Give some examples of everyday vd f/r+i4cny:h ibrating objects. Which exhibit SHM, at least approximateyf+n:d/chr 4ily?

Is the acceleration of a simple harmonic oscillator ever zero? If6. 7z9m izfi z7z cws x03b3)5bkclmdy so, where?

Explain why the motion of a piston in ano( utmhf37 f jc4bu 8s,u,uzm1 automobile engine is approximately simplez7 4uj1m s,t(8m,hf fubu3uoc harmonic.

Real springs have mass. Will the true pgq(lt/n x;/vmky 2;kf eriod and frequency be larger or smaller than given by the eqm2/;v/ ;fk(x gqnltky uations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maxim ef tn1; c-o3p vli)2xg-lsyb4um speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hooei4ig 6u/vgz5 4x uhg r.sw34zk of a vertical spring scale, and then is released. Describe the scale reading as au5.i rx v3zwgsze/u444 ggih6 function of time.

If a pendulum clock is accurate at sea level, will it gain orw 2ckn;t/ h cdfqtr2, ,7wem*z lose time when taken cq cr fwtzh* 2n,k2tm/7w ;e,dto high altitude? Why?

A tire swing hanging from a branch rexo 4ch u/cf5p+m9nuj3won.o.aches nearly to the ground (Fig. 11–48). How could you estimate the height of the brh+4/fp cjo9m3u.nc.u o no5wxanch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake the pa 7fbxo .kznies2-i.xb fq.+ v8n at a certain frequencyvbe qxozbi..7s8i- x.kffn+2 ?

Give several everyday examples of resona5,d(o wyt, avupb0g/l)8e y dcnce.

Is a rattle in a car ever a resonance phens k, hzq)e*2pg-t-gjuyt h 6y0omenon? Explain.

Is the frequency of a z0fhu,.ahj e):mhw /nsimple periodic wave equal to the frequency of its source? Why or whj /ahehw.z,mnf):h0u y not?

Explain the difference between the speed of a transverse wave travelingnj sg+w)m - c;q*be-no7us jd- down a cord cu *sjn)sweq -dm7--;njb o g+and the speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piast 8b4( prrfx:no normally have frs84x (rtb: pwire wrapped around them?

What kind of waves do you think will travel down a hycb h+kg*3 kqfu : .hbo.36lrjorizontal metal rod if you strike its end ybh .3qo*c6b.3+u:kr kghl jf(a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperat 2k)/4aqibnzgge(; 9 iv,wtp dure, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperatu/;t4bde)z 9 nvgigk( 2qa,ipw re?

Give two reasons why circular water waves decrease in amplitude as they wsy+*x q4wk)etb grn,6(j5v v travel away from vg (kv6s)r,qxetbyjn*4w+5wthe source.

Two linear waves have the same am tkytx224 at5cplitude and speed, and otherwise are identical, except one has half the wavelength of the other. Which tra2akxyt5 4 ctt2nsmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between twbilouq:7ot o6w,)jt 8 o sections of cord as in Fig. 11–33, the frequency does not )tq86u7o blj,tw:o oichange (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places you could tj(l y7kqwoa 9/ouch it with a knife blade without disturbin9qy7 l/wj (akog the motion?

When a standing wave exists on a string, the vibrati:d7 *zuqxi 30oxd1lnl+t gs(*un ,x oei s0h(lons of incident and reflected x10iqs:ox7sit3*l o0g enu(lldhz( du nx+,*waves cancel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted frmb2xay,f(to97o wkq2 i/lh/zom one place to another, how might we determine whether tayf,i/ow2m ( /29zloq7xb htk he energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total dista,4u ;y nl,mh: bbi8fgtdh53ac nce it travldugh i4f5 bm ,cah 3:,nyb;8tels in one period?    m

  An elastic cord is 65 cm long when a weigh:p.vc2;af ght 2fq6lht of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this elastic cord2 gt ;ffv:6a2hlp hc.q?    N/m

  The springs of a 1500-kg c xody0 sv2-:cyar compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the cs0yv:doc -xy2ar goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.;eh,qcu aq34 i.9cbra1arxrxxoj 58 /7-kg fish hangs from it. (a) What is the spring stiffness 9,q bc. 84 axraiox rjau3;rc1hxeq/5constant $\approx$    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 wityyhdbv(p p6 * hhaf137xuc4a5 h a frequency of 3.0 Hz when a mass of 0.60 kg is hung from ivhhb(hufy7d xp4 y1c5p3aa6 *t. What is 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 t4 r+8b gp7i;a,phyczv -4wpbrimes t gy,b zph74bc4r r+ipw-pv8;a = 0,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spiabtv)h91 1ea bder’s web. The web vibrates predominately with a frequency of 4.0 Hzhe1aav)b9t1b .
(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 sprinniu9n j3l;.d:* szvfdg vibrates with a frequency of 0.88 Hz. When an additional 680-g mass is addez ;9i . l3vjn*dfnu:dsd 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 pv n**dm7 nx+lwb .8g awtp.)ujer second with an amplitxbtjnwal8v.*g up*)+ d7nw.m ude 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 fromijdmi9n: gu0psy2w5m t69x1; v x +eou equilibrium is the speed of a SHO half the maximum valuedtm+ev5jxm6ogy;u9219 ix: i0wn psu?$\approx$    A

A mass attached to the end of a sjw yrw69*xj0bvcj o,) pring is stretched 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 theh-y 3,/b;e-cr y3+o6mcjzh kthd wv.n spring is stretched an additional 0.130 m and releaswvc r .y et d-hj,+z3cm-/o;nykhh6b3ed, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a ickh 8+t7hzqexzbs g 9ii d/i* v;5+3uspring 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 movinshxiz d57g8u3 iiq9icb+ ;hvkz/+ et*g 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 9e pucs)v;3fncompress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the s)3;cn9 efup vball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surft8t mcg ty,w.z8.uo byjlk9h-0. h n4bace 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 sprb. 0,ht.c. zl9mhy84onutkyjg 8b -twing by 0.12 m. 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 according to the e1ifg) f4ef f2kf .j+nw by/+j y(p(acbquation x = 0.45cos6.4t where x is in meters aj yi/ f)yw.j2+pf1k4ffebgn(+f(cb 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 equilibrium is the energy of a SHOny0 7 t;yol yp;2ms0fls4m/gx half KE and half PE4/g0mlp;s 2y0oymn;f s7t ylx ? ±    A

  If one vibration has 7.0 times the energy of a s v8)u79glgrl 7*bre jiaa 42ydecond, but their frequencies and masses are theluy9 78 lgrabreg 7j*dv2ia4) same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spr ( zx-mxy0;yqging once every 0.6xmy-qy( x0gz; 5 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 identical parallel verticajrj:2stz;-fvk h14 jmqwf ro ,z3.*gfl springs, each with spring stiffness constant k (Fig. 11–49). What willgv.2k3of4tz1 ,rf hs j;jz*jmw fqr:- be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x is iu+hfexv9c7 2 in meters and t is 7ce+hviu2f 9 xin seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled ;ri-,5ri uuj, ygsln) o6)qxoqd*sl2 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 sh r.rs bfov,(qbpr- ;-y:ndr0pring (k = 124 N/m) is struck by a hammer, which gives the mass an rq fy-nsrhp- ;bobv : .,(0rrdinitial 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 sti(5toz ewnz; 4offness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. 4n5oez to (z;wThe mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with m(wc jb;6mhz wr:n.-f 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-* hbh n:hyfzwzl)r+*.600-kg block attached to a fixed horizontal spring whose f+hw:h rh-z l*ny )*bzspring stiffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high bridge. After reach- uoip-bni(b+ m /qa/qing his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest pob- q b/ai( q+mniu-/25.0 m below 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 in exadrsbe.tm*0 f m7v4* 7vv lk+grctly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to m. oxyo9 6ubitmk.c9;hti g ix du7-;w8ake exactly one swing per second? (That is, one complx; ii h ou9ti b.;kcgxtu6ydw8.o9-7mete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80e5 pk7ugf::al s on Earth. What is its period on Mars, where the acceleration of gravity is about gfu:75k aepl: 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 1zdu2.dxi7; 8g kfxntcm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendmy)l* isupj76ulum is 0.760 m, the pendulum bob has a mass of 365 grams,7u psljiy)m*6 and it is released at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a v/d8zq p0du m, )m9cfwlength of 0.9930 m. If the clock loses half a minute per day, , dm0 8dqzpuf9mc/ )wvhow should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum speedw.e8 i+npupzxj (bd* * $v_{max}$ 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 it is released fr ;o7tcekq4j.n om rest starting at an q.o;74tkn ecjangle 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 everhugh cdie;0/f h31)eoy 3.0 s. He measures the distance betwe); 0h1 ec/ehdf ugi3hoen two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels withi0q /*)c dg,l7hi3 :fci ilney a speed of 343 m/ ehiiil0/g7,l* iq)c:n c3f dys How far apart are the wave crests (compressions)?    m

  (a) AM radio signals have fre/ 7z8 ptj(d njd5zl1ez8wh6bxquencies between 550 kHz and 1600 kHz (kilohertz) and travel with a speez8zn/z ljjpw b7(1 ded5 txh86d of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal wgnw0,ol fu5k0.y-0 c/)e j nadh jp+tiaves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as denseqi9 5 yze4i2sr as the other. In which rod will the speed of longitudinal waves be greater, and by wha 9i4rq2yse5i zt factor?   

  A cord of mass 0.65 kg is stretched between two sup):gyu9q zb6hiukw 4l4or nw8t-fc 3 )cports 28 m apart. If the tension in the cord is 150 N,yic tuw- qw9l4bh8r36u ko g)f)cz:n 4 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 ar;c4vnfl85n o hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends an5;8vr4 ocn fl 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 surface of the sea. He hear52kbx2/yll - u 2yiuitjezk.8s the echo of the wave reflected from the ocean floor directly bi 8zjlikk yel2 yux .-/t25u2below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, ano3-0rj4 bgc-ok9qh h nd this difference helps in locating the earthquake “epicenter” (where the disturbance took placehjg 3 okrbq-ho-n04c 9).
(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 + zf 8s++znkqeobq +iijm480sbe approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually includ q0m+szkqfz +nisb 8+84ijo+ee a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, st9zaj 4d h1;yvd8 s6 ua-)c5zklo(zzand (b) the amplitudes, of an earthquake P wave passing through the Earth and d j8;aks)ldyd 5cz vauzot( 9zh1z 6s4-etected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquakekqigas 7.:*)dz j6l1q 4dxxp c wave passing through the Earth is measured to be sq*g6a lq4 7jcd1px ):xkz .di$ 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 freq2woj 3 ,yyexw,-gsrh.k 4k7cyuency travel through the same portion of the Earth, but one yc2yjw,w3h kkoe,sgr-7yx 4.is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency.h0goiz3;7ho rivs* x, but one transports three timeh s;h0*7o3v oi.irgz xs the 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 mork10 o ,wk8zwuve up and 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 fack, wozkr 1wu80tor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) Seyoqy+o . a4lle93kkm * ex.4sketch the shape of the string at the moment they directly 3 lymoayeo4e4.skl x*e+q9k. overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates1md6 nc( d 1jmym3oq4su6d beqj(/6 bm at 440 Hz as its fundamental frequency, what are the frequencies of the first four harj 1m ojq ud m/(nqd4mdby6 b6msc(16e3monics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. Atysw 0ueye/2er ,(uj: s what frequency will it vibrate if it is fj,ey/es esyu: 2u r(w0ingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency ctw4fj b- ,+n.xpv 2scjw:0hjof 280 Hz. Name at least three other frequencies at whi.t wcjxj:2jv,cf- 04wh +pbsn ch it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of standingtrec lq 2+*um8l u5yr9 waves isl*rmcl 98u+ t 2r5uqey 475 Hz, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrat8lnv .aty vd6-yh)3p tqlk(s/ing string are 280 Hz and 350 Hz, what is theysv3/-l pva.dl k6)t( 8thnyq frequency of the fundamental?    Hz

  A guitar string is 90 cm long and has a massts dd up*s34i) 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. Wha)its4 usd3d* pt are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but in*r ) m ah/jwq)l0.rttt is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct*rtnra.hl/t wj)q)m 0 the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar st1i 4;zhw d y2ju-bad2tring is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should zt2wuj-yi4a;2d 1hb dthe tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal str j v;iawmnela9unc*x8b*2/4* sd s7pi ing is attached to a small-amplitude mechanical 60-Hz vibrator. The stine/* p* nxiwbdj8cum9*ss4 a7lv2;a ring’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the strib dke)za9g- ;zng may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns maydzg-z a)keb9; 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 fr6/ .zdcxy2fhoequency, the water 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 watero2xz. d y6/cfh wave?    m/s

  An earthquake P wave traveli3;y*cwzxts/k ng at k.0 km/s strikes a boundary within the Earth between two kcz;kt3*w x sy/inds of material. If it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “cyox,5 p+fl*lfl)43ngyi b/ wn7g(hvshelf” where the velocity changes from 2.8 myfpx(+ nlwf lyc)*, inh3gv7 b45lgo/ /s to 2.1 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 travelya j*p 6oo:b+udg9py/ co78pging in warm air when it hits a layer of cold, dense air. If the sound wave hits t9y*puo 6 /gpj+ ao78gcbdo :yphe 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 betweeno3 t, n8+vq3ll23prcq7 *ms.ua ionq v two types of rock at a 38lso+cmn.,ip 3qu v nl7 q3otq2av38*r $^{\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. Accoymuwnvb 1,67 a-:sv tgrding to the user’s manual, the dish has to be pointed in the direction of67 a1, uv-nst:ygvbw m 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 wavelengt12hg) 92xr urnxz yw7 u8qp7eph 250 km and velocity 750 km/h travels across the Pacific Ocean. As it approa22gxq7rhy 19urzpn7xe w8p u)ches 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 died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a.uwe8a,s n a.s spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, wisaenu s8,wa..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 fromxj9 znpj7 ;dsy-.hthe+a-g, l a window to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a simple spy 9ps; ,n-g.-e7l+hjj t dxhazring, 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 f(g(m0km f--hg0 fsaflreely hanging spring. The mass then fallsm f-lagf0mgk (f hs(-0 33 cm before it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speegzkuwk m xgt7, uj0m(5 ;w1u9gd of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant 9mk u51wuw0gmx z ;gkg( ,jut7of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at j)4.v yzd sm+:x1-erzz sna3 fzust the right pace of about 1 sarx )e:1zds -syn3mf4z +.zvztep per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-rpm phonog3jc bcozr 1+icem8l ) ef1.k-lraph record have a wavelength of 1.70 mm. What will be the fre lrbo3il- ccj emc1 k8ef+)z1.quency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equan o)ht(*uql;s tion x=0.650cos7.40t where x is in meters and t in secondsqo(;nuhlt*s ) . 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. Wb-ys80 hpv eg:m(qj+yhat is its frequency if it accelerates :q mg0byjv( ys-p+8ehat 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats g86 kgha 76ipusutl4 5x2tqy: on a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off,7ki4u :xl 6ugt2y5pg s6ah q8t 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 instrumentdgy56c a,7 u- rn9xpxr are tuned to play at 392 Hz (G) and 440 Hz (A).xr 96r-d7xc,un ap5yg
(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 traxp+e-wg nu ;hdl8,6nyveling down the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the 6l;+ ygh-xw8npde ,unwave 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 vibrates at a frequency of 264 Hz, and t67 grwu2sn ph2- ftu ,8-zrzsfhe tip of each prong moves 1.8 mm to either side of center t zp2 rz7- rs-hsnwu2g86fu,f. 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 simlwikc u0ibjm d.jv ns)+u:*(imx.2g- l 5jb0iple harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that*0xmk2i+ jbiijlg5.nu )i.jv - m ud:sc b(l0w 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 : b8r8v3vm7n04x t nt2n xeu5 zpxawm-attached to a ring that can slide 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 freennmxa8tx0- bevn7tuz:3mp 8v w25xr 4.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way ds l7/wfvmng cs:3+3wswing takes 1fdn s: 3w/+swl7gcm3v .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 vertica+ . ig6*ezosyu3vqje)zc9 +pz l 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 hor3yj)+zesp qu6voez9gc +iz. * izontal 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 g1/0k bsk*wx2a 1dx(e g td4daunder 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. wkedg2b/aa xxs 4* d1(tkdg10Where will the two pulses first meet?    m

A block of mass M is sus*xc7ck:xqq 6npended from a ceiling by a spring with spring stiffness constant k. A p7 xk6q*:cncxq enny 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 junkyad j zvt *+mj/),pll*hdrd. 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 ol) vphj+*zd,/mjdt*lf the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello restsew3;ox w*uf )fxl s))z8oug8k on a plate as shown 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 vibratew l u*oeuofwxgx)f)3) k8;z8s. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz