Give some examples of 7 ;nhq1wl pa/8wrlsa)everyday vibrating objects. Which exhibit SHM, at least appnal7)/8qw l 1ap; wrshroximately?

Is the acceleration of a simple harmonic oscillator ever zero? If so, whe u x nr2)g5*cumsw)(jvre?

Explain why the motion of a piston in an automobile en0i:cfkw.fj, v /hequ- gine is approximately simple h .f:cq-fh/ui kw,0 jvearmonic.

Real springs have mass. Will the true period and frequency be larger or smaller itw8,hzkdy bh7d:/ )g,l ;a8 dli x)dhthan given l,; h,gikdway7h:dhxdt 8dbi )l z/8)by the equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a sikb ;+lid(qnc3mple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring sca,sl;y6i ozq:8ecj y2zy /pvg5le, and then is relea/6yps :e jyqz;,i8coyv2l z 5gsed. Describe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose to2)8i4: fqutg uwh; w0lepwe9ev-fvp),f c( cime when taken to high altitude? Wgpe),e w cf p(hfw:ew;49 8t)ouvifqc2 0-uvlhy?

A tire swing hanging from a branch reaches nearly to the ground8hf,5f f ok:i*aa e(acvvt36x (Fig. 11–48). How could you estimate the height of the branch using only a stopwatchoafxih: 5f tev6a(ka,v3f8 *c?

Why can you make watew215v:khp *h..jujfk z t- ohzr slosh back and forth in a pan only if you shake the pan at a certafhz5uk-. :okpjthh w*j z1v2.in frequency?

Give several everydan qn0k l)r:hf -lwd0w8y examples of resonance.

Is a rattle in a car ever a resonanfz8uuz*-e 1 xthz01j nh-otd4 ce phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency -sv 2-q8fi7vgb4j39v xfktih of its source? Why or why vjxvfq-3ki gt-4b9sfvi82 7h not?

Explain the difference between the speed of a tr gs: .fkskoz)2,u4duvansverse wave traveling down a cord and the speed u )4fogds:z,2kk. uv sof a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano norma xur ;(buw;0v wc1yu5hw*wvf)lly have wire wrapped around *wu cyw1wv;0(vuxr bhu)w5f; them?

What kind of waves do you think will travel down 6(9grhi9 2u tgdc3ru pa horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parall dh i pu6r329rgc(9gutel to its length?

Since the density of air decreases with an increase in temperature, bui .xnfp rg)y/zh 0o9i 7:viw7ct the bulk modulus B is nearly independent of temcyx igvor0 : 7w/izi9p.)hfn7perature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease anhe /g83j 2w pk0k,osin amplitude as they travel away jk0 8kp2e ,sw a/nhog3from the source.

Two linear waves have the same amplitude and speed, av*ozp eu; v)5knd otherwise are identical, except one has half the wavelength of; pkovuezv) 5* the other. Which transmits more energy? By what factor?

When a sinusoidal wave crossesg /a+4 ww0yqti the boundary between two sections of cord as in Fig. 11gq/i t 4ayw0w+–33, the frequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibra *m3/7mdi.drtzz kdm63nh +ad ting in three segments, are there any places you could touch it with a knife blade without disturbing th hd3d7k6dma i r .*dz+t/mnz3me motion?

When a standing wave exists on a string, the vibrations of incident and ref j fztnm34i .n+k.pb4nlected waves cancel at the nodes. Does this meamb z+pjki3 n4nf.n4.tn that energy was destroyed? Explain.

If we knew that energy was h7x g lum d6kzmg .z5uf66n4l+being transmitted from one place to another, how might we determine whether the energy was being hg6m+uluf6d74k xzm. nlgz56 carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total distahc2 .2 ypyt 9y 6 :h,adadqfqeon7+g,l;,iq yance it travels in one peracof,7eyal:+y,t 9hy;ah d, 2dpg2q .qn 6iqyiod?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs a v-b1jokyo 62q b/to;from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k ooqv/ -kbab16joo yt2 ;f this elastic cord?    N/m

  The springs of a 1500-kg car compres5o4u) ri: , 0awivf(yass p0uas 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequency of viu)aia(r,s5 w i u0 oy0v:a4sfpbrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm whee2hs m fx0cm5q*rn:p4n a 2.7-kg fish hangs from it. (a) What is enx4m0 sm*:cqf2hp5rthe spring stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates wdxi95 ;opkwz)ith a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. )i;kxo9z5pwd What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position kihn17-9um66ktw yrt lkcf 51x of the mass in Fig. 11–2 at times t = 0,tc klyk7f11ruwt- i56t6mh9kn = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 spit3l4bfy*3bt8: qwni/ntx6y q der’s web. The web vibrates predominately with lq:wb /tyfn4*bt nt yi 38q63xa 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. 4hg :tx1vl843h7ntz 5oius h+p+ p ehaWhen an addi7:58tt xlv 34+hnaiuzhh4esgh 1pp+otional 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 per second with ew53;xaz*b qsan amplitude of 0. bez*xs5q w;3a13 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 0q +m (f2jhivh+dix0 luk n9yd3jh)5 jspeed of a SHO half the maximum value? dm (x q0+2j)3y+5vhfuiji9 ldhjn h0k$\approx$    A

A mass attached to the end of a spring is stretched a distancessa 7*lgcq/9mbq rss2 zld.li-y59 /f $x_0$ 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 sd,szgrq65zy* erg9moj*ucp xgk/ +p *c7-b,upring is stretched an additional 0xjzc65 , pqgck d r/esguz7 ob9*ym,*+rgu*-p.130 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring xv fa.u6(korfxu. 1m1stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a ku1.(rvau f1xxm. of6 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 80z8.ks9 k kfg-/(mi.lq yxth+l.0 N to compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave the gun? k l-ix fmg..+qzk9s yhl8k/(t   m/s

  A mass sitting on a horizontal, frictionless surface f6o 2 a3m7n o yillyxv,k::s7ois 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 experxoy:sno fmki7o,a7 6l:3v 2yliences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x =185g;3lfyi pw u6icsxo( 2jhb 0.45cos6.4t where x is in meters and t is in seconds. Deter o 536uiixwyf1ljsgp28ch b;( mine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of a SHO half c3 q7.w vpo9 6afrk jxo8okw,0KE and half PE? ± 6,xwovp9fj q crk8.k3oo0wa7    A

  If one vibration has 7.0 times the energy of a sexshnt5 9ym 2/ocond, but their frequencies and masses are the same, what ist osm x9h/n2y5 the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring ont-r 28r6m aszfce every 0. r2frm s-86tza65 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 idw3z 5ml1 a/qidentical parallel vertical springs, each with spring m /5lzqiad3w 1stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x/jqzxtq:oa d /;9hvv1 = 0.38sin6.5t where x is in meters and t is in secvot/a/vqdqjz1:xh 9 ; onds. 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, jys3;gomo7wi,.z8mri0m k- dwhat 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 thec: u3a5j 2celf end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Determine uc :fl3a2j5ce
(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 vfqwoa*6q3flxfu s6 5nt 42p1c4 sb9tlibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through foas9f435q c pb 6slnx14f6wlt 2q*utthe 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 connecteoi un)zk8d(bb+d ewli 3)+ ci(d to two springs, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg q3i- 8t2di(d v:,wtaex0m+ e 2ngkicdblock attached to a fixed horizontal spring whose spring stiffnesst,m:k 3wivi-+ d2x2t8adnc e0(qid ge 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. After5yp 9z 7py(zoxf;i t+t 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 bel(;yt 7t +xofy5i zpzp9ow the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations i1f q+uctu;b p4n exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swin tdy*5bqfkir tz uc5 y+l1/f0f0 otzo0/0 ddf;g per second? (That is, one fktzidcqyb50* /ofd0t 0zd/ 0 +yot5 1 fu;rflcomplete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s onr (nelzb4 .lzdpb (6l156vncl Earth. What is its period on Mars, where the acceleration of gravity is about 0.37 that on Earth? l(elnpz6b16 r v.n bdl4(5lcz   s

  What is the period of a simple pendulum 80 cqccgq bw.y*d(vy5x 928( wp hgm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulumd. n7nc 1i;pjedwr--b bob has a mass of 365 grams, and it is rel -erbd7.pnw n jd-1i;ceased 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 0.99oz;/ydiw. r/r kbc51b30 m. If the clock loses half a minute per day, how should you adjust the length of the pendulum? rd c./o;w5 krbz/bi 1yshortened by    mm.

Derive a formula for the maximum spei8dv+epl s+yq( 57o1r iz8t i8zi d4ofed $v_{max}$ 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 4 oqlr09idbj -2.5 Hz. At it is released from rest starting at an anglero-bq0l j4di9 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 cr :w* gm .h4d.vnhe.zonests pass the bow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the waves travelin n 4g.*:vzde .mwn.ohhg?    m/s

  A sound wave in air has a frequency of 262 Hz and travels wik/vkq- hz15 pqt7o8 ibth a speed of 343 m/s k/kq pt5ihbvq71-zo 8How far apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 5b5xhdc y.2o/ce 2ub ;p50 kHz and 1600 kHz (kilohertz) and travel with acu2yb5x;/ 2eho.d bp c 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 longitudinany8rqxi6 e +q7q4ahad/h3n5 ml waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same ej nz/96w/g g*pp(yo lllastic modulus, but one is twice as dense as the other. In whi6/ *p(l ngyl9pjzo /wgch 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 282r 2e3a9n7x pxdc *c5)dnj kwh m apart. If the tensde)xh 2 2kpc7rwn5danx9cj3 *ion in the cord is 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of length 620ng4nn)xng6-qeh yb7 - m and diameterg n )b--7yqeng6xnh n4 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.
(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 j15fl)p ffou:dy a dw,8ust below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How dd8)a1 f,fofyl5p :uwdeep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and this difo2vfwm og1 m a8y.9q2kference helps in locating the earthquake “epicenter” ( kyowg .fq81mov2m9a2where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated by a sinusoidal transfn- sast;/ ptiw.2 +jeverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects fjn2pa; tses.-w + /tibegin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplituz skcfy o.z6ig :6wv85des, of an earthquake P wave passing through the Earth and detected at two points 10v c5 gfzskz.6w68oiy: km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured to bedou6pp0 nk b90 6kdn9b0p u0po$ 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 tra5/nj ug.h,h2 hx f+ohi;u0 f jr;fly1ovel through the same portion of theg0xh;/ r;yih5u 2fojn flhfhj +1., ou Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling alongiz0r 5lvop ov,1b *gn; a stretched string have the same frequency, but one transports three times the power of the other. What is the ratio of the amplitudes 1 ,5oz 0blpogrv ni*v;of the two waves?   

  A bug on the surface of a pond is observed to move up y:k )ilq2 (s:qfrz 9r weu3uxj*g ;mw6+m)z bland down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor uz lx9k z*qqwr)2y:rmi;egm6+s :)lu 3wj(fbdoes the bug’s maximum KE change?   

The two pulses shown inh8nzt2. dh tr0c71 qvs Fig. 11–52 are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the vzt t.1s72hc hrq80nd 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 energy at this moment?

  If a violin string vibrates at 440 d2kcfle n*:v9Hz as its fundamental frequency, what are the frequencies of the first four ha 2dl9vne: *kfcrmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz whenk y 7pia0lf6m9-y9cr n unfingered. At what frequency will it vibrate if it is fingered9aypi7y-9 kmn6 0flcr 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 loaw l jhhy992 flu,ptvg9.j2b9ops at a frequency of 280 Hz. Name at least three ot9tll g2.999hjpahyb 2w vfu j,her 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/ 0:js)fla:kpkh5 l re2s If the frequency of standing waves is 475 Hz, hoel5la2p k:j:r0ksf h)w far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string nz4)9b6pj)rvtb+ff4b v fb0nare 280 Hz and 350 Hz, what is the fr +fvpnb0)v 4nt 9b4fb6 j)rzfbequency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 h-:2ywyh-v 50pvojxhg. The distance from the bridge to the support post is L = 62cm and the string is under a tension ofvwyx 5-0 v hyoj-hhp2: 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate 1tuc 0tq5cq w7z;eswxijnc4+ + 15fqrq6jx-r at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequencies aci+tc 4rq0z j6-ufn7qqqxrj1 xw5s+cw et51;re,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to v*qm bw9f:6pn)9yaaf aibrate 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 wq 9yfnaab9pm6*a frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mechanical 60-Hz w :hg6*uvj+clvct i ju9)u7:z vibrator. The string’s mass per unit+u7cj:t )u9wg*u:zvlh j 6 vic 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 adjusted by moving the pulley. If2l+jyunnll3+dx-bz y,* il) 4/ fqgoy the hanging mass m is fixed at 0.080 kg, how many different standing wave patternzxy3i dlf), -4+j bu+ll/goy*q2nyl ns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the right frequency,1*2aeapb u7 gb2si8ixf7- a em the watb82 *ifp -saae21b7uaxiemg7er alternately rises and falls at each end, 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 strikes a boundary within the Earv:+h l ly; r)s5nwnik() suw 9xybr0m:th between two kinds of material. If it app lv )uryl;rh(5 wsbin+ :nxw)9k:s0myroaches 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 au(yl-gg.,;s6y 6s ebnrb h8g the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests bah;6 bsg,n-sgy g 6ly.re(u8make 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, dense air. pop/ 4i gazetw1mp3jvy02h+ -If the sound wave hits the cold air interface at an y iv/m atz1j0pp +wgeohp- 432angle 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 s,mgak+ jwku i9+zntn+m3l( c:m 2lsk/ trikes a boundary between two types of rock at a j( l+sn3ak ic9n mt+/gkwl2: ,zmmu+k 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 the usewygb(yl yh.nt y8v y1q;- *0dzntd l*7r’s manual, the d*n ydglyy. ht10bt- (*l; z7yqyvdnw8ish has to 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 250 km and velocity :v-c-ijp v82v ;xavq o750 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 die -8x a:vqo2vvv ;p-cjid 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 cony3;epoikx mx94o /, oqv . t-rifmg7l7stant of 550 kN/m Find the maximum compression of the bumper if the car, wilf g/4ryvtmq7ok .xo 9io x;p,eim37- th 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 tz4z95g8ip pdt -gm f(zy3d;nc o a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a simple sprgz4p8czdi53y 9nt zf; pgmd -(ing, 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 onpc6zw1 2 j-8yiuftlmhlbm6 (f4 r(an( the end of a freely hanging spring. The mass then falls 33 cm before it stops 2hwluim(z4pba8f rtl -yn mj6c( (61fand begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 :fl99kidvteg*s 2- i nm/s (Fig. 11–54), compressing te- liinf9:t2* 9d kvsghe spring 5.0 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 coffew6ud nz6w+ghi74- 6vj wx s0wee (diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more4+hi 06xwnzugjw 6vs6d -e7ww and more 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 certainplds9+- 7 ikizguuz:; groove 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will b-:;slu ikdu7ipzgz+ 9e the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t vqr/o)a4 x7c.c udbq.where x is in meters andcqxr a/. 7o)4ucvdb .q 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 freq zo 8prr(s-a*+ w78yrfuvpte 4uency if it accelerates at 0.50g (a)s8+vp rt z fu(o7-a w8y*er4pr upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man sag tm9bk*up,6ht.yytv. .kd ; tands on the raft, it sinks 4.0 cm d t;ptdy.bmtg . y v6.uk*9hka,eeper 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)(8irwj 4bd st h3brq7- and 440 Hz (db -hwsr4(7 ibq 3jr8tA).
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stretched two-part cord of Fig.dypkyfz1w ct2 h2 :q)oh:cj) p9,zm.n 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 c yt9 zpdqm2y: z2wc.) pof:ckhj,1nh )ord or the lighter?

  A tuning fork vibrates at a frequency o;. wivj 37blkrf 264 Hz, and the tip of each prong moves 1.ibl jrkw3;7.v8 mm to either 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 frequencem qjhgf +l.h.rz j/ hv*5l+a*y 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibr.mvzh+/a .rqjlg5 * *h +hflejate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a ring thatjo: ahr pjbq2+0d q558 k q)hwyz(x3mv can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with onjxy)q5:583+qj (wrdvmqko 20 abphzhe end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-waycjnj.fji,7mvt: pf( 8g. qx:d swing takes 1nmgip:8t,c v.jqd f:(jjf.7 x.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 spri,yvtv9 4d9y,jaijzi:4 w 2oas ng can oscillate in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one iz4, yvti i,yjvjda9 sao429 w:s longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched under a tension of 255 N. A pulgc /;bbn-snp s;a q)t(se is generated at one end, and 20.0 ms later a secop;acs ( bsnn-t)b/;qg nd pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended nf b3l qt-; 4)oao 2dkfl8gm+afrom a ceiling by a spring with spring stiffness cntf +8g23 aboqdl4k ;mlo)a f-onstant 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 $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyar zrzg jpzqbs: ;(*at67d. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing;q:6 zrztzjg7bap (*s 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 Fig9dp:y vh le 3*glvb *ry2)q9vv. 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 a3h9r :v*)y*qe bllvdyp g 2v9v 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