Give some examples of everyday vibrating objb2+ addzr8h7 civo(. 7p-m yjtects. Which exhibit SHM, at least approxima2mc-d h .zrp jbv77daty+o 8(itely?

Is the acceleration of a simple harmonic oscib) w:d )vfhtj3llator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is appro:sku bx:y4( hhximately simple h sb4: yk(hh:xuarmonic.

Real springs have mass. Will the true p4js txz*2 az+meriod and frequency be larger or smaller than given by the equations for a mass oscillating on the end 4*+j 2xs mazztof an idealized massless spring? Explain.

How could you double the maximum sph(irs bttey 0v -i0bzh7:ex-(eed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring ;x tbs)f 9tdg(4qr8u9pv ;k2 sar6tl fscale, and then is released. Describe the scale reading as a functv s)skq tp;ul949(f;ar26x g dfrt8bt ion of time.

If a pendulum clock is accurate at sea / 8p+8f cpb vtd*;sb5 :tz2p:kenahlhlevel, will it gain or lose time when taken to 2b /pcnvk:+8dh t p85espt;: zfh*l bahigh altitude? Why?

A tire swing hanging from a branch reaches nearly to au41l ccpp .( yvc1sg1,7ttelthe ground (Fig. 11–48). How could yo s11 4eup7yv,ta .pgcc1ltl (cu estimate the height of the branch using only a stopwatch?

Why can you make water slosh ba/m7h ak*3 td k168s fijsygrg5ck and forth in a pan only if you shake the pan at a ck3rhjsa /md1*6 kyfi785 g tsgertain frequency?

Give several everyday examples of*2buhp szr(661kc e +m0wtdx g resonance.

Is a rattle in a car eveyim-kfaip( da +q5 (y g*ne)y9r a resonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal s4 virs.p i(h8to the frequency of its source? Why or wsiv84rpis ( h.hy not?

Explain the difference between the speed of a transverse *xfi qf hr):gbo rx..:wave traveling down a cord and th. )gr*x:f oxi:r.q bfhe speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano nxrnzdlwec4 . ,xq+nk759i4(f0 d lqzeormally have wire wrapped around thec(9ef k+ d5d4n0 7zl4q.qxlizxnwe,r m?

What kind of waves do you think will travel down a horizontal metal rod if you mq(i h l9c/lmy3y:*zk strike its end (a) vertical3(ilzy9m: kmh qylc/ *ly from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in tempera0,xci+u zm oxv -uho;-ture, but the bulk modulus B is nearly independent of temperature, how would you expect the speed0u x-c,hux z-;o+mo iv of sound waves in air to vary with temperature?

Give two reasons why circular water waveji+.dct c//8xtp fk7ds decrease in amplitude as they travel away frok jf id7/ cx.t8pcd/t+m the source.

Two linear waves have the same amplitud6ck pen 3)pkzki y)(w*e and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits more ) k)*izpnc( e6yp3wkk energy? By what factor?

When a sinusoidal wave crosses the boundary between jv8*j mjo /l*s(ru-5 gh ))zxtt+jnw mtwo sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Explain m5nu+*/tr)wj- g)hmtvzjjx 8l (jo *s why.

If a string is vibrating in three se g m;toa.j2a5hc15x gat9a p*igments, are there any places you could touch ah*j1aoc5t9mp t ;agg. 52xiait with a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibmr ptg22(b 0 tzqvtk21rations of incident and reflected waves cancel at the nodes.q 0(2p2vmtt r 2tgzk1b Does this mean that energy was destroyed? Explain.

If we knew that energy was being toq;ih4 *7 kxpyransmitted from one place to another, how might we ;xphiq4o* ky7determine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes ieezb vbeot ( ;9;xqa,6 -9qrcSHM with amplitude 0.18 m, what is the total distance it travels in one69 9v(eqi ;rbx;aec,eq z-otb period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it bbtwe* b801npm ;s/lh wut is 85 cm long when a weight of 180 N el/hm8p0 nb w1st;w* bhangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg carm-)n q 2ot30kepa:bxo compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what tqbk3:)mpx -ea 0no2 owill be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (ah , 7uwa)9jgd:acg mu)kl65 hh) What is th7wh,hk gca)udug m59)lhj:a 6e 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 vibrat;0o (:1j+j flq4v es uroky *tu3e7vlzes with a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs u3rz(*e l4evlq0skj1y7jvtfou o; +: from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11j abum7 y. maicl/q481–2 at times t = 0,t =ji/y.7au b cl 41amqm8 $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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’sd pig j5u*pv4 .vjhs7ci4 ada: /u,m0q web. The web vibrates predominately with a frequencj daigc *qj/0u4dvah7pmus ,: i.4pv 5y 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 (:9gyik)mn1-7k , gi0w xqe x mk4zifqfrequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 g 7kmfx,1 w)qmxni9i:0zi (4-kkyqeg Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vftzc+1qwbu/5jo y q41ibrates 3.0 times per second with an amplitude of 0.13 m. Determine1b qwfqucjt/y+4z5 1o
(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 spp6bdhlnfra (tg4/v1, kn bz05eed of a SHO half the maximum valub gtzpn(nd1/vf l bk6r0 h4,a5e?$\approx$    A

A mass attached to the end of a spring is stretch rs3fb2fi( hg(ed 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 +yi0vn.p:ck b.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium posb: .ivyk+n pc0ition again?    s

  An object with mass 3.0 kg is attached to a springn2 0w2 sb9g x*kva7)jbmbhs*s with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium * jag97b*m0v snkxswbsbh2 )2position, 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 popgvinoer.+ l/ 7n5n-mx uun 0.200 m to “load” a 0.180-kg ball. With wha7mn-luvier.5ox + nn/t speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attazrn (3,.tgcjjched 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 , 3 cnt.gjjrz(with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x = 0.45cos6.4t where x itiil::f9*qrg s in metef il9g ::i*rqtrs and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of a SHO half KE and half /ti o+0. hgnfigg7:; .ohxumgPE? ±fi x.og hgg mtu./7i:n 0ho+g;    A

  If one vibration has 7.0 times the energyfaq*fc0 c+2tvr1/ 9kr c2ur em of a second, but their frequencies and masses are the same, what is the ratio of their amplitudes? k2fvrm1r +0ta cr/9uc*2feqc   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring once p5rb1ul*cowc zi-, 0g every 0.65 s. upi-o ,1rbw cg*l 5zc0
(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 vertical springs, ea)8* w5iacjyn-hm km-r ch with s--m)j n 5m8hkcw*ir aypring stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according t u2oj xkj5co3(o the equation x = 0.38sin6.5t where x is in meters and jo5(kj xcou23t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A an j6 zeu1-odr;pas6w9;rxxx,n d 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 q72 7*+b (uuh fqdzw1k*avef *bpmzn7(k = 124 N/m) is struck by a hammer, which 71* q p2n( bzkuue qbw7dmzf**va7f+hgives 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 wia3 )w.w2w t4t(odickith spring stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through th2 owikd tw)(.t4cw3iae 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 stiffn .h8q2* )l b(kskwr(2-itnkpuyvcmu0 ess 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 blockaq 8(( jv;j6kmyjuz+j attached to a fixed horizontal spring whose springjjj v+;q((6 a8 mkjuyz 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 reaching his *.ot0qxfqdib7u+8s ep0z ig m4c :4ey:lb ct-lz*f tq7. byb :ue8-c4c0gmoi0i4 d+t xpes:qlowest 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 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 vibo5wd :3)tw4d mdnj(narations in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swing per secoo,j3 2 pejgvzf8a 0q(xnd? gvf 3pzej 2qj(08 oxa,(That is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a per g ibf0; -5gwxmep:m3oiod of 0.80 s on Earth. What is its period on Mars, where the m;-xmpoi e 0g 3bw5:gfacceleration of gravity is about 0.37 that on Earth?    s

  What is the period of a +i x0v.4s5i bz;gcqwum z+q j/l3cx0c simple pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple p:enwrau+uk p4p, 99 *uennmj 0endulum is 0.760 m, the pendulum bob has a mass of 365 gram0u,rnunw e*+ke jm9a4n 9 pu:ps, 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. If the clock l nm8e8my0fb5nekv zmdj4z03 9ja/e5koses half a minute per day, how should you adjust the length of the b0zfnj4k95/vm 0 5kdm83jz yeane8em pendulum? shortened by    mm.

Derive a formula forf:2 r7a5nikz yl1l/fw the maximum 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.l8b4hu g(c/+nczfzx ,sh2 cr of 2.5 Hz. At it is released from rest starting at c,2h g4l czxr b(8ufh.zsn+c/ 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 pass the bow of his26 ppe.zxhl* b anchored boat every 3.0 s. He measures the distance b2 p6l.hexb pz*etween 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 wit.2gkfn ,z j7iqj- iif/h a speed of 343 m/s How far apart are the wave fn -,zf j./ jqii2ig7kcrests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 16cp.oqxo h g,5fs01g, ,,hoqes00 kHz (kilohertz) and travel wf.pos, e s,gx0hq,1go5coh q, ith 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 longitudinal v il,jwhb77x,ahuv60 waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elas cvv5jf/n+ lvv)e *b3ttic modulus, but one is twice as dense as the other. In which rod will the speedflv /v+*nvevtjb3 c) 5 of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apa16yqvr -5ljx0b :wyrzit8+ ilr r1;iort. If the tension in the cord is 150 N, how long will it take a pulse to travel from one s86 1z x; rorvw+1r:yil ji-ybl 0tqr5iupport to the other?    s

  A ski gondola is connected to the top of a hill by a steel; (koqgntg i4(a*on0p 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 that it took 16 s for the pulse to tk;4q(p0(a ingg o n*oreturn.
(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.b/yfkb r-ht l00 9ar yoeq-brud(8,31 qi5ylq He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the eho a/,3i b qb0rryd9l5qyyq0b-1flut -8(k rocean at this point?    m

  P and S waves from an earthquake travelhj 2rl -y4zqwy,eo0w ) at different speeds, and this difference helps i-jw)w hl42yyez,0 r oqn 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 b1zm7)8s h)fdyhen9 d le approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so) 1 79z)hlmhy8fsddn e that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) theh:nq. ulyz19h 57 /zl9k9 qnbh4zbnqur :r jq* intensities, and (b) the amplitudes, of an earthquake P wave passing through the Earth5b9q*l.uyzrl qb9unrqhq h9 k j7znn h:/z:14 and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Ea9rdapx.yoke/ v :)(abboz(t( rth is measured to be axodk/ b(((9r .tyez ):bpvoa$ 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 tp7a l;9mfx-r yravel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudelr m97py afx-;s of the two waves?   

  Two waves traveling along a stretched stringrg) q2 st2ez (suoe/4i have the same frequency, but one transports three times the power of the other. What is the ratio of the amplitsuqtieo(r4 ez2 )g2/sudes of the two waves?   

  A bug on the surface of a pond is obserei5 0 3+lusio, sjqrw ow9 )c3gsymz i;,sl40mved to move up and down a total vertical distance of 6.0 cm, from the lowest to the h3s,yj0ms3e m+s ;i 5orl9c4s qz)w0g ,ioilwuighest 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. 1af5(39;lju buzb7ud nx f1hb;1–52 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 moment the pulses pass each other, the string is straight. What has happened to the enerjfbfd5; ;buu3lhz17 aux(9bn gy at this moment?

  If a violin string vibrates at 440 */d1,i0v+yowoh qck ( uz:oieHz as its fundamental frequency, what are the frek /o ei:qhz+o1owv*d 0( ,ycuiquencies of the first 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 frequw 7gkg3xhaj l5nnf* /*ency 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.) nf 3x75w/*aj *glnkgh   Hz

  A particular string resonates in four lohdz39iscs1:ohy b1q;ops at a frequency of 280 Hz. Name at least three other frequencies at whic;z 1yodhs: 9bic h3sq1h it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string dgwb.mmio61iw1tjue +j c: 7( is 92m/s If the frequency of standing waves is 475 Hz, how far apart are t: wimt1oec w61b.u jjmi7 (dg+wo adjacent nodes?   m

  If two successive overtonka *ckal4sxym lxp)qm+.o*(8es of a vibrating string are 280 Hz and 350 Hz, what is the frequ4.)+q *lapys* 8x(kalx oc kmmency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance from c 6zd9oohmvhy xl (8 8cqj350kthe bridge to the support post is L = 62cmxk cvo(86m hy 3 0ocjql5dzh89 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 string is supposed to vi 583cqp fbpb+ubrate at 200 Hz, but it is measured to vibrate at 205 Hzbu+cb85q p3fp. By what percent should the tension in the string be changed 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, but it is measuredo7f4/hk w)xxt to vibrate at 205 Hz. By what percent should the tension in the string be)hf7x x/t4o wk changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a sm ,vyb9+o d,qyuall-amplitude mechanical 60-Hz vibrator. The string’s mass per unit lengd 9o,yqbv,u+y th 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 adjustedc3 h lbo)t fhobq/hzudo23 2)2 by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how2 )o bho o2fhq)th/ d2c3lub3z 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 for i c(9e4aasi; jdk3e;gth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the ce;s; (9ieijcgk43deaa nter. 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 strikjvs,c: 2v9s 7qtenh/c bq7 )yses a boundary within the Earth between two kinds of material. If it approaches the boundary at an incident angle of 4 yns27v c/)qbh9,7:jqstc esv7 $^{\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” wherwdx9j r6bzfsf( 6 34rle the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave (fldf94jb 3xrzs66w rcrests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air whe 9kbfg/uo97i916tp.jnxcx epn it hits a layer of cold, dense air. If the sound wave hits the cold air interface at an angle of 25ox/7xp btk69fecginp j 19. 9u$^{\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 earthqua ncur-uh1ff vfe5 69xg2h /c8f k;r9koenq/c+ ke wave strikes a boundary between two types of rock at a 38n u1 fgk/oec cuhkr5-69q9 fc+en/ 2;vrhx8f f $^{\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 ma:exb x:o i+)wlnual, the dish has to be pointed in the wi):oe x :+lbxdirection 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 and9n+vn0k ts ,rx p0kyn2 velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harborsnkn0p2knx r0v s,+t9 y. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 550 kN/pqqr-3) fxhsx,4qx)zz5 dj)om 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-xqqoh j5zp3 s d)r f)zq)xx4,/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a win(cnxm ksd8q; ;dow to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a simple spr;x8 nk(s; qmcding, 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 placed5ys s5k)rb;cqyl/xkn-h r+l/ on the end of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is x-l)ys yr;klnh skq5cb/5+/rthe frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), comprevl5 jvl :923tsp :1g vhs;ux+k 6 hndd(5dtejessing the spring 5.0 m. (a) What is the spring stiffness constant of the sh :; 6ute3vdkv e5x1gjsdvj +(9 d25t:shpllnpring?    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 (diametkkhy8 h ogq397x ti6vh4za0w /er 8 cm) at just the right pace of about 1 step per second, thwoai8t7 y4hkv0 h/ hx69kzq3 ge coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from tt+iz5p+e. -p/hg yihwhe center of a 33-rpm phonograph record have a wavelength of 1.70 mm5pwtii.yp+ z h e+h/g-. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according toy7q66sqtr /0ooyx jcmgzb1, c/4hjf2 the equation x=0.650cos7.40t where x is in meters anbtsh2 66 o4oyjqqy07jc cx/f1r,m gz/ d t in seconds. 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 oscira2e7/i;ore v llates with frequency f. What is its frequency if it accelerates at 0.50g i/o7rve a2r;e (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands wydu-5 8n ,z8aio:irdon the raft, it sinks 4.0 cm deeper into the water. When he stepsda ,n8w58:iu- o dziry 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 ins*rl0)/3pmmsbyrwqi 3e5+fv: .9 bh b+y pndpqtrument are tuned to play at 392 Hz (G) and 440 Hz (A). .9 nmi5y0*sp +m pf)+:h 3qe yrw/bqbdr3b pvl
(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 oaecl/6u ; gr2ct5kbv9f Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the ligv6kce/tbg ca 5l92r;uhter 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 tip of each prong movpri1,bx2 ucchk/p2yp,mqj 67es 1.8 mm to either side of centerxhmp,kcqi u c yj612 /p7p2b,r. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscilla0(i ofayuy,5kz:/p d btes with 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) will not lose contact with the board durkuypy:i 5o /(0 dazfb,ing the oscillation?

A string can have a “free” end if that end is attached to a ring that tduk)2xvn63p 19ci bxcan slide without frictiipctk xvd3 ub12n96x) on on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exacjpp3ckv72w zf/mz 6rmc s91,ytly 2.000 s — each one-way swing takes 1.c,wppvcs7mjzf m3 9y2/ 1zr6k000 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 vertxk (p;4vg y-jtical direction or can swing as a p- v(k ;ygxjpt4endulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is*by;;xs0xfhc7d s3hhf l()sp stretched under a tension of 255 N. A pulse is generatecx3hh 0;f(s;s7 slhd *b y)xpfd at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with tejsa/ob )2bny x5)0dspring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny /yb2dte)5 x0bs o jn)ato 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 cabl qjxxy 5l2idlis,s *zosa)4/9, lko7ue is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the ca k5oq9u xyz4do sailj2)/7,* lslxs, ible. 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. 11–58zbt:yo: :owm+ (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 modulus (m:tyw:bzo+ o :Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz