Give some examples of everyday-xdw j8 0e vlh8r 5fd25bipxg380oxbc vibrating objects. Which exhibit SHM, at least approdw-r35xxhjf5 0 b obdi l 80xgcpv88e2ximately?

Is the acceleration of a simple harmon*x7p ht x5/syn;eg3qnic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approx y h-ylv1x 4cpe9a z.q:k9(uteimately simple harmonic.p9c4vly 1kayeqtu . z 9(xeh:-

Real springs have mass. Will the true period and frequency buyq1uaw1 4+: wyo5 bbue larger or smaller than given by the equations for a mass oscill+ o1uuw y5u: wby41qbaating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple ha +w-gmwybj;wt t7 7*furmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scal/*rn 5xq-ji yf0ohwi: gj* f/te, and then is released. Describe the scale read5n t0 jg*/:woyif- /i*fjrhx qing as a function of time.

If a pendulum clock is accurate at s qvz mq1jb8pj75ptr,vc c+s7-ea level, will it gain or lose time when taken to high alti7qmjbsv- p j zcv,rc7t8p+51q tude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–48pfo2; fug(8e/ 1 4johv mosf,a). How could you eso h,jp/o84fouvfg;s 12e(fa m timate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan onlk g x ;+p,w9ds*jfw1evy if you shake the pan at kw f +vpg*1s ,ed9wxj;a certain frequency?

Give several everyda+h ce a5;dliuz7jdqg2y +g7u:y examples of resonance.

Is a rattle in a car ever a resonance phenomenon? Explj96 d ;dqll*2;mky)b vons/ qdain.

Is the frequency of a simple o0eilih-1 9jh9 o :rpmperiodic wave equal to the frequency of its source? Why i 09-ioh:9roehlpj 1mor why not?

Explain the difference between the speed of a transverse wave termh -+b2fjhps2m;u) raveling down a cord and the speed ;-2 sr) uhmpbfmeh+j 2of a tiny piece of the cord.

Why do the strings used for the lowest52c o agc 9xypwm2)s8 f4sm.gv-frequency notes on a piano normally have wire wrapped around tsyg c )w9vc8mmxf22asop5.4g hem?

What kind of waves do you think will travel down a horizontal ) ,l xv.h-vpzbx,rtb4metal rod if you strike its end (a) vertically from above and (b) hp,x ) x4-vt bv,hr.zlborizontally parallel to its length?

Since the density of au s2d93ll2o zoq+l ;zmir decreases with an increase in temperature, but the bulk modulus B is nearly independent of temperature, 2omu+l;ozd 9 lsz3q2lhow would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in lrzfqlboi )3-84)xm 6 7 uiddi2wpm u)amplitude as they travel awaymwu-)) m4)ldulirob86ip 7q dz ixf 23 from the source.

Two linear waves have the sagwqodo k+9oq) c9wty/az5; g8 me amplitude and speed, and otherwise are identical, except one has t yw9 o/5 cq8)k9; woogq+gadzhalf the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the qmvw/j)6og*myllg g* /s:o(cdu)* ve boundary between two sections of cord as in Fig. 11–33, the frequency does not m)l l/mge osc*w gvyjd*(qu*g o /:v)6change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there anyu:oc8.1 bm bs lm c;n4jn;66 ,cmdeyqecr6)ae places you could touch it with a knife blade without disturbing the m.ne4c ;a6b 6jcscub1ocmq yr em)l,;de:68 n motion?

When a standing wave exists on a string, jdm96x)h o0ji the vibrations of incident and reflected wavesjix djm96 0o)h cancel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one placeng(mfkuk uq56c -g/jb( 8h5rj to another, how might we determine whether the energy was being carried by rqj5-g fnhjkbm (8(c5 /gku6uparticles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the totxyjs2/7(oi*fuvz* dt:kh )ze al distance it travels in o)ft2jxys heku7zd : *i/zo(v* ne period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but is 85 cm ld)oy.(r /dak hong .kh/y)ro add(when a 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 compdw4q*j o vzi 04gri.uzxn*s0 )0g4vuxress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will s04rq04wdx u 0.gnvjuizv)gi*oz x4 * be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.udy p* 6c2w4pb7-kg fish hangs from it. (a) What is 2 dp*cwyp4ub6the spring stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates witt rkkjf. g); :l4xtv.kh a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs from 4t;g:ltvkk ..k xr)fjit?    Hz

Construct a Table indic icpd+h/4 ai;fating the position x of the mass in Fig. 11–2 at times t = 0,t = d/; pai f4ich+$\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 spidji h g/tn 8;/hmb3oq,ger’s web. The web vibrates predominately with a fi/ ,hhtgg ;qbo8j3n/mrequency 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 withoe/ rfiwm c-m+h:x+;7* m9 ujzdm.h ub a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency-+ mdfh.r+7co /*z ;b ejumu:iwh m9mx is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrat6y h;v1s2 ,apdmuq 2usq z/1raes 3.0 times per second with an amplitude o smuq1 z/6duq2vsah;pya 2r1 ,f 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 4 8 gpk9 .:fc;jbqzuut3z0vjv speed of a SHO half the maximum value?pjuvz4 z0.jtucbq9:fg 3k;v8 $\approx$    A

A mass attached to the end of a spring is stretcbon ti d xhlg,58q22-nhed 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. .vod+( li tf;+0i8vd duxokr8If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilirl.td08i;xv(od v u+ k8 fi+odbrium position again?    s

  An object with mass 3.0 kg is attached to a spring with sprzn ky0uck6zy:l ;ma ;,-d7z tring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from ymk n7,;6kr;czzd:tzu-y 0alits 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 compzllewr) ht53/3*6uu5uuusem/xg h n: ress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what se hrnu g* xu3wsu t/ml5 u:)u3hle56/zpeed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attacheds ya6yjg(z f7, to one end of a spring; the other end is fixed to a wall. 3.0 J 7,j6 ayzs g(yfof work is required to compress the spring 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 equation x = 0.45cos6.4t where x isevi2 s0cro fxf444nqy dcj /1- in meters xsd1ijecf nr /2qvo0- 44cfy4and 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 SHO half KE andnt9n )*7lhd vativ 2q9 half PE?9aq dv)vihtl9nn2 t* 7 ±    A

  If one vibration has 7.0 times the energy of a second, but their frequencies1b1ijs wzq4, j and masses are the same, whjw1is, 4zb qj1at is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillatxryem-0hu ;;1ukf5 c a3md0h res from a vertically hanging light spring once every 0.65 s;afmh01;cud me y5r3ux0- krh.
(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 su;gj 5syecc5zug 5:qu2 pported by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibration?5 uqu5;:cce g52gszyj

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where5rjog7o p+/h5 q ) eq/-8hu6rwrdjoz w x is in meters and t is in seconds. Deteq7rhopqr5e+ /w-uz jgdhw / ro8 5jo)6rmine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and B. For ead s79*gse- -nds* xttmch, 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 hrx.2w 2kvi9w q(;e7num:pbzof a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Determ.p2ekh2r 7vx;wz :imw(9u qnb ine
(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 withfhs31e wt*7t o spring stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. Th hto71ts 3fwe*e 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 spring stiffness constak1q37b7luent y566do :q (km:dmxlnr nts $k_1$ 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-kus9b2 qc.syr .:k*xpc g block attached to a fixed horizontal spring whose spring stiffness yx9ssub :c *..qk cp2rconstant 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 bridey+z;p3f4(3wk1jzvj 3 nfqsdge. After reaching his lowest point, he oscillates fyze31dn ps 4z( ;3wq3fvkjj+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. 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 vl v or;n0dbd9+ibrations in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swing bnuyiyne) *95 per second? (That is, one complete vibr nby)9u*5niye ation takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What i v npmavzr:1(,nen6ct66 7xcxs its period on Mars, where the acceleration of gravity is about 0.37 that on Eart6v7 ctn6rx: (n1m6napvz,x ce h?    s

  What is the period of a simple pendr(ls f.yb+:r6 hqmsv 1ulum 80 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 has a t/e6dqb*ct( mm0+l qgmass of 365 gramq0 m qtdb(+e*6tcl/gms, 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 lj of q9 (j;pbio,7jg.a2lr2f jength of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pend glj.fpj ,oi22q;ja(9 7jrbfo ulum? shortened by    mm.

Derive a formula for the maximkzvz7x9klbunsg l;;7ig( u-0 um speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequqr3)uybog/2 w,, h tknency of 2.5 Hz. At it is released from rest starting at an angle obg uq,nko2,/y 3 )twrhf 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 hi35ingl0u)xu r s*gu r i xemg+,29oxx6hy(pc1s anchored boat every 3.0 s. He measures the distance between two crests to be9)m1peluy,25n ioixg 6g uscg rxx*hr(x+3 u 0 6.5 m. 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:y2d -8jytfl, ypo lev-yl *w, m/s How far apart are the wave cresf o8dply yv:ylle,,j2-* t w-yts (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 16 htf0/l8w+7octvi+ zca uj43v 00 kHz (kilohertz) and travel with a speed ofa0vwc/vtj f c+48u 7 tozli3h+ $ 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 loc;2jv 6chrg -cj0nxs: ngitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have thxds *edc/9ks 8e 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 wckd*/ xdes8s 9hat factor?   

  A cord of mass 0.65 kg is stretched between two supports 25cmo,eq8gs 7(1 gyl dv8 m apart. If the tension in the cord is 150 N, how long will it take a pulse to trave75d8o(meys1q l vcgg,l from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable 2py;76vna+w rhcm pi mf 2+6dzof length 620 m and diameter 1.5 cm. Asa 6y ;d26pm+ +2f rpmnw7zvhci the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the surfmb vb*z+w: nvdg *6ji*3ff/l1vo km9kace of the sea. He hears the echo of the wave reflected from the ocean 3v*b: idk1g bn6ojw v k9ml*+vmz*f/ffloor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds,n*h8om4(v;uemg qt*e a7.gwmnit:s : and this difference heg sm :;o8.mg4h*un:miaen e(t7vqwt * lps in 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-produce:1ptby(c ec/ qd surface wave 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/ te:bpcc(1qy the acceleration a>g]    m

  What is the ratio of (a) the inznw-re3a8 ) matensities, and (b) the amplitudes, of an earthquake P wave pasane m8)raw-3zsing through the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passi9x yoj f(0c(dqng through the Earth is measured to be 9 cdxyjqof(0($ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency travelbgrjr; n. rd(z)3k pk; through the same portion of the Earth, but one is carrying twice the enerr3;k;(k.zg rdbrnjp ) gy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched strizp3 x+rvd3cpjaz60gkp .+ x z3-w vw0tng have the same frequency, but one transports thzrp6pg+j 3 3.cd-ax vp+0vzzwt0wkx3 ree times 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 move upzk206ls7 exw lbie ;mj *f+1qt 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.lt +s60k * jiezx;lwm1bq2e f75 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig.csgvl- zh8z(uv5z0 o8- x8lh qa2grzymim .45 11–52 are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch xlzr88qh -oy aumis(4lz 5- z2vc 8vm zgh5.g0the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamentck/)5pyh mzg ks/3hu9al frequency, what are the frequencies of the firstu //mghkkhscyzp3 59) four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingere3-by q;liit1jd. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the s3 1q-y;l jbtiitring vibrates as a standing wave.)    Hz

  A particular string resonates;pk/(ls 8l /rx3;hhrmqdhx0 s in four loops at a frequency of 280 Hz. Name at least three other frequencies at which it qr380hr;hhp l; s lk/ xx(smd/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 freq a(+(t w *(t4eehjf8jjamz bb:me8(heix9o z +uency of standing waves is 475 Hz, how(fe j xz wzj9 bthe8:+aj(*a(him8oebet m+4( far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz anw6w*1h 8(qkjt gr wcx1d 350 Hz, what is the frequency of thewwj1 w81xh k tcr6q*g( fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 xgey5t q1r8s7lcm2(eygt j4 0g. The distance from the bridge to the tl8t0r eg yqg514m(e7c2 jys xsupport post is L = 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 str nl lw:fmef29(awr..qing is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequencies m2(w9rw:.leffla nq. are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed txa -daud+fg95v 7t )wvo vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what pewx5t +va va)-9d 7dgfurcent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a*aoyx h5 ec27i small-amplitude mechanical 60-Hz vibrator. The string’s mas2 yc eia5hxo7*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 maza2wh8wr qrlet.i1+pmu (99v y be adjusted by moving the pulley. Ifhma(8pir v+w9r w2qz9lte1 u . the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub ab)jkty/de.2 at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wa)ea/ ykt.b2 djve in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave trab0iowx 2h+8 1jz3ezohveling at k.0 km/s strikes a boundary within the Earth between two kinds of material. If ize h1xzo3j0woihb2 +8t approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velo7)u.klr fs*b(ku6 rezcity changes from 2.8 m/s to 2.1 m/s If the incident wave crests makezk )u*u.rlkr6b7(s f e a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling : np-fvk vmg8ptn/:e)9(lp a tin warm air when it hits a layer of cold, dense air. If the sound wave hits the cold air interface at an a:gt 8mn ntapkpe/l-v:9fvp() ngle 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 rr* z( )gxzvj,9dweo)u1bvcq * ock at a 38c)e9 zvdb )w*j* rqv xzug(1o, $^{\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 3:mmg mdl/);yugut 4 k0.5 m in diameter. According to the user’s manual, the dish has to be pointed in the direction of the satellite, but an error of ld;g:yu/)m kmu 3g m4tabout 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 k69k*k ygdt 4lkm and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbor9 kktlgy4k d6*s. 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 spring stiffness constant oftlxcjb;t s+ 0eq/7dmg 2/js 7f 550 kN/m Find ttjfl+b0g2m /scq/e7j 7;dstx he maximum compression of the bumper if the car, 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 i-y ; 7zjb5aocfire net 18 m below, which stretches the n7cjiz;5 oyb-a et 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 sa :.icbw+ho3end of a freely hanging spring. The mass then falls 33 cm before it stopw+i :b 3.oaschs 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 j,q)ud d86eoyx 8z0.mrw am7u(Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of the spring?y6m 8)7euq,dadj8 u wmo0xzr.    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just tgzi 8w x yl.xr5)+ t-rfouoc3:he right pace of about 1 step per second, the coffee sloshes more and more until eventually it uox5 .zgi: r-f8l)t+3 ywrxc ostarts 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 thek :xeo6h5; zngaod ;o7 center of a 33-rpm phonograph record have a da n57ezohg 6o x;:ko;wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates accordinj b5/ak*toa03hy -n jwg to the equation x=0.650cos7.40t where x is in meters and t in second/*ba-wo 5han 0tyjj3k 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 wi(.ll :w grvxmg1bew c l0w-*;pth frequency f. What is its frequency if it accelerates1mg:rwcwl -xw *0b peg(vl;.l at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on td5d- ok16m(t rcefa, a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When hat56de-1( mtrcf,k d oe steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tun3d3vgz ;kc g)ied to play at 392 Hz (G) and 440 Hz (Ag3 vic3dkz;)g ).
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stretched two-part co46r z.rixr+7 f*ytajprd of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequejr4 y *fzxrr +a.67ptincy 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 *ubnc:gdil5x7v9qhtlt8 b -0Hz, and the tip of each prong moves 1.8 mm tol-u *7 tnqc8x95ghdb:tvlb i0 either side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of 0vlr l (y,8xeyfrequency 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 (Fy ( vlye0l,x8rig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is q-uqi4q3 y ce65fc:caattached 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 qqey-cc ca4536fuq: i other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way 8gi* wtz;)a439( nopxgih tdpswing takes 184 g wt;dap9oh3x(t*nzii pg).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 oz+ 7-lhmbef+zaux9o9scillate in the vertical direction or can swing as a p+mxezuhl9a9z 7 o+- fbendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched under a tension oflu)lr w5 4eulg p)(lj7(mx.fb 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. llr(4lfg)w 7b5upm ). luejx (Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with s x(a-l9kvl/wf pring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will vllxf9ka(- /w allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-t(*)j8ye)y suhki:h lkg 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 cabuy8() ylksje:)*ht ihle. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which also gives26s-iq g og9zh the dimensions of the block). You push it q sg-g6z2hi9o 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 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