Give some examples of everydralz icb.t*u 25 mk7boh-0rr2ay vibrating objects. Which exhibit SHM, at least approxzr7ha0-r *rbkuilm5c tb.2o2imately?

Is the acceleration of a simple harmonic ,vk.;mxhp /0f,3 npe wh5 wplfse 5o(aoscillator ever zero? If so, where?

Explain why the motion of a piston in an automobil6 irur9 tq/i/ee engine is approximately simple //rrieti9q u6harmonic.

Real springs have mass. Will the true period and finino s(rivj 3yju4 h .6;:jp( .u,sywrequency be larger or smaller than given by the equations for a mass oscillating on th,iipjw. . r:3y ; 4( uj(nsiynohs6vuje end of an idealized massless spring? Explain.

How could you double the:7aptjhk5 ,u* uteu5w maximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertickxglfzt b g a :57i8t)ae8k;r,r+k1ysal spring scale, and then is released.;kg k t+5tr1zr,8gb87 sk:)fe yxa ail Describe the scale reading as a function of time.

If a pendulum clock is accurate at sea lpg2 i, otuv9*kevel, will it gain or lose time when take * pg,u9i2votkn to high altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig.s98u4a 9r. uo+fqnfoi 11–48). How could you estimate the height of the branch using o48i+u. a9osu qffr n9only a stopwatch?

Why can you make water slosh back and forth in a pan only if you jz9vn ad n3,chtr3/,j shake the pan at ah,3, rn/dza 3n9jjv ct certain frequency?

Give several everyday examples of w7a z) a58pzq2+5dw/)qmf vrnk-a frkresonance.

Is a rattle in a car ever a resonance phmc/q)e76 +p -/-wm6l h y3aqizqsccltenomenon? Explain.

Is the frequency of a simple per oava hf-bj(lg. ry/(-iodic wave equal to the frequency of its source? v/bj.h-g aro (af-( ylWhy or why not?

Explain the difference between the speed d9 f;k5.z nbeqf+g)gzof a transverse wave traveling down a cord and the speed of a tiny piece of the cord.b ef)z .g;qd9z+ gkn5f

Why do the strings used for the lowest-frequency notd , ff*ug/rs: em;vjj:es on a piano normally have wire wrgeud* j /f:mv,: sfjr;apped around them?

What kind of waves do you think t- 3fxpbh u+5 2b+x8fxftm;jauk-w 3hwill travel down a horizontal metal rod if you strike its hbkxu3 tx-m u; 2h-bf aw3f x5j8+fpt+end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an incr.)iv)l mq acd i)i8r0kease in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary withii m)i)0 d8a.rc qkv)l temperature?

Give two reasons why circular water waves decrease in amplitude as the2/+mcvlsxo-h* l6dv)j pv a-uy travel awadp*hv )ajx2vvlu /mo6+ --scly from the source.

Two linear waves have the samervxh4)vi:j3g gv;9f n amplitude and speed, and otherwise are identical, except one has half the wavelength of thi:v3f r gx)vn9h4;g vje other. Which transmits more energy? By what factor?

When a sinusoidal wavu;k:*gz7b:75 g poc yr.ifda4 iebq7 h:/zfy ae crosses the boundary between two sections of cord as in Fig. 11–33, the frequency .pqrbi7 coke4:7yh7yz *:gf/5agiuf z:b da; does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any p8j3qb *rnw3rp/ i3 yoylaces you could touch it with a knife blade wiy3n/ 8 3b3prjyr*o wiqthout disturbing the motion?

When a standing wave exists on a string, the vibrations of incident gnh6nk* . -6xjwdex :jand reflected waves cagjn e*6wkhdxj:x -.n6 ncel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was bizc/we45 zsjb0 rm 61qeing transmitted from one place to another, how might we determine whether the energy was40 bjmcz/ 16wi q5szer being carried by particles (material bodies) or by waves?

  If a particle undergoe2*0,i mpm tf h2)4e lfht 5a-bzdrwq/qs SHM with amplitude 0.18 m, what is the total distance it travels in one ta)h-rwdeh mz 2,ql2if0 f bm t5p/*q4period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it gi6bp/34y*r e tkd)6 h(uhlbkbut is 85 cm long when aukh6yki63/tdbb lge* 4h p)(r weight of 180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver getss;jj-3dr*j e d into the driver’s seat. If the car goes over a bump, what will be the frequency of vibratj;r-dej dj *s3ions?$\approx$    Hz

  A fisherman’s scale stretc;lslh ,tpzch- *w6sxvwk5:i7 hes 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffne7;iscph* xwt ,6ll-v:wk5s hzss 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 jdga: dn6f:4./kvdlh n ai v(9lo5de*of 0.60 kg is hung from it. What n: vkf/ga hd5(edd*o6: li94.a dlvnjis its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at times t r. j-ntw5p.r f= 0,t = f.5-prwr. tjn$\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web. The web vibrates pred i gz;2a(+(tcckspme im74uv b6v:zl9 ominately with a frequency of 4.0 Hz. m+vc;:46ks72ect9bzmpii l(ga zv ( u
(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 mh3/r vrr,y3wbi)nx ;Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What nm3x) ri3hw,r; /y bvris the value of m?    kg

  A 0.60-kg mass at the end of a spr1 llh9.p;q9ep6it s pging vibrates 3.0 times per second with an amplitude of pqp.1e ;it6 9g9lphls 0.13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed of ajy;/ct ps9ur4 SHO half the maximum value9 / sty4;jcpur?$\approx$    A

A mass attached to the end of a spring is stretch , o y6:5bu-b jmywcoirx .9kvtp*ch0,ed 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 upt(bu,th 7ceh 5l;po0 0(uknspring is stretched utu7kp0 ;ct0eno,5hb((l hupan additional 0.130 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* ase qlv9*2xz to a spring with spring stiffness constant k s*q eav92*xlz = 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/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 spr9z fwfjin- 5 j09cxp4cing of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave the guficw 9n90jfc z p-5xj4n?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one end o7rd) wxi 7mu-vf 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 exp -xmu7 iw)v7dreriences 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 accordu 27 kqar51i q(o1ldqpdfuf;vk;;r3wing to the equation x = 0.45cos6.4t where x is in meterpdu 7uv3q; d alro i12;r1ff5;qwk(qks and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilin+; -bdsn, 1fgag;hlq*t .rsa w5klv+ brium is the energy of a SHO half KE and half PE? ±5flnas;1dr.v,n+ q* hl g- bgw;s+kat    A

  If one vibration has 7.0 times the energy of a second, but1mb h rv*5el+t their frequencies and masses are the same, e*v5rh +1 tmblwhat is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscilw)z4ef94 2x8mpi kzhclates from a vertically hanging light spring once every 0.65 s. 8kihx2 c 4f9zz)mpwe4
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallel vertical springs, eacjehg, dw yhy.mv;-*/ch with spring stiffness constant k (Fig. 11–49). What will be the /*vhyycg.dmwjh ,;e -frequency of vibration?

  A 300-g mass vibrates acc z0f5z -c3fyme9cllajr;7z9 s ording to the equation x = 0.38sin6.5t where x is in meters and t is in secoy- 3r9zl 9f c50 lczs7zmfjae;nds. 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 t3q)ffiox8 s4yy gi 33wwo examples 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 sprin ap7s7 ybwkz(fjm lu,i8m3ww/7 t)c+2 :kefwdg (k = 124 N/m) is struck p:uemw /j8kw)7fl+237ctf yid, msa zw7bwk( by a hammer, which gives the mass an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring st5 rhk9k5nncp7j kau*7iffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity at c ru7nj k*kh9ka5 p7n5
(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 st*3xsuh04*hx rxn /lo.zu we r9iffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fi/ o5i 9ka)d 9bo jk/nis8(orioxed horizontal spring whose spring stiffness cons)ks /j/od9iaroo(8i bokn9 i5tant 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 bripq dfo/j830 pedge. 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 brjqppfd 03/oe8idge. 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.1+t y.slo: oa5gemw( m What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make l*5*f1wdsne j exactly one swing per second? (That is, one complete vibration tfjns51 d* elw*akes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period os 77bb ozxmk/:j. 0k; ohntqu2n Mars, where the accebhx.0 t k 7uo7os:;2/njmq bkzleration of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 0xq vito a9.:u-,jlrd xy) (sq80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulum bob qy zr/6ncbw+t4w .it c:dcarv)- g5v3has a mass of 365 grams, and it is r 65tc/.q3ic4 c:ngd-y+rvt baz)w vwr eleased at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 m. If the clock loses pz9 iy2dcvs zv 1)54lbn6s o9mhalf a minute per day, how should you adjust dbl 9mv)sc 6vz95s1n 2pyiz4o the length of the pendulum? shortened by    mm.

Derive a formula for tnqw03p).2m le o jeoa(he 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 of 2.5 Hz. At bm+ze va0agu0al7 5.git is released from rest sta0+lagba.vgu7a0 m5z erting at an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchored boat to9w49vda) q wevery 3.0 s. He mewa dt) wvq94o9asures the distance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a pdgwy) +or (*8ybid ,qfrequency of 262 Hz and travels with a speed of 343 m/s How far apart arp(yg ,oq*d+dwy ib)8re the wave crests (compressions)?    m

  (a) AM radio signals have frequencies 0ul5rusnf h3/x7tuyqbs(8 1 ybetween 550 kHz and 1600 kHz (kilohertz) and travel with a speed rh y7 tun/xlsf( q58s1 b3uuy0of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal waves 5cd-4uc de+ dbin
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but orzo4dush ,8-9-lfqhy ne is twice as dense as the other. In which rod will the spzr4lh--fo,s9 u8yhq deed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between t7xmp/48g lkzf3 gk 4epwo supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulsex 4ze/3p87l pggfm k4k to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a 6bt j5 2.e:rrkps )lfbv-ud y*steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal2.pvu)r s bkr6tj y- fe5:b*dl 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 just below the surfa 2 hd+jjsr8e96l eu ((ns8sbuzce of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at z8u(edr s hbss9u+(6 8jje2lnthis point?    m

  P and S waves from anomws 2w3nx9 0c earthquake travel at different speeds, and this difference helps 2o0xn w3mcw9sin locating 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 approximated by a sinuja*f ji* rom*zl l-+es)l,(eysoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mi(ls i)e+ ro-ae* ymjfzllj**,xture 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 ampl7lldc x06 m; km7rk4 meq1xg8dtdz2n;itudes, of an earthquake P wave passing through the Earth and detq6d;4dmzk xmnxlrl m7108g ;te d7kc2 ected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measubwpv .-mwt1 2sred to be w1 b2.-svw mtp$ 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 shgl,o0bfzcb r q. 4m5 )vval8/ame frequency travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of,. vf)54h/m oblz8aclq v0brg the amplitudes of the two waves?   

  Two waves traveling z,ie-f ,;olhc p 4ta,xalong a stretched string have the same frequency, but one transports three times thelze4,at o;,x-hp, cf i power of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and d;w1 9k 9tm9xq(lojclm own 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 d mt19wk99jo(ml;cq l xoes the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 :*uoup -+c xbdare moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (uxo:-pc bd+*u 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 energy at this moment?

  If a violin string vibrates a j :()nu(pwtijgr8,igt 440 Hz as its fundamental frequency, what are the frequencies of the frnuwg ,)tp(j8 jig: i(irst four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequ,i gkz+-r *xzco6jj6rfn+)bw ency will it vibrate if it is finger gjbr 6 z+jwiz*)f-+n c,k6roxed one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at vdcg kt8:62jz a frequency of 280 Hz. Name at least three other frequencie t6c 2:gjzd8vks 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/sl-b9kwgs b:n9 8)lsyz If the frequency of standing waves is 475 Hz, howlbw : slzgb- y)9nks89 far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 28 kneujop,v,+u. v,fq*1gact :0 Hz and 350 Hz, what is the frequency of the fundamental?e.,f* t vk, poc1vjnuug+, a:q    Hz

  A guitar string is 90 cm long adb(j.0 -cfnj nnd has a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are thc bjfjn(0-.nd e frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is measufo .9j lymfh93red to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct theolfm h39fjy. 9 frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, butd, 0roa.:7mlp5zx i(4 tyq(v zp xe(ppkth/5n it is measured to vibrate at 205 Hz. By what percen0kxip dpo/5y,n4z t(( a p tlrp:q(z.mvh x75et should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a sma: (t29st. ws+crytbqnll-amplitude mechanical 60-Hz vibrator. The string’s mass persqrys2t+ .(t:b9 wntc 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 motba b3fp 42p, t*w5pzkving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave wa4k5t*b,p pztpf2b3 patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth i*qu+h ecn /fy/n a tub at just the right frequency, the water alternately /enf h*uqyc/+ 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 lmah-hv(/ne- )r9x f zthe Earth between two kinds of material. If it approaches the boundary at an incide9flx/ha(m-ne )v- rh znt 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 changes z 0zdgl v0+ -x5lyz5vq8rf2 nufrom 2.8 m/s to 2.1 m/s If thl85vd5+r0f0 xg-z2lny zv q zue 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 when it2 1 irv:bw5epv hits a layer of cold, dense air. If the sound wave hits the cold air interface at 2vvwi1b5rpe : 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:9z.oxcil/0n u.s 6bzv-(njnx:l tov a boundary between two types of rock at a n:tovin s.cj(0uob -v /zl .nx:96zlx38 $^{\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 ab5-td9qcj.)xj-se v8 wm8sis aout 0.5 m in diameter. According to the user’s manual, the dish has to be pointed in the direction vtjq c9-e85. x8s)- dmjawiss 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 wavelen or5)lcov.6 csut() fmgth 250 km and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in )ctfom 5sv)(co 6rl.uthe harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spri(ncf ;nbd-ofi+sd*ubjk0x70ibi w4 2 ng stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of (uf0+xdj4sncb2 on0i7ifd-*b ib ;wk 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 ad y cw r:5jgk**y9 sknza26c*an ,ae(18 m below, which stretches the 5r 9j,c*nyz **ad:eg y2nacas6w(k aknet 1.1 m. Assume that the 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 hangi * iv-q/wmvue*ng spring. The mass then falls 33 cm befoi vvwu -m/qe**re 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 of 22 m/s (Fig.k75 qoy yvlhjbw 59td7y- 3ma5 11–54), compressing the spring 5.0 m. (a) What is the spring stifj v 5mba57dqtl y9w 3yyk-oh75fness 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) athyg b /hrx9. xjk.v-:c just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55)yk/ xhx- vbcg rh9.j.:. Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain gr:u1adkeyc6dsg rx*g 2:zs 6 o:oove 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sound emitted?cug6or y2:xa:gs d 16e*k:zds    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.408dsqxd95 v2 spt where x is in meters and t in seconds. Determine v8s5xqd9s2d p
(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 fd j(rmg2xro3,s +(w8mi2o vozrequency if it accelerates atogjx2omswrz2 v( r8(m+3,d oi 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raf02nelzo0h,i qt, it sinks 4.0 cm deeper into the waten0i0ez ql,2 hor. 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 kzijl( ; lpuzkyrkw6e n+74+4 bjdy*4are tuned to play at 392 Hz (G) and 440 Hz (A). j4k *l4n6wej7kyk 4zbu y+;(prz+idl
(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 df*0x3cyv-srm yq /f3.toq;n0 g -ob (x 8davhaown the stretched two-part cord of Fig. 11–33. Detc --yfxo;( .0sy/vrdnvhbq x3a 8qm3 g fao*0termine 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 the lighter?

  A tuning fork vibratem) r;* fnuo:jehtk h/.s at a frequency of 264 Hz, and the tip of each prong moves 1.8 mm to either sidee*m;nt. )hu f:ohkr j/ 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 1.5 c6hj8n ;ylb5o-nxnm-qyu 8 4wwycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble q-xwy-;yj nlho6nbnw 4m85u 8 placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free”etkd/wo16g 4 p end if 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 vibrations e dwp/ kt14og6of such a string with one end fixed and the other free.

  A “seconds” pendulum has a peri :d l zeo1m*7v+2kcdn76v0cmkpes 0c pod of exactly 2.000 s — each one-way swing takes 1.000 pd cozv70enc72m1e 0vm*kskpl6c +: ds.
(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 zqw-a-pf s8gp 5maob:5o k0f ;spring can oscillate in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amou5s; bqwaomp-o: f-80g5kzaf p nt? [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 nazw(tnt -yuqo p-(c4k:;h9 r m6fn l5123 g is stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first mee -nra9z:f;yh( n kp(45tc6uon w-m qltt?    m

A block of mass M is suspended fron, vc;,nt*zm vm a ceiling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on topmnt ,n* vz,;vc of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel cran(80yw at cfj/+emisr 5e cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.5cmrs wi8a0 +/(ejtyf ]    s

  A block of jello rests on a plate as shqz4 (rlim 4xs:y: 8xdqown in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibra8qixz 4s y d:rm:q(x4ltion, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz