Give some examples of everyday oew 0v0m8t9ym vibrating objects. Which exhibit SHM, at least approximatevm y8wm0teo90ly?

Is the acceleration of a simple harmonic oscillator ever zero36h crkvgp-,mo bh;:a? If so, where?

Explain why the motion of dvkgb8g y,9w. a piston in an automobile engine is approximately simple vw, 8bdg9.kyg harmonic.

Real springs have mass. Will the tr68 t jirdco b4cv,6-zque period and frequency be larger or smaller than given by the equations for a mass oscillating on the eqzb c-,68i otr 4djvc6nd of an idealized massless spring? Explain.

How could you double the maximum speet, *u ra6u ,(qn8/fjelu/ld wtd of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to theidcn2qf:t+;m,m d d8o hook of a vertical spring scale, and then is released. Describe the scale rea2mf+ t,ci d d:;odq8nmding as a function of time.

If a pendulum clock is accurate at sea level, will it gain4tgfd0i5xx w0*gd qj + or lose time when taken to high altitudj*gd4qw + i0df0g5 xtxe? Why?

A tire swing hanging from a branch reach(otu*j a:fy; gpm7fi3g50 ntqes nearly to the ground (Fig. 11–48). How could you estimate the height of the branch using only a stopwatgttpm073y( fgojn; q: if*5uach?

Why can you make water slosh back and forth in a pan only if you shake the p1,1kj naw0 vpvan at a certain frequenc,w v n0p1vjka1y?

Give several everydayagm)bb0f p kf6d4-f 58gn*bh4r k1 qv/iub/uo examples of resonance.

Is a rattle in a car ever a resonanc :;ev1nck0 scl 4namgdv k a8fd.*5un2e phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequencvij);f 7 vkbn5;gwdz7(o w 7oky of its source? Why or why77kkg7 o ) if;wbwvv;jno5(d z not?

Explain the difference between thl7z, wh2y.mt;z(oq uee speed of a transverse wave traveling down a cord and the speed of a tiny piece of oy(t,quhe.7l zm2 wz;the cord.

Why do the strings used for the lowest-fre6)x yk*) 4ynicr njw*aquency notes on a piano normally have wire wrapped arojy wca *6nxk)n*i4ry )und them?

What kind of waves do you think wilj7y *g td3qnl9l travel down a horizontal metal rod if you strike its end (a) vertically from 9q nt3*g7yj ldabove and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature, but ngemas wx/+,x:;gct *the bulk modulus B is nearly independent of temperature, how would you expect the speed of sou ;:/ax+*m t gxnwgs,ecnd waves in air to vary with temperature?

Give two reasons why circular water waves decrease ijweb ;3lqd4u9l m/vs(cvws -bh3l *7fn amplitude as they travel away fr4l3( vh7wfvdbj m9 ebs*q/ 3su-wc;llom the source.

Two linear waves have t(yg k, ,4emtlcaj-7 dahe same amplitude and speed, and otherwise are identical, except one has half the wavelength of the other. Which tranta,e ( jm,a-4cld gy7ksmits more energy? By what factor?

When a sinusoidal wa dqf886oj,uy/0d ,lt4p9 :kwea ibdxqve crosses the boundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change)ptjo q4a8x/qwku9yd, f d6d8el0:ib,. Explain why.

If a string is vibrating in tgix3dxq*s k/3f .pd5vhree segments, are there any places you could touch it .p3x5 ki/ vfdgqsd*x3with a knife blade without disturbing the motion?

When a standing wave exists on a stringjk rd5n9q u-5u, the vibrations of incident and reflected waves cancel at the nodes. Does this mean tha5 rjdu -95uknqt energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to another, hou-omkcmznyy: + : y(naul j54)w might we determine whether the energy was being carried by particlesc+:au)l(: kzu-j 4mnyoy yn5m (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total dghq6ye gjep 0 6,do(+cf/*gdsistance it travels in one o 6ycfj hp(, *g+gq0ede/g 6sdperiod?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but is 85f*6u7non b3db cm long when a weight of 180 N hangs from it. What is the n7*nbbdf6u 3o“spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver gets into r(y hkp 1h 8xv3z.1n0.,bjfr/bt ncx lthe driver’s seat. If the car goes over a bump, what will be rl py n01.t /hbjxrvhknc1x .fbz8(,3the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm whenm cg6k 1d4swru;1 s;6dqy yc2e a 2.7-kg fish hangs from it. (a) What is the spring stiffness consta1; ycc6 s rqygme 4u6sdw2k;d1nt $\approx$    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 jw hjrt i06, zncyqy:5b9is:1 is hung from wcin:05qjr z s1yyj,96hitb: it. 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. 11–2itg*x yd0o7k8 u07 7jxpwe7 el at times t = 0,t g7 dwiexkp l0e7y *u8x0o77jt = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web. The web vibrkl89eqy, *3uhu -s qgjates predominately with u u3, he9l8*k-jy qgqsa 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 frequency of 0.88 Hz. Whey bky ua; qn2a)12 rcj*27ondnn an additional 680-g mass is added to m, the frequency is 0.60 Hz. Wh7r2dyk nnon1y2q * 2ac;ju)baat is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibr ka v.o3nmk 5xhi+hz43ates 3.0 times per second with an amplitude of 0.13 m. zkahhm 5n+ vx.o3i43kDetermine
(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* ef+wi w 4c:era9c:cgy/gwofqf( k speed of a SHO half the maximum value+ec y:gc4ffi9(/g we4 wr w+caq :fko*?$\approx$    A

A mass attached to the en 9* 1*jsoy+f nj6thdrad of a spring 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 keg3x.4hao u*spring 0.315 m. If the spring is stretched an additional .x euo4k h*ag30.130 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attacrale;x.z 0 o.yhed to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 me.zyar xo0. l;/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): c0k yjwk vgg7xm(c6 compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave tc(g 7vk0)kjwg:cymx 6 he gun?    m/s

  A mass sitting on a horizontal, fridr5exx b55yc1g jx*b5(j xk0mctionless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration1bk(5x dxr0ex5 5yx jcgbm*j5 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 yhjq*gv;fhs 5aoy9 w05 1h;gn according to the equation x = 0.45cos6.4t where x is in meters and t is in seconds. Determine fna; 9v; hy01ghq 5 o5jwhygs*
(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 u p .ttlgypm.x.*k nu:k./e;zenergy of a SHO half KE and half PE? yuu.plx ez k;.np. :.gtk/*tm ±    A

  If one vibration has 7.0 tim )3ma1,/pshhvbzqp) s es the energy of a second, but their frequencies and masses are the same, what ipb qs1 z, /)s3pamh)hvs the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring onc /w9xhr /5uzxl* ivk9te every 0.ihw9r9/z/ kx vt *lx5u65 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 b ftjm24c9jydos12 9 bxy3 /vatwo identical parallel vertical springs, each with spring stiffness constant k (Fig. 2 jfdb 93/ya1t4so2b9 m yxjvc11–49). What will be the frequency of vibration?

  A 300-g mass vibrates v7akhg1u 2q gkx 5o)bko,z 2b;d:1fi saccording to the equation x = 0.38sin6.5t where x is in meters and t is in second,b5gf)dv21si ooah;12: qk kkxb z7 gus. 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 A and B. Foru) xk2z)lhf9 40qjft r 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 re be 9m3-e:iobcst on the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gimo-: iecb 9e3bves 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 constant7 wwgajuzui*v -s -h3. 2arav2 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass pa- wrui-j*ws7v2haz2ug av.a 3 sses 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 connected1op23as4ap mw gnz2qf+ ym5b; to two springs, with 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 azojgh :)uc91 ; gayqgb3z7ad 9 0.600-kg block attached to a fixed horizontal spring whose spring ag) 9zgy19qoaj;: h 7cubzd g3stiffness 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. Abd /qeu)ga)0u do+ gg3fter reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstreoq/d ggau3ub)+)gd 0etched 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. ti5a+ j+,. h-mktm xfn ,et,iaWhat is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly ontl,u)(y kr n+js5hj29pja(fs e swing per second? (That is, one)k(ujsf+( 2sr jyplta j95, hn 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, wh6*zc txsxv5d -ere the xv cx6*s 5zd-tacceleration of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pend q3pc9tvxoahv,now+6 9hi n 6*ulum 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 pendulac5x8ld u s9arm3+f8ewj+6a g um bob has a mass of 365 gramswg 9ar+l xcfaemjusd6a8 83+ 5, 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 length of 0.9930 m.+lpf4tu.inh;;y. sxzhz2v s7 If the clock loses half a minute per day, how should you adjust the length of the pendulum? shortenedh7..stp z;v h+4 yzu2ixlfs n; by    mm.

Derive a formula for the maximu 6yj4ho 2aytsz9 eq0+qm 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 oscil9cm/:;9 jdlfxuizc6m pn+zw +lates at a frequency of 2.5 Hz. At it is released from restcpxmjnc +zmd+w:;i/zu l9 f96 starting at an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pas;d; h4yq to(z7zu b;gxs the bow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the w;7y4;b xt(gd;huzo qz aves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and tr7yu 6;g d+syzravels with a speed of 343 m/s How far apart aysy+;u g6 rzd7re the wave crests (compressions)?    m

  (a) AM radio signals have fren;j 8tt.hmz2 zrde jxf18 4r3pquencies between 550 kHz and 1600 kHz (kilohertz) and travel wixtzfetr2j.m 88hj p nd; 43rz1th 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 4:zgej8.k*9gget rs8jyxng : of longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic mo ny*qbkd8 13 0ticf,sedulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, q,f1icbey0 k 8d3* tnsand by what factor?   

  A cord of mass 0.65 kg is strety z6;d8) 5l03,u +fkqevn,cz qmnzm epched between two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travell8zf,ydm, q+;)n z5k nm 3qzupec0v 6e from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of lengtt*g2m.zhouf l3v20n d: sa/m*qlub.o h 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the termi hfl suo:a.z2m3o/l.t*2qu*nm vd0b gnal 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 sijj7/b2:rp m hh9xj a6h nd5mgwm 3i,,tde of his ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0hrpw2tjd95 m ,h3:anjjib gxh m/,6m7 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different spe k4(c.a:t e3j9odu9ia 9zh .amcpdm l+bz3/zheds, and this differencecz 3o94h:aza /9dzb (l9du j.m.c tiahme k+p3 helps 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-produced surface wave can be approximated by a sinusoida7-h jbjhn8at* pa+tp5ljw:hmh87 w -vu *r*bul transverse wave. Assuming a f*jrtlj t7 ujw- w hva8p: hmh5ab -bu78hn*p*+requency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intenou 1 2ql,cxp l5qsx.p0sities, and (b) the amplitudes, of an earthquake Pq1 puqcx5,ll0po s x2. wave passing through the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through tw9f lksb + 6ijv;8wrx0y.zuz1 he Earth is measured to be siv9f+wkr .8l6 zbu0 jy;x zw1$ 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 throz5rus );t 9wikugh the same portion of the Earth, but one i r;iwstk)5uz 9s carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have thewq;; :od cw,0(e blybn same frequency, but one transports three times the power of o(;:nd,blwcb0;e wq ythe other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up anl 0.b: zhajd6b+s- tc,oi 1rz2kkl6lcd down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave bk 2s z 0az6bi locckdh-6l+: rt.,l1jpasses. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) Sketc x h.in1f6 t24zh1wyukh the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later.1ufyxt2 z h i6n.k41wh (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, wvg54r.ueo/ ;wmiwvxu129tb qhat are the frequencies of the vvtxw b1o. 4e; iqg2m5/ur9wufirst four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency will it vi7p)is2( 0ndhq8ik pwfbrate if it is fingered one-thirdwp0 i fh)8nikpd(72qs 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 loopso lj5dbup75b -* hrrc- at a frequency of 280 Hz. Name at least threrbo*5bh-up r7d5l j-c e other frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves ov-- 9 oq70l *u6bh s/f rrp*tokz9knubn a string is 92m/s If the frequency of standing waves is 475 Hz, how far aparq u ufhb - ts9 n/zkpr*v0*97okl-b6ort are two adjacent nodes?   m

  If two successive overtones of a vibrati;a4sg) f -w7a3k ufqu -7kmwbhng string are 280 Hz and 350 Hz, what is the frequency of t;w7)4 gsu3kq-7whf aub- amk fhe fundamental?    Hz

  A guitar string is 90 cm long and7vg*x*t wsx.br6 mry , has a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. Wyb6rwm tr . 7*svx*xg,hat are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is su ;e0,wa/uplfl o.kf8ley ap1ru91)ncpposed 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 frequencilw0.re,9 apcffe1;)y1/n po lk 8ulaues are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, bu;b21-, vpnunojzv fcv/y. l 2dt it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequ-j 2.nbv vuycnl;v/,o d2fz1pency? decreased by    %

  One end of a horizontal string is attached to a small-a8-uzbol(t,az.yl mj 6na ,)w;o9adk cmplitude mechanical 60-Hz vibrator. The stri, nollj (aykaod t6-m8)ac.,;zbu9w zng’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 br8se9as w7 dd mj; ue17)onkk,e adjusted by moving the pulley. If the hangiw17m8ndad9,;srs) u ojke e7k ng 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 at just the right f,8jgp/us g pfwr:9 o.orequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency tou p.,o rf:jopg98 /gsw 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 kxpf,k+ezaov ni8/ 9 8vm/s strikes a boundary within the Earth between two kinds of material. If it ae9nx8f/ao+vizpv k,8pproaches 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 ccf4 9 wmihb/hag)6a7q/-s :x br y0buvelocity changes from 2.8 m/s to 2.1 m/s -bmhw /fac4ay)g/6bsb qu9hxi7 0:c r If the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm aif8:t:r:qz go9h,qg/ rq 1 tztmpy6xo+r when it hits a layer of cold, dense air. If the sound wave hits the cold air interf+tzqtrqy:9gmo8ztg61,h: qrxp /of : ace at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary between two types oe:kl) wj(ja 8xf rock at a 3 aj)ej(w8klx: 8 $^{\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 us4lgo 4)r6igkyu uu- y13z pu4tdhbe 1;er’s manual, the oip1uuu6e;hruk1db4 zy)4y gt34lg - dish has to be pointed 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 wavelength 250 km and velocity 750 km/h travels a66k1::wsuf d5g wkckq cross the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people havs kfk1dkc:wu :5 q6wg6e 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 constanx w)tc1c qk5l3t 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). [Hinlq1xcwtkc 35)t: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which str zckafbh*4pg:thr e /. +zsd+-etches the net 1.1 m. Asssat+ ./hpgh+ e z4f:b-*krczdume 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. The mass tg 93* rt/pvhlyhen falls 33 cm before it stops and begins to rise. What is the frequency of /3l ryvht9g*pthe oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s +l uyql-. 0 qdv5 jyyb+/rdq(m(Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring srdlvyql-d +um0yy( .5q bj+/q tiffness 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 cjqsu(4nfw3tr;upj0j p310 r q+v r(ycm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the spf(rcutjq301jwyu+03p j(rn;vrpq s4eed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center oflf4 4tli6emykms 8(r7 a 33-rpm phonograph record have a wavelength of 1.70 mm. What will b 7lil s8(f4r6mkeymt4e the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x is ina12+y xawdrxyv /g3g. meters and t in se rxx.ga vw3y 1ady+2g/conds. 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 fre( r20vvva/oxequency if it accelerates at 0.50g (a) upward, (evvvo a02r/x   f
(b) downward?    f

  A 220-kg wooden raft floats ona pgp7l-b1 l-pff6qss8k4bb i6.. e fz a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps offgpblek.qsa4 fs6.8z bi-f l -f 6b71pp, 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 arwloq9 ., weq 7fj:tul-e tuned to play at 392 Hz (G) and 440 Hz (A)-q .,9 wu7t:qfoweljl.
(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 cord of Fig. 11–33. +ckv .lv 7bbgj/n*c1tDetermine a formula (a) for v. 1* 7 bkjgnv+cclt/bthe ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and tudy(p 3,cht 4vhe tip of each prong moves 1.8 mm to either side of center. Ch,(pyu 3t4dv calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates wau5q2m5row 6u ith simple 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 a pebble placed there (Fig. 11–56) wiu6a5wr o5m 2uqll not lose contact with the board during the oscillation?

A string can have a “free” end if 0cxal ek2z u 8c4a.7wathat end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed andxuc zw4a 8 72al.a0ekc the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — eac1 jsn :c)e)goemn,up4h one-way swing takes 1.0encmo gn j4u) :s,ep)100 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 osciloy- vtef2/)h7 s 6pxw3tmhb)j late in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical h 3t es)ht7o)p vw2yj xm6/b-foscillations 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 )1eg) wcpl2m,z(ggk dof 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposi kg1d2 egzc )p)l(,wgmte end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring 0 f1bl1se.:crc 4wece with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillatiolre w.b0cf 4 e:cc1se1ns 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 steel crane cable is4bdta :o 6df.n 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cab4bn6dod. :a tfle. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a(5 j lsibrs;.o 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 vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, gb sl(s5.iro; jiven that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz