fcj ompressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilohertz) . (h gxjp. p6ftho*:owap .. gt:hjxoh p*o6fw(nd travel 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 longitudinal wavesbmt9 twh;+ysae .06lr2 qb ,6pc (db2pmutb9w in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is clq5 znj( *8rq bh 1t01 4)fy egx4rvfcjv55fktwice as dense as the other. In which rod will the speed of longitudinal waves be grea5 jfrbc cx *v4t01(5qfkyv 5rl8)fnez jgqh14ter, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If thl(.;l cbth v-ke tension in the cord is 150 N, how long will it take a pulse to travel from one l;h.- v(tc kblsupport to the other?    s

  A ski gondola is connq+pqd cnc-eud9 ha ;93ected 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 f9n+ecud- d3q h 9caqp;or 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 sinbb53bd7 js -zde 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. Hobn jb5b3z-s7 dw deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and this difb p79 qmal n:tog4os,6ference helps in locating the earthquake “epicenter” (where the disturbance took place). 6pqsgntol4 oa:b , m97
(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 cax5p k,a *itc x5l x8)f6k(lixwn be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually , fa6ikxl(cw5 k t5i*8lxpx )xinclude a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensit jvi9frg90lo7ies, and (b) the amplitudes, of an earthquake Pilj0v 7 grof99 wave passing through the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an ear y(of0ki w.x2vej,7 aqf-8lx)bopfw 1thquake wave passing through the Earth is measured to be (f a72opiw)vfef xobj,qx k- w8l. 0y1$ 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 throuo fit- u.r1 7h-q t:f/s;fy-scm6cvp kgh the same portion of the Earth, but one is carrying twice the energy. What iss;krtv. tfcq1-sm hf67 -/p:ouc i-yf the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched 8)1 o4utxiip7dmb l,bstring have the same frequency, but one transports three times the power of the other. What is the ratio of the amplitudes of b u)l4p1 idxtb,i78omthe two waves?   

  A bug on the surface of a pond is observed to move up at;jzkm nntdnt0 +p-.9 nd down a total vertical distance of 6.0 cm, from the lowest tt zptm9;j+n 0tndnk-.o 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 h4(q gim*wj bsbz6;3xare 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 la4xshz jb;3ibw qg(6 *mter. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental fw/t cj0:dspqy: k61 ffrequency, what are the frequencies of the f0k1fj6t sc dwpyq: :/first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. d,i,bo3v5qy hj,7u f-b0gfn eAt what frequency will it vibrate if it is finge-,funv 5heqdbg3i0joyf,, b7red 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 frequency of 280 H.af vjq-mn6ve fx*q 7+z. Name at least +qe* n 6xq-fm.7javv fthree other frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of staiv*okfz1 qz2 )nding waves is 475 Hz, how far apart are two k2 fv)zq1*ozi adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz lbjd9, 4.,.ojzxrkjf and 350 Hz, what is the frdj4l.. x, krfj9bj,zo equency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distgj4do8+ :nsl yy 0m+qp r/zbr+ance from the bridge to the y4+grbdyn/:o0 sr z8++qj mplsupport post 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 *l --(wcj oid trt6ekx/f,vq 6supposed 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 f cf/ tol -rktix6qwd e,(j6*v-requency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate ve8t yj3)z2;pbs8 ibsd+bv 5sat 200 Hz, but it is measured to vibrate at 205 bsj5 sv+bp3evyd8t8zb2)i;s Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached2wit)dle-+z u to a small-amplitude mechanical 60-Hz vibrator. The string’s mass per unit length isztw2el -)idu+ $3.9 \times10^{ -4}$ 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 adjust q6-xtm lk0n9tg2,29cma ettjed by moving the pulley. If the hanging mass m is fixed at 0.080 kmt6- ln g,20 9ttk9jcaqx2etmg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth 32zi l4v*rrkz0fb( vrin a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produ kr2*3 l0izfbv z(4rrvce 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 td;dty5jt-*bvxs a 4+strikes a boundary within the Earth between two kinds of material. If it approaches the boundysvab- *4xd;5tt t+ jdary 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 m cql npb9a-0mg mq,1 a/a*-kuw33au gthe velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests- 1a*uagqau 3m,am3w p/9nqlkg0 b mc- 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, densq+cp.uul5p7o1 l7ph08qv wll 5 bfll4e air. If the oq+ll4lp7 .lv0luf8cbp u l175pwq5 hsound 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 a boundary between t1gh4h.jrb2 c iwo types of rock at a 38 1rh gh. 2cjbi4$^{\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 diame gzgcwhx44a+8cp d 1r(ter. According to the user’s manual, the dish has to be pointed in t4+8hpwc(c 4 1agdxrgzhe direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocityxrn +vqy5v7- k 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual k7+- rynq vvx5decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constanf q(w(he+spl;t of 550 kN/m Find the maximum compres+l(h(w qsf;p esion of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, whicvmqpdj5,k 6g(g.ro / uh stretches the net 1.1 m. Assume that the net behaves like oup,jg(.v 6d5qk rg/ma 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 mass then : /b6q2o vllq+ttn(;bca/s rd falls 33 cm before it stops and begins to rise. What is the frequency o;2/(bv cqlo /b :rstt+lanqd6f the oscillation?    Hz

  A 950-kg car strikes a huge spwno:el 7pohj/ x9(- t zq7-c5cb4we yfring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is thhj pow5xcc7e9 -(tz le/-:bof47qny w e 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 cyh)rlyz ebo- 773krp 7up of coffee (diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves i 7ezrl k-o7ph7yryb) 3n the coffee.    cm/s

  The ripples in a certn7t l.4sp 8ms qk-nid4ain groove 10.8 cm from the center of a 33-rpm phonograph record have a wavelpdtn8.47 nl-ksm4qs i ength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates zi;/nzy06 tv4vn 3 zwyaccording to the equation x=0.650cos7.40t where x is in meters and t in seconds. Determine wviv;yzyn/z z06t n34
(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 ossoonz*f6cv1ofd o8xhk:0f +ct/a ,7 qcillates with frequency f. What is its frequency if it accelerates at 0.50g (a) upwardtd,xc0fcna oq1 h/*o87 k:ofso6fvz + ,    f
(b) downward?    f

  A 220-kg wooden raft fl i(xoam i33p:soats on a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he im a3(3oisx :psteps 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 r ) isx6dv kt:zt+h m-.l(un/3zbw0i oare tuned to play at 392 Hz (G) and 440 Hz (A). iz)ub.hsd/v + il3 x:0n o(k6twrtz m-
(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-p-2t rd.zrd i/kart cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the het idrdk/z-r 2.avy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, andko: scqpw +h g61.ruget7uu/4 the tip of each prong moves 1.8 mm to either side of cquc .tr7k 1g6w/eu:hpog+4suenter. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of frequency 1.5 cycles4x ( l+ u8h /pipqz/rv.mzoa: 9opf;gs 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) wilx(vgu: r/h;lzomop a9/sq pp+f. z8i4l not lose contact with the board during the oscillation?

A string can have a “free” end if that end ih r .wfyc1- j-3jbjfr;)z.zbfs attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wawjr - f.bh zzf.;jbyr-cf13j) velengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of 4byt(t(,o wotbtwo./ 5l hem 7exactly 2.000 s — each one-way swing takes 1.000 s. t7(ettw,obt m (ybl/ 54owh .o
(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 osciyi efnd4e/,0c 56r0c gvlp2n mmy n6m)llate in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of tfcmr 6 nl)d5vp6,0n 42ey ey0cmgnim/ he 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 1236j ech:-b;k2t myl 9bf g is stretched under 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 end.b9e 6-l jh; kftm2b:cy Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a f d3b)u qtiq50xl5me/spring with spring stiffness constant ki/5q qtbm x0fl5e)u3d . 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? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyarpb 3fpcu5 *z svmx,03cgpzd74za1yfi4n vn**d. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts t14gbn* dz *5 4*v3cfx07azuv n3s,cpfm zi ppyhe car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–(vwv / 5rrefu5qo;nj7 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 vibrating on a spring, estimate the frequency of this nrv5 q; eor(uv/f j57wvibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz