Give some examples of everyday vibrating objects. Which 1df 2e-olg52-k h e.0oashuqy exhibit SHM, at least approxima5 h-2 lkeay 12odhof0e.q -sugtely?

Is the acceleration of a phf4w(r(6wa1it jl:: 3whq wg simple harmonic oscillator ever zero? If so, where?

Explain why the motion of a pkai-j zr8 bj(st+*h2 kvah l73iston in an automobile engine is approximately simple harmh biklkh(jr v8 t*z3 a27ajs-+onic.

Real springs have mass. Will the true period an3xy61cqhj b o 77lepi)d frequency be larger or smaller than given by the equ lxoe ji16y3qh7p7bc) ations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double1 exuhe n.c,bld8 n0-w the maximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a verticalrz0yf8q ) ke8g spring scale, and then is released. Describe the scale reading as a functi8z )g8kryf0e qon of time.

If a pendulum clock is accuqu z1 w--.)rj c//uiidf .rbayrate at sea level, will it gain or lose time when taken )i ..bcufrw-iz qu/ad-rjy/1to high altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–48). Ho jdp) ooi)fhkl4v20q5 w could you estimate the height of the branch using only a sto25o0dj) kf ) lpqohi4vpwatch?

Why can you make water slosh back and f :u1e3g):h 0mlnjlla z d58xjkorth in a pan only if you shake the pan at a certain freque5ek :)n3amuxdll8hjz gl: 1j0ncy?

Give several everyday exa(-s )e u xq5y8dj6(g;zeeq jlamples of resonance.

Is a rattle in a car cjfzie:* d)3 oha8;ws3 p/bc)ikvb3qever a resonance phenomenon? Explain.

Is the frequency of a va yyb:1 h+8+a nern+)qzx5nngmm38x simple periodic wave equal to the frequency of its source? +n8+ym ey:ma5xvharn) n8q xbnz13g + Why or why not?

Explain the difference between the spe;mihh;jm :wa84f6o( qti w6pj6-fgmyed of a transverse wave traveling down a cord and the speed of a tiny piece of the f( f: ah 4-qm6w;yjj phmmotw8g6i;i6cord.

Why do the strings used for the lowest-*kgb7wqc k1/p lxg*e1frequency notes on a piano normally have wire wrapped ar1 w**b k17qlgx k/pecgound them?

What kind of waves do you think will travel down a horizont3) ptdz.g,fl2mnk:j :zs/n;sthhsv9 al metal rod if you strike its end (a) vertically from above and (b) horizz/ mfh,ps:jns;32:. sn)9ltgtkdvhz ontally parallel to its length?

Since the density of air decreases with an increase in temperature, bk;0tytqg z2 qzvv5ax.:8 g9qout the bulk modulus B is nearly independent of temperature, how woul9g k5a goq:2yq ;08tvzxvtz q.d you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water wv0 uf lmat ppa+-46z5yaves decrease in amplitude as they travel away f4 pp ftl y06a5z-u+mvarom the source.

Two linear waves have the same ampld; )iayguo/0q m* w(awitude and speed, and otherwise are identical, except one has half the wavelength wam*/qo0(;udwa g i y)of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between twdihy1:o,h7m; vxsb/* l6nblp 02jhn ho sections of cord as in Fig. 11–33, the f ydobi;js :b m, p0/l nhhvh12*6nlh7xrequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segmecqf7wc):l v ;fn0bbxsg1p 3o8 nts, are there any places you could touch it wi )3nxc8 qfc ;l :bpf01owv7gbsth a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of ina-amk ozfa9r.k 4r:h son ;(4+. yljjucident and reflected waves cancel at the nodes.az y;r4lrojs9j-+nok.: fk (uam4.ah Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted fr nfdpx:*r+k;lqpawb q 3d+-ml(9av2 fom one place to another, how might we determine whether the enefqn kv -x+dalrd39( qbf :m2ap+p;*lwrgy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m,hzid77mb5bn +zv8+ b h what is the total distance it travels in one perimzdhib77n +85+hvzb bod?    m

  An elastic cord is 65 cm u0t,z2ma ,clwa+0d dblong when a weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this elas0b+,wl au am0dz d,tc2tic cord?    N/m

  The springs of a 1500-kg car comoi *be0 lk5d3cpress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes ov3eck i50o d*lber a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm wh5ck8 ,lez8 7k aobbv-x0h fl1qen a 2.7-kg fish hangs from it. (a) What is th 0zbxflael-k q o,h71k8bvc58 e 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 with a frequency of 3.0 Hz when a mass of 0.60 kg is hu7l-rv/(/ ykf- bv3tdh1m ikuxng from it. Whatkbv3kv -rt d/imy7(/lhf ux-1 is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 1i5i, q1 o2cxer1–2 at times t = 0 51, eqix2oirc,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 i3*swq yral *6q933nl0r cbamnn a spider’s web. The web vibrates predominately with a frequ3*0 canlra bm6 ry9 *n3lswqq3ency 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. When an adff4x2 + xurizdo25;ym wbl* )vditional 680-g mass is add5m ly2;)xi42 ux* dz+forb wfved 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;71+ nfv+vg q0f rttkag vibrates 3.0 times per second with an amplitude of 0.13 m. D+fft q7rg+vktn01 av;etermine
(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 ofnu5)bc b+ocp. a SHO half the maximum valueonc.uc +p)b 5b?$\approx$    A

A mass attached to the e834cd9soft 1v b7yn-loar tbt 9e6b 3end 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 spring 0.315 m. If the spring is mg-b s)d j(g50 nmlfx8stretched an additional 0.130 m and released, how long doslg8b m)dm 5(j0gnf-xes it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring wi*x,ro;ia( f;gow bw/xth spring stiffness constant k = 280 N/m and is executing simple harmonic xoib ;w*w;x(afg,r/o 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 t h,r)dh /:hjmdek z 3nm-6ht+koy popgun 0.200 m to “load” a 0.180-khhn dmh/36 :)jkkhr+ezm,-d tg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one end of aj*p b.h3/pgqygz 4t, 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 wihj y*4a, gqz.gtbpp /3th 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 is uzu0.q a:bg)pin meter :auuz.g)0b pqs and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrs;byezy ;/t4pk.* ii (wcqqc4ium is the energy of a SHO half KE and half PE? ± .ti4 (cy;k; e pbq/z4 qiwsy*c   A

  If one vibration has 7.0 times the energy of a second, but their frequencies aby5mp7pk vzg1 fz23,jnd masses are the same, what ijvyg 7mpf,p32bzkz 51 s the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vjkhp6 4r27n)r c :a8d,aczfqy1i. hirertically hanging light spring once every 0.6qyh8dpki7 r41c , injc.) 6arr a2hfz:5 s.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallel hhe)tbqgcvsj e/el+ -y0)r6 8vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibration6v h csy+g8 tj/er)b)e-el0qh ?

  A 300-g mass vibrates adz*jg pm e:ph3 o lz gp;qt19*yx:i;i;ccording to the equation x = 0.38sin6.5t where x is in meters and t is in sec3*;;i1exz qigph*d ty:l o z;mjgp9: ponds. 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. For each, whgo q*g4ig/1 ronct6( 6u+ev zrat 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 strtw*0h3q pfc57qi my+r9( sjhuuck by a hammer, which gf 9y*0qc+ us 3r tq(hij5wph7mives 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 32 ci*vu /d10;a :xozoxnux/js05 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes througx vi d1nu2zox a0 ucj/;:o/*xsh 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 t7qlo1x06 q4qs okj0 lvwo 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 a 0.600-kg block q coye0*kr41-ll exd rw1zrw v0-t r(83ld 0avattached to a fixed horizontal spring whose spring stiffness constarl0( elz0o 1 v*rw-r det 10lv-arc d3y84qkxwnt 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. A(i::p-jvp um lfter reaching his lowest point, he oscillates up and down, hitting a low poil:m(:jiupp v- nt 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 vibrations in exactly 60 s. Wsnvczsz j7z8 9,g-m ,v02 xhnihat is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactlk fxl*f6uzb1 g/+8bu py one swing per second? (That is, one complete vibration takes exactl8 fu/1xupz +6l *bkfgby 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period oc s/9w s( dg yaa3;t+qjpjvj/5n Mars, where the accec(wq9 p5 g;a/+jdys3jtvsa /jleration of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cmin/b qn -0he7 j:-uy9qlp ukw1 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 m )z/fjb ;hdk9tass of 365 grams, and it is released at an angle of 12.0 hfzt); bk/9dj $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 m. If the clo 5pk;dw/hml jin+w+4 k2+nfce ck loses half a minute per day, how should you adjust the length of the pendulu4;hck n k+fji+wplm2n edw5+ /m? shortened by    mm.

Derive a formula for the maximumudvyxfh 5;1gg mgkv at62la4 l)1/pagu /zd *4 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 fro* eid;drilc/v,v- 3tequency of 2.5 Hz. At it is released from rest startrdc;ved3i o*ti -v,l/ing 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 r ./rf 4k,crql6xb9 1whg2j5 xc9zpndthat wave crests pass the bow of his anchored boat every 3.0 s. He measures the distance between two crqrf94.5dx/kplzh2x19r,c wjg rc b6nests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air haslco ;*ecu-s f* a frequency of 262 Hz and travels with a speed of 343 m/s How far apart are the wave crests (c*e lscc-; f*uoompressions)?    m

  (a) AM radio signals have frequene( r dzep8wz::cies between 550 kHz and 1600 kHz (kilohertz) and travel with a spd r8(:wz ze:epeed 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 +r9xrxbvv6u 8longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus,u gjqm*,ick z1ntz 9nlt .b,4q(iy f65 but one is twice as dense as the other. In which rod will tn94 tqncmj1zig t.6 , 5*b(uy ,ilkqfzhe speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is frw6 u;,athg9stretched between two supports 28 m apart. If the tensita9ufrh 6g,;won in the cord is 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected tozg/ .x.e, dau.4jwi ts the top of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sen..xeg jwsz / 4da,ui.tds 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 si l wk4.eykw .dnh*by9:de of his ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deewyb ke*.:yh4w 9dn k.lp is the ocean at this point?    m

  P and S waves from an earthquake (t1 f ktwhr44zff 56lmtravel at different speeds, and this difference helps in locating the earthquake “epicenter” (where the dtz1tfm lkw56hf4r 4 f(isturbance 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 ah7pqpq4w v8 *x sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually4 7 qv8hpw*qxp 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 intensities, and (b) the amplitudes, of an earthqmbm3d1ffx -; quake P wave passing through the Earth and detectedmf1q-m3 ;dfx b at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing thoi 8tum gli.j.qq+ m/;rough the Earth is measured to be +8 mjtqq/ il.u; i.ogm$ 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 fri.ie tjq3g1 0z49 i rpz-1f1 pmwjg7lfequency travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of jg j9 i3 -.4fl zt7pw1ir0iqm1epzg f1the two waves?   

  Two waves traveling along a stretched string have tw viofej 2r-90kpe)y2he same frequency, but one transports three times the power of the other. What is the rati efpveikw90 j22y-)or o of the amplitudes of the two waves?   

  A bug on the surface ofi:dfziy;k,(d9f+ze b a pond is observed to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If ykzediz fb;9: ,d+( fithe ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown 9ea .bgxu3e,bm-q ye6in Fig. 11–52 are moving toward each other. (a) Sketch the shape of 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 m-x9bbeg.3 me,e q y6uaoment 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 axwko ) t05keezm1b5y/ re the frequencies of the xk yz5 t5 1m0kb/)eewofirst four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hnk7 -k6di z8tr9xh0g lz when unfingered. At what frequency will it vibrate if it is fingered one-third oftnr 8 -0l9g7h 6dkkxzi the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string reslt8kwt k5 r4uz u68n1uonates in four loops at a frequency of 280 Hz. Name at least three other frequenc4zt tkuln5k1 8uwr6u8 ies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequenclz/ 5aww.mezt lp:-l31d ja/w y of standing waves is 475 Hz, how far apart are two adltwam5-/zj pa l.w3z/wd l1e:jacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, what x0bw-j1t7y x dis the frequency o71djt x ybw0-xf the fundamental?    Hz

  A guitar string is 90 cm l kgys1a3zm(r jn hv;*0lo,uh6ong and has a mass of 3.6 g. The distance from the bridge to the support post is L ha ok,1h j;lzvs6gu 30 (rm*ny= 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 striusx c0w8y6+hwr1 b+9 go:hzcvs75ilx 7o n-ljng 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 cha7r c5yno-zjixx+lo9h c0lwv7ub6+hs1sgw: 8 nged to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, biciba90 qh+ v4ut it is measured to vibrate at 205 Hz. By whq+bha0 9 viic4at 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 smbf6kyh /8 k8sdall-amplitude mechanical 60-Hz vibrator. The string’s mass persb/fk8h d6k8y 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 adjusten c:9k*b yzl m.6phyvp0,c+apd 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 varyi9y6c lh,pvm n kba.*c:p y+zp0ng L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the rigm6u nbcc rw4*8p- 1 p+3byzgisht frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. Wpbsmucyipr34+w8cbz6 1g*n-hat is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0ffvto;.a 52gwbah ;9gi q8 zx, km/s strikes a boundary within the Earth between two kinds of material. If it approaches the boundary at an incident aqa.o,9gzv 5 h;fwbxag2;ift 8 ngle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velocity changes from 2.8 qlzv94l(x 8n29efks. tsy+pb u5 ol3wm/s to 2.1 m/s If the incidentw4ke5otlnp3x us 92q l(b sz. vy89+fl 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 hits a laj+l-2v: gjm wayer of cold, dense air. If the sjv+j -w2g :lamound wave hits the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake tsmg8ax vl(+ (fzqmoel31 l4 +)f0ocnwave strikes a boundary between two types of rock at a 38ga3vz(0 +xm f)1mos(ltl 8o+lqfc4e n $^{\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 manual, thv,y k/:vly 5pbe dish has to be pointed in the direction of the sate yv p:yb,/l5vkllite, 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 cjpyia)6g 0*jg ;2mla 750 km/h travels across 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 ljajg;cp myig2)*0 a 6the 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 r:64*a 1ughmkf 5q)ifbje m*qspring stiffness constant of 550 kN/m Find the maximum compression of the bu5ab*m fujm6f1r:i)gq4*e hq k mper 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 fire net 18 m belowb 8m* 6jj y7il6uwd5ro, which stretches the net 1.1 m. Assume that the net behaves like a simpl6 ij jy*76o8bdlruw5me 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 then f zrpgcxjr6lgw67uk6xc1, 0 r5 alls 33 cm before6rlz51xug0g 6cp7, k 6xwrrjc it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed p3xy + 0d(firdh gmu)-of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffnemu3 fryh)x -d+(p gi0dss 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 (diame k4ajmyu ap3k2s h0-i6ter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more untilm2 ika psa3k-yu4j06h eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certais( 5n8 7ie/n(bqzb;ucvqxp .u n groove 10.8 cm from the center of a 33-rpm phonograph record have(7;bs /pcnqq5zuen.(u 8xi bv a wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equati (-1:y1aro4aykfcqj q on x=0.650cos7.40t where x is in meters and t in seconds. De(y1:o 4rqfqck-y1a jatermine
(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 ur2(umlkud2q)s 7/; :mtnl pwf. What is its frequency if it accelerates at 0.5(m2r; nl k)uqud2p u/w:7s lmt0g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lag (ifanqy4 o(+ke. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps of((i gnq f+a4yof, 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 tuned to play at 392 Hz (G9 61zq4bip *mne/ gtps))a/ xvovcsu 7) and 440 Hz (A)1p/z x pv/t a*)u64 eibm c9ssgq7von).
(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 -iul,rw::8esz pmrm4pmmu9v x3o71r Fig. 11–33. Determine a formula (a) for the ratio 1lpoeim z,um3r:- :4xmsu7r w8 r9pmvof 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 the twsuf so6x+:dn t6+ :ixc0)oqcip of each prong moves 1.8 mqxct+:6dis 6w+)oxfcs:0unom to 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 frequency 1.5 c fyal xlw,sk:qor-k 1)-uu..cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placflywxk-.)sl,-1ku c ru.a oq :ed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if yk25 04tse0e ydu5erd that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the w0et2ue ds ke 4y055dryavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exact)jscu; y1z )xcly 2.000 s — each one-way swing takes 1.000 )szjcc y1x); us.
(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 directifnv2y*-asrn 5, 9gz gion 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 os n5g*i 9a gs-2vnyr,fzcillations 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 1sjcv;o jk6 *a jz)dos6vwg148 fu )x3u23 g is stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses kx oug*8;)cfsuzjwvja346 d6ovs j)1 first meet?    m

A block of mass M is suspended from a ceiling byi qokfg +c(- cdz5vs,m c*)wg8 a spring with spring stiffness constant k. A penny 5g*( wi)cms+vcocf qzk -d,8gof mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-78xd2vis t38my fyv4 tkg car at the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze2y 4v3tty 7mv8 f8xsdi 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 Finz x40fb)p54 h9b62tv u6m6 hzd 0bjpu,txzwyg. 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, given that the shear modulu4wzu nhm4,bvbhzbpt 0 2y 6jtxp0x6u9f)d z65s (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz