Give some examples of everyday vibrating objects. Which exhibit SHM, ad1xt(/ri tft3t least aptf1/di t3tr (xproximately?

Is the acceleration of a sim63fu88awrh kgyaxuj8+w ,yz/:* xb8jz ytcz2ple harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approximately*+gv*kry 2cbdu 1y8.wz*rbtx simple harmo bgrdr kv *y8 .bw+12*cyxu*ztnic.

Real springs have mass. Will the true period and frequency be larger orswn*l 0hx ngx0,biho sl7u.;/ s jkk)f3u2:cw smaller than given by the equationi,7 xnsl/* w3xnu;2jhk ocf:0lsb0gw. ks u h)s for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillator (SHO)ffo rccq6) ko pl,bq,f55 (4qf?

A 5.0-kg trout is attached to the hook of a vertical springp 2x* xuhsn6w/-sx/b axby08m scale, and then is re-nba pyxxb x x602/m*u8/ sswhleased. Describe the scale reading as a function of time.

If a pendulum clock imk9t,a8:nmep lx3u0y s accurate at sea level, will it gain or lose time when taken mteyka0 ,u9lmnx83 p: to high altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig.z9 :ur(z-d2tuu e92nktnzk2q 11–48). How could you estimate the height of the branch using only a stopwatchu9n(kqkezdnrzu9 t 2z t2 :2u-?

Why can you make water slosh back and forth in a pan only if you shake me *kwh (cx q;exu,u* iv./se7the pan at a certain (huew/secm v7 ;uqe,*xk *i. xfrequency?

Give several everyday examples of resonance.cngm: .mikts 4m f.h*f.ro.h/

Is a rattle in a car ever a resonance phenomenon? Expllnt3su vr,1tc0c4jjx2,* h 3 o9sm ltlain.

Is the frequency of a simple periodic wave ek27j tx l5(lp.ixo0k tqual to the frequency of its source?0 i tkx2jlk5p olx(t7. Why or why not?

Explain the difference betweeja33jq12 )y. cw ted .vf0q dsyzyft-2n the speed of a transverse wave traveling down a coq0j-d.js)2t.e d cvytf3w2 zyf3qy a1 rd and the speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequennc3 xks, 3j4zkcy notes on a piano normally have wire wra xjn4ks33 zc,kpped around them?

What kind of waves d( /kd8rf;z aaxo you think will travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parallzf8d(/;kar axel to its length?

Since the density of air decreases with an increase in temperature, but the bule mkokf(3l;jp: fgg;l7,p lh(qo *3z ,cq8by bk modulus B is nearly independent of temperature, how;z k3bqgqfl(,* ep,g7 8;o3 b (flp:jhmlkoc y would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as they travel lc l)/szx rri l75:gfddo+*5mawa:7mgfz5 lc+d i)*rlrxl5 s/ody from the source.

Two linear waves have the same amplitude and speed, and otherwise are ug 9,dc69ph3hww xi( zfot*a7 identical, except one has half the wavelength of the other. Which transmits more energy? By what factor?h (ww9hgf cipo*,z36 td ua97x

When a sinusoidal wagb mks1 )1qyupszkcg: 0mmh446su2t :u x* /guve crosses the boundary between two sections of cord as in Fig. 11–33, the frequency does not change (a 12skgm* bkm6cu4g:h sg 0qxus):m zu/u14tpylthough the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are therep 8:w9qnkwp5p c2 k)my any places you could touch it with a knifqp8 kkc)n92pmpw5 yw:e blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incident and r,m.vubxch+ y3sk2y- prr4y s*eflected waves cancel at the nodes. Does thi ,cx.s-hv*r4 py 2s3y+mbyu krs mean that energy was destroyed? Explain.

If we knew that energy wasqjl.3+;od uaz9be9ndewt y 73 being transmitted from one place to another, how might we determine whether the energy was being caa;t+uzy9d3.3b en e97lj qwdorried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total distance*o*- w lmq-.5dcb xzn 9 7)xbcbyxx;it it travels ilxz-cxbyb oq;-5b mn.t*9x i*dx wc7 )n one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs fromo ;mo7c9qzi n xlm:(;u2osrn44b s8 la it but is 85 cm long when a weight of 180 N hangs :nr (oou4 x;mo8m9sal ;4il z2qs7cbnfrom 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 driver gety8cr(ci5o+ia ygyq + 8s into the driver’s seat. If the car goes over a bump,cyoy+58+ qic(g iar8y 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 i7+by vm6 cx(g ((mkc b:jkacw+/wk *ozt. (a) What is the spring stiffness constany ( 6cm/7+ *bcmczkwwago(+ j(kvbk :xt $\approx$    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 vibrq5lktw()uqt9 tage 7. l 8nhh.c2tq c,ates with a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its fr9 a 8gqh,tu5q c7t. l2(lqkwct.)thn eequency if only 0.38 kg hangs from it?    Hz

Construct a Table in-ej-z/z 5e.bhfmcd v5dicating the position x of the mass in Fig. 11–2 at times t = 0,t z/vhb5- eefjdmz.- 5c= $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 caughw5tu ij/c+ rt1apfbf8v9 45o9g+kl sxt in a spider’s web. The web vibrates predominat8+r 95fit/ x+ug19loacftvspjk 45w bely 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 frequency of 0.88 Hz. When an pqjt:+2wgv+g additional :+2wgjq p vg+t680-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 per second with q.l; .t ol8mxyrj9a,lan amplitude ofmot , la9qlr;.ly8jx. 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 equ;ic+t62pu 7 w9osyx h9jzaum5c)o +ldilibrium is the speed of a SHO half the maximum value 62 5t po9y hia)9ml +cwszdojux;uc7+?$\approx$    A

A mass attached to the end of a spring is stretched btf :lp3mcp5cut q88,a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. If the sc8fqwssg3heg 8 kds1t- q(8f ,wl(8ir pring is stretched an additional 0.130 m and released, how long does it take to rea(h8ke(fl-fs8 dg gqi, wsq1c8 w3st8rch the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiff p,h;teom-7dm ness constant k = 280 N/m an; - 7m,mdehotpd is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring ofsygev d 5 ez8syg89:p* a toy popgun 0.200 m to “load” a 0.180-8vss5y*e yd89ze pg:gkg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a hori+;z.daxhmt /(a sw. bvzontal, 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 spri/zt ;a+bshd.mv xwa( .ng 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 equati ahyw 4c35pf i*+h)8rg .5se+ljsby jron x = 0.45cos6.4t where x is in meters and t is in se .8jr)yp4s jy5l c+si 3f5be +hargh*wconds. 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 equilitokxc0ng 3u i)8,v4/qqv bsw 4brium is the energy of a SHO half KE and half PE?qxi,nt34c)vubo0 4sw8 k v/q g ±    A

  If one vibration has 7.(9wnh+jyu q7o0 times the energy of a second, but their frequencies and masses are the jonh7qwy(u9 +same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging l:v9s *qxt q74fq/eekxight spring once every 0.6ke:*q47xs /qxeq 9ftv5 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 identicajdmt* oa,6s2i : rgn5rl parallel vertical springs, each with djo*ir 6 msng5,a2tr:spring stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates accordi54bycwtp5p sw81 . x kdfy(bzl,:rq /yng to the equation x = 0.38sin6.5t where x is in meters and t is in seconds. Deterl1yqkb xp t(:8d/bp.fysyz wr 5w c,45mine
(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 examplj)w3bl68 bf,tmdkr1les of SHM, labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal spring (k =)r2ga f:sc6dke6r3z b 124 N/m) is struck by a hammer, which gives c6k:erz)g6s3d2 r abfthe 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 N/m vibrates with an amplihl+0qe)2 kr-e p csej2tude of 28.0 cm when 0.260 kg h)lkehe 2e0p rj2+cs -qangs 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 nr t9kwj 3g9p5springs, 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 stri)rgtoi//-w yv+j3/o fsz7y vn kes a 0.600-kg block attached to a fixed horizontal spring whose spring o yt7+jnrg3z-fsy vo/ v /iw/)stiffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high bridga,9kpu7 gvic)+y-ud me. 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 tp-k i,vum+7 ca uygd)9he level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 60 s. What j3e 7jp0x 1vh40enfbf is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is tai h- w0+:c2ut l2;j0vogco cmo make exactly one swing per second? (That olc-h20tagmjcw i:v2 +c;uo 0is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s 7+e5mtpiw1 tvon Earth. What is its period on Mars, where the accelp 7 t1itme+vw5eration of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm lon*/allf/y (3vcx amazg,2vw8ng3 a 6jv g
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.o(lw-7n z +g.mnm ww7h760 m, the pendulum bob has a mass of 365 grams, and it is released at an+7.-gwo7hw z nwnl (mm 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’s1r 6kk,.gk 7(otedz yo pendulum has a length of 0.9930 m. If the clock loses half a minute per day, how should y,6o1do7g(ekyr zkkt. ou adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maxim c -2rfsqy02*mu.a fai elzp+-um speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2/4 yf2yi k6gqyu2+bao, a1irt .5 Hz. At it is released from rest starting at an angle of yqf+ o 1 gayk ,/2bytai2iru6415 $^{\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 hi 5.jpiv ;cxgd0s anchored boat every 3.0 s. He measures thc.0j ; v5gdixpe distance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 2ag iea-kj7 iif3;i 0*q62 Hz and travels with a speed of 343 m/s Hok7i3j;i0* aai iqe-fgw far apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600q-y l6;rl6buzuiq04vs 35qubp2ct7b kHz (kilohertz) anpz6ily7tl u6- ubr bbq; 3c2qu4s v50qd 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 lv.i/e s) kxqv6ongitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but on*-y)wrg5:m pum zz c 2v3xsy8xe is twice as dense as the other. In whic g5z:8y*vpum y2zs-3 mr)cxwx h rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m ky)/ubq;8h3 yq ;l mp506f8k hypucvoapart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one supp3)by;p58uc6yhqk v 8yf lu0omkh p;/qort to the other?    s

  A ski gondola is connected to the top of a hill by a ste; 82nie905lkwalj nc jel cable of length 620 m and diameter 1.5 cm. As the gon; l il0n582kjjcwne a9dola 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.
(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 sd,11 2yg yllsyide 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 late 1ly2 gl,1yysdr. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and this.. 027b c34gsqe yotci-2 qv(msjpwpf difference helps in l-.s 7q2 mfsit2c(cov. ge y34pwjpb0q ocating 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 approximate4wus/qpo 5ua *d by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical os qu54pu*/wa of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudesh lc3 cg vi j/0rb(byd)ai5-b5, of an earthquake P wave passing through the cd(v- a hr/b0y55jligc bb3)iEarth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is 7gh62lnr ) xifmeasured to be 7 fx6nh)g li2r$ 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 of4( cn,wzo ;m;x0 lnqvx the Earth, but on0( zlv4;nwxmq,nc x; oe is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same freq1vq0) r 6hqgkpuency, but one transports three times the power of the other. What is the ratio of the amplitudes of the two wave k)10 vgqh6qprs?   

  A bug on the surface of a pond is observed tohj:u+) e oh1vp move up and down a total vertical distance of 6.0 cm, e uj1ov +hph):from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown ii5 *yvxo8yocy2r6qb( n Fig. 11–52 are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the rbyv2 y5oqco 6* y8(xienergy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, what are n:9bp6bx f(1 -gpkh.kthh6dk the frequencies of the first four harmon6 1 bhk gb(fxkphhnk-t9p:d 6.ics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz ekm.wh o /;20t+3go gcy8sldu when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string v2 m/lhk0+eo8wg cd3ty.suo; gibrates as a standing wave.)    Hz

  A particular string resonates in fouq;tv0*e 7g/too uwp; gr loops at a frequency of 280 Hz. Name at least thr;et/o0 q g;vtwogpu7 *ee other frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves c d-y,dc9i mjdy4;wvl14 fc d3on a string is 92m/s If the frequency of standing waves is 475 Hz, how farl 9,d1cdmd3;wdf cj i4c-4v yy apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 357q4 / vm,jfv*zfqd;/bhzt ;qi 0 Hz, what is the frequency of the fundavq h7q4d*b ,fz z/jti;f;/v mqmental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance from the brc 3vv kwa dt fg++tfo4d6qw9r8u4 k+/pidge to the support post is L = 62cm and the string4 8rkc/3+f+ wu a wkpt96vfqtdo4+gvd 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 aes (c2zhku +i.74 nlhy .lo6kkt 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequencieu .72o.cy k4 h6shzlil(ke k+ns are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposeb-i a1p o a7wbs57c-s z6jnj(od to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By -(7-a bp7sj6 zbnsooj w 15ciawhat percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is 3pk j)oyv z2ijnc(:h 5attached to a small-amplitude mechanical 60-Hz vibrator. The s h o3icjk5ny2( zj):vptring’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 len;(c q(uvkp m6 3shjtc(gth of the string may be adjusted by moving the pulley. If the haj qpv( t6 umh(3sc;kc(nging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water mg (ng8.d6ydz back and forth in a tub at just the right frequency, the water alternately rises and falls at each end,d(d 6zy.gn8gm remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s str6wiw 7vyvw- i pwz-/)hikes a boundary within the Earth between two kinds of material. If ii w/hy6v-w p7v-iwz)w t 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” wheresg0uzxr+9e* ;g 4smjn;oo3me the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crzgsm+ 3u esj9;o 0nem*4o;xgr ests 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 layery)m+gw6fwav 0 of cold, dense air. If the sound wave hit)60vfw amwg y+s 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 tw8j djk6:-ay(h ipw 2dwo types of rock at a jjda8w(2 wdyip k- :6h38 $^{\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 ekvx8.o 2 qut; .6sdx;f 7jubothe user’s manual, the dish has to be pointed infs7t;o.2 bqk xud.;xuo ev68j 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 2o5m 2n*cjxzkwj9wgqvh:iqn 43+3iw j :0 m7 qj50 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?9wqjw0nojmm5v7 q+qcg i:kjxn2:i3z3 4hw* j (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 of 550 kN/m a5.q/p r7hu/zmfyi9s :g(lc nFind the maximum compression of the bumper if the car, with mass 1500 kgcsr.h /gm y:qu l( /z5a9if7np, 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 6(fngy*zx 3li window to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a simple spring, (*xgyzn6fil 3 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. The88c kyls c+tghm3;7ez mass then falls 33 cm 8 l+gzysct e; 7hkmc83before 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 7ysgd+4/8ki. gus 5acedh2pgof 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring se /4 g sasygdkg.7u 8dp2ihc5+tiffness 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 the right pace :w7gqw1e ml;x of about 1 step per second, the coffee sloshes more and more un7gqx1m lw;e w:til 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 certain groove 10.8 cm from the center of a .p31k imz2 wxaur8vg wv9 4+ii33-rpm phonograph record have a wav k+im2 p4rgw 1v9uz3wa8x.iivelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650coshg;1 r8sdxy 3f7.40t where x is in meters and t in sec 1 hsdrgx3fy8;onds. 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 igu rk /-,npq2ys its frequency if it accelerates at 0.50g (a) ,qpn rg/k-yu2 upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the2o,tqx aib/(r raft, it sinks 4.0 cm deeper into the water. When he ,t2b(irqoa x /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 l6+;,er asptr yyqi+kr5z)l, zn(w 6eto play at 392 Hz (G) and 440 Hz (A).yl(s+n6rpryq ;)5tw6 aze,li zk,r e+
(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;z(4fgryv67 yyln)me traveling 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 the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the74zyn;v6r)( felyy mg lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of each9jux.sk8h9 qb j7g 8yzbjz;uita t:(9 prong moves 1.8 mm to ettish8x: kuq9bzju.7j8b ;y( gj9 9za ither side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of frequency lpjb.vih kde. p*a):81.5 cycles per second. What is the maximum amplitud:p.j.bl)*kd hia v8 pee with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end ifd.dpr kk1f.;mj;sqm5gpana r:b i/6 5 that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrsjrr b;gd id5nkq;:.a5 /mpfp m1ak6.ations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.0f)a1gum t( nh300 s — each one-way swing takes 1.00)umf1tnh3ag ( 0 s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate iqu9r,g( sgi6g 0r+ lven the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [H6+q ers9ig (, vulr0ggint: 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 s2to7;/ awxqdl )j, qsa tension of 255 N. A pulse is generated ,t 7qjs laqsd/o2)xw; at 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 spring wziukx6yt8ghzj9 mnn 8+ h:-k5ith 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? (Assume +tj-z: mz6u k8hni98hk 5xg yn$m \ll M$)

  A crane has hoisted a 1200-o-2fq:iskfi*+ ku1 xwkg car at the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of tskw ui+i1x-oq 2:f*kfhe bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests owuhmez/ e7 x b7c8a31on a plate as shown in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shocm78wxe7z1hu beao/3wn, 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