Give some examples of everyday vibrating objects. Which exhibit y1vr k g8w ,5:yj91va3uz/mnjh -zclk SHM, at least approxiv5- y1rw:khc v/ gjzaklu3 9zy ,8jmn1mately?

Is the acceleration of a simple harmonic oscillator ever zero? If so9zaub 6u98*fv8mi zn b, where?

Explain why the motion of a piston s/if7f90e.src rwpl * in an automobile engine is approximately simple r 7si s*.l0pw9cf r/efharmonic.

Real springs have mass. Will the true period and frequency be larger or smal3tskwy h7as3 jj( +n:aler than given by the equations for a mass oscillating on the end jtss k+hna3:w3(aj y7of an idealized massless spring? Explain.

How could you double the maximumqk*g 1n zie agw1)/,pg speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scqs *xv 5t nssoh).j9c9ale, and then is released. Describe the scale readosq9 jc*.)s5h9nt vsxing as a function of time.

If a pendulum clock is accurate at sea level, widd+:*9xfd hb pfnps1 *ll it gain or lose time when taken to hibs+1dh p p:ffd*dnx9* gh altitude? Why?

A tire swing hanginguh/p,m,jw eca7;62:o l( p1l jpdbqmu from a branch reaches nearly to the ground (Fig. 11–48). How could you estimate tpb(q,u:dm l o2phw7mj c/l;j61 ,au ephe height of the branch using only a stopwatch?

Why can you make water s) bwj3bh x:75f7 m0lx3l r2scvoonim4losh back and forth in a pan only if you shake the pan at a certain frequmv:l7bl0cxsh4fj3 oi3 obr72nxw 5 )mency?

Give several everyday exampp2 p1fzkfz)tl 6f 26dfles of resonance.

Is a rattle in a car ever a resonai fak- yd g)8 b)x1cn1bs43g (gahy7zwnce phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of its c.y4 zyn9 vlz8il wi.e;+y f7bsource? Why or why n fy9l;n.ze8 +ybc4z7wyi.vi lot?

Explain the difference between the speed of a transverse wave traveling down wr8kj:e( v;r2wggx 2qa cord and the speed of a tgq(;:xv2w8k gwre j2r iny piece of the cord.

Why do the strings used for the lowest-4g q ,.*bncg3u kxzn7ffrequency notes on a piano normally have wire wrapped aro7gngbzun3 4x fk.,c*qund them?

What kind of waves do you think will travel dorgx,e. ib7v p0wn a horizontal metal rod if you stp.7gi e0 r,xbvrike its end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature, but th+g u2w33 t *ggg6vyy idkcd(a7e bulk modulus B ta *iyu(gwvcd62 7d3ggg+3k yis nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves dec2ayn+lc owt /7rease in amplitude as they travel away fromy+ 7on w2l/tac the source.

Two linear waves have the sa )nwtzb3(x6 l 8r5sfry p6i9:ioniuy;me amplitude and speed, and otherwise are identical, except one has half the wavelength of the other. Which trur rbw5fox 9z 6; l8nyyns6()ti3ip :iansmits more energy? By what factor?

When a sinusoidal wave crosses the boundaryy2/fpb 9cv1zc between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Expla2/cpy9fc1 bzv in why.

If a string is vibrating i9mcam ho ;fx; 1z(ew4xn three segments, are there any places you could touch it with a knife blade wi( 4mwah9 1 ofcmz;xxe;thout disturbing the motion?

When a standing wave exists on a string,9mwk7;hwsv5 .unp2 tt the vibrations of incident and reflected waves cancel at the nodes. Does this 2;tws.5vnku9 tw7m hp mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to another, e o62n*tl8xwu how might we determine whetherto6 2x e8uln*w the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what idgfsa :9r2fev s30*has the total distance it travels in one peg9:0a dvar *eff hss23riod?    m

  An elastic cord is 65 cm long when a weight of x27b;tn2s 2c) t .gpju+bfoau 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 ofpbacj +t2nf;b ug22s.x7)tou this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver gets i-k 2c rdiitjp -)uf9y0nto the driv-iji02 cydfp-9r u)tker’s seat. If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a6twj.ff;(uwa 2.7-kg fish hangs from it. (a) What is the spring f6uawt wj(;f. 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 with a frequency of 3.0 Hz when a mass of 0.60 kg iodn;t7c qe+w3q5j 17qg,vd y+5h in*tlo/yzfs hung from it. What is3vyt g/ct7 5 ejh++fonqz57qld,;n dy o*w1qi its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the positjg7sbj9 hnmn .*;9agbrf /cv m2/px,nion x of the mass in Fig. 11–2 at times t = 02xjmashcnpb*mvfj.9/ nrb, n79 g/ ;g,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 spider’s web. The wi;,3lx/mg rrv,zuk * roj0;dzeb vibrates predominately g z,*jox0rvzu r; kr,/il;m3 dwith a frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequ*d p-)z zvm4gkency of 0.88 Hz. When an additional 68p-g) *4zz kvmd0-g mass is added to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a sprin)jbsn q/r)wa p7q0) nqr3aok 8g vibrates 3.0 times per second with an amplitude of 0.13 m. Determine)ojqp /wa7r)bk8n0a3 )s nrq q
(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 a SHO;c(8 wu xe,oabo5. gs)jfe+tu)xc4fl half the maximum valce5lgosca+uxu; w)4ef to. )j 8(b fx,ue?$\approx$    A

A mass attached to the end of a spring is stretche i 30m3se)s42kjg,roegce3bnd 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 spring is st :u 2xpg hj2lt)5.uxbtretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium position again?5uht)2.:lub pgx xt2j    s

  An object with mass 3.0 kg is attached to a spring with (k0zwy gi: xa0f/zuv4 spring stiffness constant k = 280 N/m and is executing simpl f: x(k 0y/awi4v0zgzue 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 spring of a toy po( s2 10 eshffz1n4mr5lo*uf zt0ewm* cpgun 0.200 m to “load” a 0.180-kg ball. With what spf e4f 0(t nw*zh*mfs0c5er sm12ul1ozeed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attauzfv 5z 2e)b ehl)gjd73tj8c, ched to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by cbz8l,)hv2je5jt )uzedg f73 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 whevw 8pql ab7108cr dw..ujpuj 9re x is in meters and t.bjjl9awvu8w 871purp.qc d0 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 bs3* y1acbefw no2z(ty031vx s(h. icand half PE? e(.whviaxs2cn1 0y* 1tbyz3cf s3b( o ±    A

  If one vibration has;,-gxtu w wb;c 7.0 times the energy of a second, but their frequencies and masses are the same, what is the ratio of tux;c b, ;-tgwwheir amplitudes?   

  A 2.00-kg pumpkin oscillate +7bi/u o+bennhf o/o(jrzo*)s from a vertically hanging light spring once every 0.65 s. ub) e/o+fn b+(/oj7 ioozr*nh
(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 verticaljsrgy5hl4/qr)p+d1d1- tgy1ew hku , springs, each with spring stiffness constantd-y/dej g1rw4r1p51+g s q,uth )hkly k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x f)xef+*. dp 32ae84gd yktb ol= 0.38sin6.5t where x is in meters and t is in seconds. Determine dbef2klxpy3 *fgt 8o+da .e)4
(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 examplee snj,xqk b+)t7ub+o 7s 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 spring (k = 124 N/m) is strujey9vol)9z9w3 - unku k5,t huck by zkyu9e u)jnu-o9 9v ,lw k5h3ta 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 stiffness constant 305 N/m vibrates b7r1xax dx7zg5t+1a x with an amplitude of 28.0 cm when 0.260 kg aa gtdx771x15br xz+xhangs from it. The 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 stifff-d/si .a8 z zx6h.sogness 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 fixed q,er -ywch0xpo:ua3*z b/tq0 horizontal spring whoseqh : y*3x-r,0uowpz/tacbqe 0 spring 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 r *nonm,os7hi8flgypi1 4v3wca,bj)7 +okg y* eaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes tomf3 o, g g*4 nin8syij yl) wobak7c*1v+o7,ph 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 vibrations in exactly 60 s. Whhc gm;d( vtw n9ztc),wqi*+(pat is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly : ski ,b)qs7rlone swing per secondrs)7 ib:slq, k? (That is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, whefb j4o 6*kjs::,5p( psdy xjt:wa4mq dre the acceleration of gravp j*jsd joy6:m :d,4x : a5kbf4s(qpwtity is about 0.37 that on Earth?    s

  What is the period of a 4bu8181c7mbjleaz c (bt e 8ytsimple pendulum 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, tk2 p5y)2w(a kzll(:b(kbdiw l he pendulum bob has a mass of 365 grams, and it is released( (zkblp)l(5 w2 wikk2bya: ld 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 lengthnf bdto5/pei c*msxs/ 2a2 */c of 0.9930 m. If the clock loses half a minute per day, how nfm 2 o*2*c scsdte xb/ap5i//should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximtx-k 0 x(n;;ia p5i oc17,zpiw yc1jeium 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 it is ru pc7v;8bs lsq(* gp-2s6s ureeleased from rest starting at an angle of 15 g;s86u (slsq*ep psc 7b v-2ru$^{\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 anqkr, p(05sm2hlbh,k z+2qt8u (y 0qvlgsbk;e chored boat every 3.0 s. He measures th vu qryqb,b;5h2l(pq0t ekzsksm82h0lg , (k+e distance between 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 with a s7j o+ x:(hq nv60khvosih ,qc+peed of 343 m/s How far apa hn k+:cq h0h,ovxsvq+6(oj i7rt are the wave crests (compressions)?    m

  (a) AM radio signals have fr -bm:qq 9+cnmsl*)eyu 6bad5requencies between 550 kHz and 1600 kHz (kilohertz) and travellm*d)my9q- 6a u:s+ rbq cb5ne with a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinalp f.vdw )van04 waves 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 .x(r:t+ rew2cu2x sezuaj :i1 dense as the other. In which rod will the speed of longitudinal waves be greater, and by what factswaru(j z+:eex1 c2:.iux2rtor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m yb2 w5no79agfa6ly p2 apart. If the tension in the cord is 150 N, how long willfwoyal2p a79nyb g56 2 it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steewq8 +e**d(uk0w nff dtq05ughl 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 a wave pulse along the cable. It is observed d0*qfuf+ unw et0d5gh8q*w k( 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 hak*j d2lvt-n7: fd )isears the echo of the wave reflected from the ocean floor :tj*2ns7)kl-av didf 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 l5lcwa wln6 yc.s)p*,ql0-a m speeds, and this difference helps in locating the earthquake cm*lcawy-ll 06a.s5 nqw,p) l“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 sur/9 6aejrhtqa4 p,5w itface 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 neede q,46te5twh airja /9pd 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 amplitudes, of an e .oa;fuint 7+hg)vl- barthquake P wave passing through the Earth and detected at t f+tag7 ;)hvu b.-ilonwo points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured ttdl 7k x-9mc, qw1g6rso be w,1dr9c q67tlm-sg kx$ 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 travel through the same portion oy)5tbx9jy3 myf the Earth, but one is carrying twice the energy. What is the ratio xtyb)3yym59j of the amplitudes of the two waves?   

  Two waves traveling along a stretched u ::b0 vn tnv5(mtkf (ep i-94tfqk:tistring have the same frequency, but one transports three times the power of th nft:bnkv5iki et 4 tp::q(t9 -m(fu0ve other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface ofpc)lp 1r*g-b) hjth1k 7(c bko a pond is observed to move up and down a total vertical distance of 6.0 cm, from the lowest to thekr phjpbg) cck1tlo(7-b1*h) highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 1 2o (eu6qm1pwo1–52 are moving toward each other. (a) Sketch the shape oqe2pw mu1o (6of the string at the moment they directly 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 vibrates at 440 Hz as its fundamental frequency, what are th;5sx zy4.f)ompan i(f e frequencies of the first fou;) i(sy4ffa n .mozxp5r harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when un +zu4hw0ke14a(npehm r6q lc0fingered. 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 string vibrates as a standing wave.) qca 4+zew06ke410u(nh pl rmh   Hz

  A particular string resonates in four loops at a frequency of 280 Hz. N g -v,o7vm/e9lbl.rgeame at least three other frequencies at which it will resoneo,lmgl br9v./g7 ve-ate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If ty (1cm(-u feqahe frequency of standing waves is 475 Hz, how 1 q-a(u(eyf cmfar apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 2 h u ka)asq5;agb8./ba80 Hz and 350 Hz, what is the frequu a sg;hbk .5q/8)baaaency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of (u p23ufv r2gt2*nyhq 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.f pquyg2*tv2(3r 2nuh What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is m-b6 -p;1j 6gzzc e7mppz(j lnmeasured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the thre z g16cj;6nplbpzz(7p em mj--e frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it iq nz1*,ewxrh+s measured to vibr* +znx rh,qe1wate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitr;;,.ewav . xqiladq(ude mechanical 60-Hz vibrator. Thwrqel.av; a.,(;qx d ie string’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 string may be adjustedhx+ bdb3smxm /s*-:, -xwy/b sxfb9tp by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L betweehdxfb/*bxb+,smt9s3 msbyw x/ x- :p- n 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the right freque frjmi7v8q t)cl4w8/uncy, the water alternately rises and falls at each end, rema cumi4j 88w f7)qtr/lvining 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 ;rag :nu,8 b .7dru6twsh uix31 3muyathe Earth between ;tb .un 8sw7y :mrr6ga3x1idu3u,u ah two kinds 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 g 6u1qnfe; p/zc m*2rfwmfe:g-n807i n3 uzwd“shelf” where the velocity changes from 2.8 m/s to 2.1 m/s I z :2i6u ncnwzm-f0qn epe/;37w8mfu1*gdg frf the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it-n wo(2db+l aq hits a layer of cold, dense air. If the sound wave hits the cold air interface a d -(2+anlwbqot 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 strikes7:9mi3pkd io qtvf y o)c+dc;9 a boundary between two types of rock at a 3fi7t:vk)9o+cq9id ; yd3 opc m8 $^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m in diameter. According to the user’s manuw qm7 hqh2nk j r8iq-ius*,v35al, the dish has to be p7qn5i h,j3rsivk8mq * 2qu hw-ointed in the direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of waveleng j (kv8:*o0x en0yb f6:ylryjgth 250 km and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea levelyjygv6r:kyl ( be :o*x0 08jfn 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 bumpe93 lp1ak*ygfl r has a spring 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 2.2 m/s (approximately 5 mi/h). [Hint: Use conservlgl3 p9ak1 yf*ation of energy.]    m

  A 65-kg person jumps from a zsqc )sq(m kof7-j4 (pwindow to a fire net 18 m below, which stretches the net 1.1 m. spo-sqqf( c4m(k zj7 )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 hanging spring.1k iq3 u f6.ybrmnxp3; The mass then falls 33 cm before it stops and begins to rise. What is the frequency of the oscilla3uqnr p;.ym 1bx3 fik6tion?    Hz

  A 950-kg car strikes a huge spring at a r cd -hz*)zd4dspeed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the sprd -crz4hd) d*zing stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at j3)uoxr qvxgynr 6nh.n/8 cf(0ust the right pace of about 1 step per second, the coffee sloshes more and more until eventually it startsxr )ong.0qynrx8 /u6 chfv3 n( 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 8l hge)pyq-s*) d txk:center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sound emitted:sl)tykq-dxp) *e 8hg ?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x is a.eiw02 ff0fl in meters and t in seconl f2.00fwief ads. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. What is its frequjy*q)hypa;k* dt4 c 2dency if it accelerates at 0.50g (a) )*yhdk2c q dj* t;p4yaupward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on t mi2jzv2rihsty3g(7 m7oz. r)he raft, it sinks 4.0 cm deeper into the water. When 7syvro7 i(ztr h 3j2)gmmi z.2he 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 instru(cpi/2r(rxe ab9 6edy ment are tuned to play at 392 Hz (G) and 440 Hz (Ae 2/6rpxb riye9(adc().
(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 tr8av mj8xw29csp :4has aveling down the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is 9j8a:pxwa 8 csm2s4hvthe same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at ady5i*gb(o/yrdm+ vsn fch ..fch(-2a frequency of 264 Hz, and the tip of each prong moves 1.8 mm to either side of centery .f+va2 rib g/(dc* chy5dnh.mfo- (s. 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 mou,ci,2vy/om i783q d7 lck fqrtion of frequency 1.5 cycles per second. What is the maximum amplitude with whii/vc7ym 3 ,ikl qdf,u8r2cq o7ch the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to axmcujd z/ 7(5)ip/hbawmqu, xej+7.u ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such(b i,jqm mju .h) pe7d a75x/uwc+zu/x a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — eajx-z9z u 8vn,wch one-way swing takes 1.008 z9uwnjz -xv,0 s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertical dir cgkxh -)yx32rection or can swing as a pendulum of small amplitude, but not both at the same time. Whichkxx )2-h r3ycg 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 teea ysu o1emz p 1 e)e/q)elw9 bjg8pt,-4n14dfnsion of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is wpfeo -j,s uge )abty19e) 8nldm / z4e4p1eq1generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a sprine iyxqu58r zx/:3n gl7g with spring stiffness constant k. A penny of masg:nqyu/lxx8r3ei57 z s 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 junkyard. The steeumdhd 8e1)h1l-aa *ypvy60dtl crane cable is 22 m long 8apy6- tyal d1ehh 1*d0uvd)mand 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.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (whi0a+/rr7tuxeq y7 qty9yu i6-qch also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins7ux7/tu9yr 0+-aqqiqy6 eryt 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