Give some examples ofbu/dakg(dd ) + everyday vibrating objects. Which exhibit SHM, at least approximbud+)dag/(d k ately?

Is the acceleration of a simple harmonic oscillator ever zero? Ij7;qf 7rbi -yviku7e9srh ,o7f so, where?

Explain why the motion of a piston in an automobile engine is approximatelf *8 )4oc24 zboldtzxty simple harmonic.tof*bct4)zox z24 8ld

Real springs have mass. Will the true period and frequa:8h mneh:q 6nency be larger or smaller than given by the equationne 68hqm: nh:as for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the6,izgv f3so.:2um hy q maximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical sn+goahbzl6j9 m/ w0a4+bba3 dymqz 39pring scale, and then is released. Describe the scale re4 3a 09mnbajwldozg +yb 6m/ zhq9ab+3ading as a function of time.

If a pendulum clock is accurate at sea level, will itkpzd7 1g-l:uijl5pd 3 ea6;yn gain or lose time when taken to high ;dn: jp l3ei-zdgul yp15a 67kaltitude? Why?

A tire swing hanging from a branch rearm7 xu7f,3/urenm i)zmf9 gq7 ches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch using only a uz3x9r7gef,fumi7m/ 7q mr)n stopwatch?

Why can you make water slosh back and forth in a pan only if you sy 7f21mwwvt:ghake the pan at a certain ffwtvm7g1 :2y wrequency?

Give several everyday examples of resonanceba f f.qmlng fzw)a ;k3+8l8q5.

Is a rattle in a car9g6 kifz a9cn(+/4ifxptyn5a ever a resonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequencyx*iz-w 7ld1g-rqpjdu 7p03xu of its source? l7ri-x3u*x- jp1z0q7dwdug pWhy or why not?

Explain the difference between the speed of a transverse wave traveling down a cw; berw avh2-rh*;z9p ord and the *ebh-; wpz rv w;92ahrspeed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a pianot1mav d3/ dd3u normally have wire wrapped around thedud/t331madv m?

What kind of waves do you think will travel down a horizontal melm x7hz4 e6ai3tal rod if you strike its end (a) vertically from above and (b) horizontally parallel to ite4 zlxm hi367as length?

Since the density of air decreases*s*)ju8nc5o,uw0u s va hq8vz with an increase in temperature, but the bulk modulus B is nearly independent of temperature, ho ,0u sq)uc8vanu *hozv85swj*w 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 p,uzwu.nue:omwu , +cfw.qz u*1 x:h 2they travel away from tu2zuc , e:.h w,f qomuu1x.+ nwz:u*wphe source.

Two linear waves have the same amplitude and speed, and otherwise are identical spdhft/0pw2), except one has half the wavelength of the other. Which transmits morp 0s d2wth/pf)e energy? By what factor?

When a sinusoidal wave crosses the boundary between two subwh ,4)uvvrfrvm;.5y hk t;( ections of cord as in Fig. 11hf)t(hbuw5u rm,4v;; vvy.k r–33, the frequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any placesvlh679 2:aif*13 pcao peuktn you could touch it with a knifee6lfua h a9in31k p2 c*7tpv:o blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of inci dqos.* dq,5yn b51-:a lscgttdent and reflected waves cancel at the nodes. Does this mean that ng5tadc . s-s1q dtq:5byol,*energy was destroyed? Explain.

If we knew that energy was bei0brpa1xpkxok;,t:(ax oc6l c 1 c(ck 4ng transmitted from one place to another, how might we determine whether the energy was being carrieda0, acxr(;pok1 xcc4obl x:k1(pk tc6 by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18:xwv*e40qv7ex ;jqtqrm . g*f m, what is the total distance it travels in one xr x*4 f t:je.qe;*7vwq mv0gqperiod?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but is1b+81vjw tp xe,ys eo; 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k ;s wy,1t+vjopb1exe 8 of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when it7 i6o6le dtvc, t5dag.s 68-kg driver gets into the driver’s seat. If the car goes over a bump,t vdg.56e tiacd6o,7 l what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.:2mafd -gk7r+wvhc0b ya c 0:z6 cm when a 2.7-kg fish hangs from it. (a) What is the spring sad+2h:wygrc :00-7 m ca bkfzvtiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mass of 0.60 kg i9y*hw) std gf6s hung from it. What is its frequency if only 0.38 kg hangs froy wh6s9ftg* )dm it?    Hz

Construct a Table indicating the position wslsj* edjbzhuw;1, 57n e i/+x of the mass in Fig. 11–2 at times t = 0,/ wuzb;jdil e+*enh1s7 j ws,5t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 gy :(9bsu7*d; i bzqin6s,saz y(x7q co is caught in a spider’s web. The web vibrates predominately with a f;cs9d,y y(i:xb z( qi*us 7b7z n6oqasrequency 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 l)ntoegaag o4 p7 0orn64b79 ca frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. gne6boo90 p cnla74)r47tgaoWhat is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second w; qpojhhh mc+7(8kg/ wny96b(0fuu txith an amplg; hn (whmhpk0tou uy/j 6 (f+x7cq89bitude 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 equilibriumt z8axnvb w,nj) ncw0bi2./(a is the speed of a SHO half the maximum valn xwnac8n0 2i a(tb /bj)z.wv,ue?$\approx$    A

A mass attached to the end of a spring is stretched a dk(u:nmu0i+pvkt+zx:( z p w cyy/r86pistance $x_0$ 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 stretchesnuct0 9-z lr 9:ziprf,woh9.scjah6 2 a vertical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to rea9cnc96af:t -zrw jh. sol0hizp,ru29ch the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attach tt6h42lra w, qt1coapuzj(v3xjt2g+-e, +bded to a spring with spring stiffness 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 speed of 0.55 m/swl 3zjjct-e2q2g tt4x,ba rhod1(vp ,+ t6+au
(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 of a toy popgun 0.200 m to ;vo7+1m z5b- umzwg q9mh/ asz“load” a 0mm7zz9ao;wg1 z uq /-vbs+m5h.180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a l/ -a7o5kg:8qnslh gf horizontal, 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.f lo nk/gagq7l:- 8h5s If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates anpgw0 l: ac2u0bl8l.kccording to the equation x = 0.45cos6.4t where x is in meters and t is in0 8cg2:a0lkplwlb.un 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 equilibrium ij vyv h4 qj*l9ibs ew5fn):;r6s the energy of a SHO half KE and half PE? n:w46byh9i*srqvl; fjv)je 5 ±    A

  If one vibration has 7.0 times the enerlvx cl.*t jo2un*x v/,)op2w ugy of a second, but their frequencies and masses are the same, what is*o ltc/j)w2 xlnuu*o . x2vvp, the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from3kngz3v0 n( a;f8er prjpp*i3 a vertically hanging light spring once every 0.65 s. ar03p * (3e z8p3grpik;nfv nj
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical p. y.2kesyj n4uarallel vertical springs, each with spring stiffness constanun4s .kjy 2e.yt k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates ac,s3z,zs8-mun) hhq y ncording to the equation x = 0.38sin6.5t where x is in meters and t is in seconds. Determiyhun,q)zmzs ,s 83- hnne
(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 ip/j fn oedho):9.mvmq5yy7me * nc59examples 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 horizontohh f+)5 qwihv:i j+6eal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.9)+ivqhhfo6 j5e+ ih:w6m/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 stiff 4lshf *c1cqg,ness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through ts4g f1*lccq h,he 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 8vx5zfk 6 i30 uzrcu(xconstants $k_1$ 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 fixelhd7a7 8 k,o6aa gz7asd horizontal spring whose spring sz67dg a7 a8hk,a 7olsatiffness 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 fr+j-68xea fc3 dfvhc c0om 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. Ca8df3 0ax6e-vh+cfc c jlculate 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 pkrmu(hn 18ao7, i cx/yq(xw5is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exaamcrgyb0 1e8q bu4 h)k3-s;d kctly one swing per second? (That is, one com4ae1c ;bu k shkdgby)8m 3q0-rplete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, where felxke;dxr 4*l.g -0ythe acceleration of gravity is about 0.37 that one* 04dly ;xf -k.erlxg Earth?    s

  What is the period of a simple pendulum 80 cm long 3(n ja, zko07m; sssdoz(ls6 s
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulumk s eu :x+/5b.qta*myhgg/x2 w is 0.760 m, the pendulum bob has a mass of 365 grams, and it is released at an angle of2.e u*bqx t+//5mwhxy agg:s k 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 pezdqs6i5:i ncs;l ; bvq9b r5/indulum has a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pendulum? sh 9n qqidl;/i r6sv5bi:cs5b; zortened by    mm.

Derive a formula for egi cqbf7,iyu9vob bf 4ww):59u0kn. the maximum 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 ork86z)w jc- aif 2.5 Hz. At it is released from rest starting at ac )zkjia-8rw 6n angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his an/ :oq gvhmd5;i ere8:gchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. re:m5q/eg8v i:dg oh;How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed of 343 :hlv ,lor -nu)m/s How far apart are the wal-)u :nl hrv,ove crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilohert ml)hkb4; q85upa ,sc 9hfqt)iz) and travel with a speed,t8kmcpq)l4uq5f i9h b );has 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 :d;p zc20-promdcy g (longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have thetye45yvmvj7m127 q oue0 6ahu same elastic modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, and by what fuq ey1 tjv m47vyo 7uae6m520hactor?   

  A cord of mass 0.65 kg is stretched between twmgc x,0zb/je q1zu e:01i+ yjxnyz. f7o supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one s/1:01 fejmizj,gx+ cx7eyzb ynu0qz . upport to the other?    s

  A ski gondola is connected to the top of a hill by a steel cab(qy.+ ,bhcfqv le of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pcq b,(fh.+v qyulse 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 s2-;- yrnvv3k() d4hhfqzajlpfu3m 4 eide of his ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directdn hlpv43fe q4zv( 2kmj--r) fu3hay ;ly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake h v. pk1 xovk1g0.o:imtravel at different speeds, and this difference helps in locating the earoohv gxp0i1k:.. k1 vmthquake “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 ooq5i/ebu, z6p u560 3zmgoit can be approximated by a sinusoidal transverse 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 begin to leave contact with the ground? [Hint: Set the acceo,i utub 0e5mp6i3z q56/oozg leration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplituq+4ioa )wf *5udjcdkv (tv50rdes, of an earthquake P wave+(5d*4v0 5jqa uv kwiot cd)rf passing through the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquaj )o:e78wmggfizu6/q5mjou8x vq 3 w +ke wave passing through the Earth is measured to be e7/6jz5u+)qqxvm:gf u mwwo8 3 go8ij$ 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 m)1m7gapm ;jq-w tik2of the same frequency travel through the same portion of the Eartqmmamktp2j i7wg1;)- h, but one 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 sameek yiw;8ek02sx7e dt; frequency, but one transports three times the power of the other. What is the ratio of the amplitudes of the tk2w;7ixees k;ed08y two waves?   

  A bug on the surface of a pond is observed i a q/;a; lfjmyh /(8lh/i-tzqto move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave pqyma -l h//iih j/f8 t;;q(zlaasses. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving tocs- q7z q6izps5ixz2;ward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a pzz- q 6z 752q;sscixifew 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 Hzd0/x6trdjh6,fk f;o j as its fundamental frequency, what are the frequencies of the first fo/,drk dftx;60 6o fjjhur harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequencyacy( 8 c2qgkd. a6ze:x will it vibrate if it is fingered one-thirdex2.:ka( 6yaqcgcz8d 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 Hveupcd 7/a- 0hz. Name at least three other frequencies at whichpc7/d a 0vu-eh 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 +6c sh9;2c/4* bfvckcn,jscs bd2 myghcp3t(the frequency of standing waves is 475 +3n (2 tvksbcjc9cc6 h2m / fg,scp4d;bh*yc sHz, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are pin- a h22s6mz280 Hz and 350 Hz, what is the frequency of the fuanh26s2 zpm-indamental?    Hz

  A guitar string is 90 cm long and has a mass h5:tan.am x1j of 3.6 g. The distance from the bridge to the support post is 1j5t:n.x ahmaL = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200rowx l80fy83sbh ( w9c Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correh9cowb f8x80sr(yl3wct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar s iew2mj fa,j;.b-(+hag9yw gh ebx0 l0tring is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. Byf2gaab (wy-j9bjwi., lh0eh m; xg +0e what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is a tpxid88:.xdd o3zn*h +t4p 5ocw)q sattached to a small-amplitude mechanical 60-Hz vibrator. The string’s maspdtcso 4t8* inqzxx+.h3po 5w)a8dd : s per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be adjusted by moving th) 4x-pb r5b;joere/w we pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying pw5oe-br;jwre/4 b)xL between 10 cm and 1.5 m?   

  When you slosh the water back and forth inx)m c78c zya9uxre5ra-m(5g w a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequew8muc5 )yxaarrz5c e9m-(xg 7 ncy 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 str /5wum(ytukj9 ikes a boundary within the Earth between two kinds of material. If it app/wu( mkyt9 5juroaches 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 the velocity chan lr/ta74 m sjwhd;k yooi6(5w-he 8yo,ges from 2.8 m/s to dol 8(-,ohhe6 jwwyso4aki;r/ 5 7ytm2.1 m/s If the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air w83 ovz+kh:wu jg7ml3lhen it hits a layer of cold, dense air. If the sound wavewm7v8h3 3jollk:z +ug 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 two types of rock at ctc2 o1 zbf+2y 4ylj8cat2col2 yfjy8bc4z1 c+ 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 thqmpm/e *(xw-6zwng het6,:nl e user’s manual, the dish has to be pointed in the direction of the satellite, but an error of about, zp:nel*nw /meq gw 6x-(hm6t 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 velocf (cjoo wyjk6z. ;is ;yg*wks,pos93 3ity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warnin3;jsc.f9ook(spk3oyyw , s* 6w;zgjig, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumpep2kad 9dwj/3j r has a spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the carwkjdd 93ja2/p , 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, which stretches y 1+j9ujaznm1the net 1.1 m. Assume that y9az+mn1 j 1juthe net behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely ha)x-xg:1, +mi lrglc jcnging spring. The mass then falls 33 cm before it stops and begins to rise. cci x:rjlg1,m- g)xl +What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge sp4t20l plnjm1n8kmw uw )5i9soring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffneio jww 8n2l)p9ntm51k4mu0l sss 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 (diamqjmx717 noi6lb;nnq/b va0+geter 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 /jm0qovq7 n b 7l;anbn+ix16g. 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 a8 o lupky8)5fk/mwk 4p 33-rpm phonograph record have a wavelength of 1.70 mm. What p wp flu/k48kymo8 )k5will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x is in2pp,p50esf1hie o6bd meters and t in seconds. Deth p1 efosie ,2p0b6d5permine
(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 frequenc 48i/a-mgox , v1iqu9m)kx ilvy if it accelerates at 0.50g (a) upwardvg)m/- iq8 ilm aux,vi19k4xo,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When ny xmq1v )+6 rem1lm5cnsm(6 la 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft v m n)mm(m6e6rx1lvnc s1q5yl+ibrates 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 instrum hddr ji4pf;c6/)wm)p ent are tuned to play at 392 Hz (G) and 440 Hz (A). m pw4d)d/p)hcr6;j if
(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 +nuuohya)/n*2aq- mzthe 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 shqn )o*um2/-aay z+nuection, 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 2bf7 ;s6tq-m1pp; einq-hbag(64 Hz, and the tip of each prong moves 1.8 mm to either side o;p -fg b1s(h q 7ea;pm-q6tnibf 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 l4ux2gm+t5 06jnynk *lz tx 9gof frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) uylg+x0m9 x25jznktt 6l 4n*gwill not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a ring that can slide+,y qf)hyj urjl:dk mzkn yi m0.ei*9tz+60o 9 without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free *djt kk .+y0)zf0 m9uyijozr:i9,yhq6m+l en.

  A “seconds” pendulum has a period of exactls2gi lkyj2o2w ) qq,vo1 -l5jly 2.000 s — each one-way swing takes o-io)5, sq1g2 y ql2v lljj2kw1.000 s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertical direction ormfaqe t e*0j iq1b+6o3 can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period ofae1e*bf m +36o0t jqiq 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 tenm2e,,o h;ggw 4bd)cnjsion of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is gene c4d; ,gonhw2j, gm)berated 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 with spring sqo oiw -t0 fa 6i(hf(lwa+n(h5tiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that wiofal a(50 hotw(hf i-6qwn+( ill allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-koo+by q( );fj6jv-q1ea h je.ig 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 the bouncing? [Hint: Refer to Ta1ayeiq of.-bqj)+ o(h6je;j vble 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which also gifd/(;a*-b 8bvagr5k 88 agkewny myg( ves 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 vibram ; gade y8 b (f(ybvr-a/k5an*8ggw8kting 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