Give some examples of everyday vibrating objects. Which exhibit SHM, at least a-z s.v qjjlo,*pprojv,.-ljz* oqsximately?

Is the acceleration of a simple harmonic oscillator ever zero? If so, where.imaod b 8 he,h2nk,emj 4i*0q?

Explain why the motion of a pistobx 88:vnc704day pst. fhqv0sn in an automobile engine is approximately simple harmony 07 vs0cfp.atn8b4qxvh :sd8 ic.

Real springs have mass. Will the truev2a)1c igpif96 g.x8 miaxytcd+w s 87 period and frequency be larger or smaller than given by the equations for a map289 8mis viaxtg6 i+.wagf1c y7cx)dss oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple hantqin ,u1-3cf 9ng9ebnnyl 58rmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook bv*p x:rh u 0iv7:ivi1of a vertical spring scale, and then is rele ii7xp:iv0 u *v1bvr:hased. Describe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain s-k6z62cureaor lose time when taken to high altis-2z6 cek6u ratude? Why?

A tire swing hanging from a branch reaches nearly to the groundd yvpn *(-9imz.az9i p (Fig. 11–48). How could you estimate the height (p vi*9ydi.zz9-mnap of the branch using only a stopwatch?

Why can you make water slosh back x m7,y(zxnc3w and forth in a pan only if you shake the pan at a certain freqxz wyx,m7 (3cnuency?

Give several everyday examples of re-iw;)u ibmj/ mgdc1i3 sonance.

Is a rattle in a car ever a resonance phenomeq el./2c +o:t o4ibzw cpra;n(non? Explain.

Is the frequency of a simple periodic wave equal to the frequency of 2p4mu ky6 1*hiq(raubits source? Why or why u14rmp62*quihy(ba k not?

Explain the difference between the speed of a transverse wave traveling jqvf 9(s/m(o-kml-az down a coro -kl/zf v -(qma(jsm9d and the speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano normally 4hk4evkv ,bj1;ym brj4e3v 6khave wire wrapped a1j4v6y kj3ve b;mk b r44,kevhround them?

What kind of waves do you think will travel downj dlxlxi4d:4xzn.0j/ iw5z 0y a horizontal metal rod if you strike its05 :z0l inzl/.yjdx4xdwj4x i end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature, but the buv8 h(w-hsg*rid3u *b6 erl9wu lk h s*9r(3edr whuw -gb l8i*v6umodulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in am)l rl8 1pm+.ftz k+w7holz( nxplitude as they travel away from thenmzo+8kx1+p )7tlz fl.r l(wh source.

Two linear waves have the same amplitude and speed, and otherwisep,6b v8py 6 wqvl8 6+d3knhsib are identical, except one has half the wavelength of the other. Which transmits more energyk npdyhpvi, 6bq+68638b wlvs? By what factor?

When a sinusoidal wave crosses zixos o)ezy(z0n/46sthe boundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Explaixs / y( iz6o)s0o4ezznn why.

If a string is vibrating in three segments, are there any places you could toulkgao5euc9 zx2 gp.0zb- e--wch it with a knife blade witxka. eggou0lc9w-z z -e pb5-2hout disturbing the motion?

When a standing wave exists on a string, the vibrations of incident and re.k*hgxn y( y.4iixw:bflected waves cancel at the nodes. Does this mean that energy was( gkn:xii*yy b.h4xw. destroyed? Explain.

If we knew that energy was being tranp3pi so +vg+;usmitted from one place to another, how might we determine whether the energy was being carried by particles (material bodies) or by+3+vgsuop ip; waves?

  If a particle undergoes SHM wito1n0uo-2 tjzk g4l8y jf86c ny n(wnx0h amplitude 0.18 m, what is the total distance it travn8t wzflj20 ko 1yg46cnxn8 (jou 0y-nels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hanb)m uzw/u -b)kgs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “sprin)bwuz-mb ) u/kg” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kblqa)2*gb n/c* 2n mfri u9q8qg driver gets into the driver’s rg qni nqu22a9fml8b/** q)bc seat. If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (a) sj.s lhh/ ;:hzWhat js;hl h:./zhsis the 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 frequencyeud0is f 2/a+dda*gx3 hkwk8 , of 3.0 Hz when a mass of 0.60 kg is hung from it.0dsfk+,w*xa32kehd ad/ ug i8 What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating th pvyp h gab0nxph fw//g piai2/4vo65u8mx;+9e position x of the mass in Fig. 11–2 at times t +8fp pghovu6axy;vw5i/ 0 ab//nx2pp4 hgmi9= 0,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web. The web3x nqv//2qyk8 -vid efya o;8f vibrates predominately with a frequency of 4.0 nf/8-kxe3ay/iq vo;2ydq 8f vHz.
(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 spr.*z7f it+k aviing vibrates with a frequency of 0.88 Hz. When an additional 6+.t7k vi za*if80-g mass is added to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrate mgns 1rh7kk:(s 3.0 times per second with an amplitude ofmk1kgr:(hsn 7 0.13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed of a SHO :vx q0vy0ohd h)46pcihalf the maximum valud4yhxq:)vhv0i po6 0 ce?$\approx$    A

A mass attached to the end of a spring is stretched a dista5uxm1wde; qqqr. 1 +ajnce $x_0$ 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 0.317 7gy4pdxu +xh5 m. If the spring is stretched an additional 0.130 m and released, howghd77yux px+ 4 long does it take to reach the (new) equilibrium position again?    s

  An object with mass 34xj5+yicwnqm-ad8w) *axw e3.0 kg is attached to a spring with spring stiffness constant k = 280 N iynwq8e53m x*wax)cj ad-w+4 /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 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 8i qa913(aqcpmo6y y1 ni-p; gmp;fds80.0 N to compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave the gun?igm6p1 y ; n o9;yadsf(q831 iqac-ppm    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one ,a6xzy2w- kvkncb3t2i5j tu ;end of a spring; the other end is fixed to a wall. 3.0 J of work is6kxuk 25wty-nba,zt;2 3ivcj required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x = 0.45cos6.4t wd)r69 yupb1 tqhere x is in meq)rbu6dy tp 19ters 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 hal zf7p iil/t t3pnj/z2tz7ch 57f PE? inp 7c zitt2lp7 7 j/fzz35th/±    A

  If one vibration has 7.0 times the energyvq 2pl bt0 h vtkrfuqu87,c-4.85hss t of a second, but their frequencies and masses are the same, what is the ratio of their ampvtstcrpb quhvfs0u -74qlt85h .82 ,klitudes?   

  A 2.00-kg pumpkin oscillates from r+cc,9 on 506e xx/pfuk1wopda vertically hanging light spring once every 0.65 s. u+c/0depx9k1nocw rf, x 56op
(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 springs2o2s l/tfw )gr, each with spring stiffness constant k (Figt o)wg/ f2sl2r. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5otbs dp d8 oycmcxnj86d-8:7ui/ 5jq5 t where x is in meters and t is in seconds. Determineb cdo6-uqpxdom7y8j85/ dc 5s 8jin:t
(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 examp (wmzu4a*-prc/ ,cbfnles of SHM, labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a hb2z:w io8p/pg6 x ikp som+58tri1 dw5orizontal spring (k = 124 N/m) is struck by a hammer, which giveskpb itip185zgm oxor8i2 dps/6ww:+5 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 3053cmlu: s4,+al 2tmwxbgdj-g jbh8 .8m N/m vibrates with an amplitude of 28.0 cm when 0.2mbmgwx:jubj 3- + l8t.ds,ch8lam4g 260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with springcv t:s z,9hu,hns)hr2 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 attached to a fixed c d ka,7j6g(-ry l2tvvhorizontal spring whose sprindkryj2,- cla6vv gt(7g 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 highql4l x fht n/v1r;/(qb bridge. After reaching his lowest point, he oscillates up and down, hitt1q4nq l br(hf;v lx/t/ing 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 v an4l94)xbju4gjo3 c librations 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 h) o *c;ocf7wtkx8(lhmake exactly one swing per second? (Thho8f;w7tl xo)kc* (c hat is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its perio(,i+f)nrl o1wuj65khd 2krca d on Mars, where the accel k ,cda6(lu)rhrk2wi5 +1njfoeration of gravity is about 0.37 that on Earth?    s

  What is the period of a simpl:0r 6k8xzo+dw17zxh8 bs kx ble pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulum btcu8zz, e1 uo(b xfv. (9qu2tcob has a mass of 365 grams, and it is released at an(butz1 vf2, q .cuc(t89xueoz 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 clockljn vn(r0f w3; g76ylp’s pendulum has a length of 0.9930 m. If the clock loses halfpw3gn 6rf; 0llyvj7(n a minute per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum spee 1odu(cm*.9uuay1a6bmk dw0dd $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At it is released f 5gm -l(7 5* c,sfl5vu1u 7cpqeneoztkrom rest startlsoq, e-zeg*(m upku5t 7cvn1f557c ling 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 pass the bow of his anchored boat every 3.q0uf)twmtw ) 2fj na.40 s.0qf)n2j.u4 ww t)tf ma He measures the distance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with vm-)igu hp((d5 vx.oga speed of 343 m/s How far apargu5h-mvgv (px.dio( ) t are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (hh-c)k) l.xvgiu1x q0kilohertz) and tra)0q)u-icvhl1hx. kx gvel with a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of l2 qbyik75. ce/omoyg1ongitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as dense pwn o(e0wvs .967 r2 ;p2yxjih, orynfas the other. In veo7i6yrw2.x 9jr0 s;pnh, (o f2nypw which rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between t3qnqb*i6zln1hpq:d eiyd35p fq;5w: 4tgs k7wo supports 28 m apart. If the tension in the cord is 150 N, how long will it take a puls5p;gd1: fe*y :ls5 7qtip3q4iwnqzqd3k b n6he to travel from one support to the other?    s

  A ski gondola is connected to the toy/bs qfe;5e(vp 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 bu yb;q(e/ef5vsmps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the surface of the se mabs)k/j5w3 hm* udym*)z-s r3phi q5a. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this poib ar-d5pmzsq3 5/smwh*u j*m y))3ki hnt?    m

  P and S waves from an earthquake travel at different speeds, and thikvutz hxf.,n 7v,,c7 hs difference helps in locating the earthquake “epicenter” (where th.nvtf7kvch,uz 7 , ,xhe 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 pq3t) o.vitd*) tck rrr x3 v-il:lb1gf(81giapproximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquatrq3ikp1rv)1x:.) (l fgd i vt biorg8l 3ct-*kes, 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 intensities, and (mq5mzf r 5;g9vb) the amplitudes, of an earthquake P wg95 zfqm vm;5rave 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 throughs;qkvtv9x zij 5 w9a3cbo9m,y;s,lc5 the Earth is measured to be 9;wzcj 9ssxmkv ib yv9c,;a5l qt,53o$ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency travel through the same portion of i m 19t0ilhccwoxm e e;r/4-r6the Earth, but one is carrying twice ;omhwe0r9ir/1c m l ei-c4 6txthe energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched wnc3g2o 7.p,jm; nfkistring have the same frequency, but one transports three 2 7.nic3gwp m;jnok,ftimes the power of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to u(*oq6hwpi;bq9: io ve,bgb0move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cmqhw: q6vpiu;9 0,gibbe oob(*, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) Sketc7lh h 7r33yrawh,d de7h 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 energy at this moment? ry7r 7lw,h33eh hdad7

  If a violin string vibrat1-y6ji/kv w)elp dj5ees at 440 Hz as its fundamental frequency, what are the frequencies of the first foudj6 5e i/-lkvp)1 ewyjr harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz2lykr.h (zz ur, pd6)w when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates 2,dyl.zhu) r(r6 wzpk as a standing wave.)    Hz

  A particular string resonates in four t 0y-rka+ans t:,i7brloops at a frequency of 280 Hz. Name at least thsran r0-yt:k7i,a + btree other frequencies 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 frequency of standing wave hqgg(*s1,(g/x ep udoqyig42s is 475 Hz, how farx,sgdg( g*ygq q4 e(o12i/hpu apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hzh)-j-n.d re qrkbs/r6, what is the frequency of ths.r/nr)-erdkq -6hj be fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The di+a8( a wiv.fspstance from the bridge to the support post is L = 62cm and the string is under a tension of 520 Ni+ 8 w(a.fvspa. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is suppcxk ;(: fj/uqzi67q pb2gmx95pwogw5 -i;y pg osed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string b 67bm z;xqy- g 5xf;j52wpiip9gocg wkup /(q:e changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is suppose uy,(fv2nnsuff9 :u.k1 qkry: thks)5d to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tens n15rsyfhuuy:2v fk)9u. nkkqt,f(: sion in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mechanical 60709cyc p 0 c+jtbwgpc1-Hz vibrator. The s 00+c wp cp9jtyc1b7gctring’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be adjusted bychnih )cf5()g *a1pco moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L betapf)hi*c ncc )5g1oh( ween 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the right yvyj gfh z-knw8,m, 0(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 ynh0y, j-,8w( vgmkzfHz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundarygkc6 d,9sl,olb k8 xv* within the Earth between two kinds of material. If it approaches the bocxdbok*lk,, 6 9slg v8undary 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 velocity changes frobib83cjz-r) e fna lw7 2m2do:m 2.8 m/s to 2.1 m/s If the3bi)z:7m8 cjabnor e fd-w22l incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer of cold, d -m avmsy*29en)18ryy5t jiliense air. If the sound wave hits the y5my19-8) yjevil nm s*ri2a tcold 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 wave strikes a boundary between twomq.gl z0ukn,6( zmzyz 0r 8ud8 types of rock at a 38 qm gzzu,0yl8 .uk6zrd0 8(zn m$^{\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’sze3hy3ncw65 vi8v bs + manual, the dish has to be pointed in thy5sz 3bhvcv+wi 6n83ee 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 7,axjy) -nwl oq hs2m,1y d j3r2v--iib50 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in t jr1ylov-j3-hx ,,sn id w2-mqai2 )byhe harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a springhrmy/xp bml gi.9b 3hl-)w ;5x stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.)m/ibgwl.3 h x;y5b9l rm- xhp2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps fromr,h4fqgf9z e7tz1:p*.xet(q,cqz jv a window to a fire net 18 m below, which stretches the net 1.1 m. Assume that the e4qzgfhv(:z7fx,je pr c . ,qz1*ttq9net 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 plat2 k59/x- rwa,h mmwrjced on the end of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequemmj /-whtw,r2a95x r kncy of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a y bwf e0yqwil*o3ey* u6uf m*7+zotswa* s)((speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring*(*u3 *oowtea)f6 7 *+msy bw( sqie0lfzyyuw stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a (zo zmie-dx6zhuf6t 04ni;2dcup of coffee (diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it startf;ozhm46u0(ie n izd-xzdt6 2s to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of ayq we/i(.a . m:kwwac/ 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sound emitted? w .(a /myqcwew/ai.k:   Hz

  A 2.00-kg mass vibrates accordingli o hsxu a2ixw069t*wfs24 g: to the equation x=0.650cos7.40t where x is in met202l 4tx9sw:a* x oih g6siwufers and 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 oscillates with frequency f. What is its frequency,dj.4/ bkdnv e7jm:uw if it accelerates at 0wdm dn4 j. vbu,ej/:k7.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft float6ooxfa;wx7/09f4axn46s :d fkvf fd b s on a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into tdox4x7 06/4d fx o:;b aavn 6fwfkfs9fhe water. When he steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play at 392 Hz (G) and we40(mj+ikeui7xyj w1/jm22i k uz8v440 Hz (A2/1u2e 7m+kii mzy8wjwik(u4 jx0e v j).
(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 1syer)8 3szjtftc bwm ji )u5h58yh-* stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the we8sb) c)*srmf 8huttyh zj-w35y 1i5javelengths 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 frequencyhetxn+esi; nr 8 )u;c5 of 264 Hz, and the tip of each prong moves 1.8 mm to either side of center. Calculath e+scrnx8;;ten5 ui )e
(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 motiz;u,mz-:w. ax sqv* hion 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 during the oscillatio*wiavsmzh;u:-z, q x .n?

A string can have a “free” end if that end is attached to a ibbgg flcn7;;w2h:j5 ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such ai;7; w:l5bbj gc2fhng string with one end fixed and the other free.

  A “seconds” pendulum has a period of exf5hck ) dg:lve 6ub+6pactly 2.000 s — each one-way swing takes 1bg f 6ck6 p+d)hu:evl5.000 s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring ca590pzhz x2g 1x 1vz;s:hcyqq kn oscillate 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 oscillations or the period vq:q c x h 1k12;5yx0gpzzh9szof 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 of 255 N.z uufu5m.vh35n.lt(iw mb8t. A pulse is generated at one end, and 20.0 ms later a second pulse is generlzm t.vth.5 m8.5ub3 f(uwnuiated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceilxov+nv 7zd0;mmd .cwj we 7,m*ing by a spring with spring stiffness constanm *+mnzdv;0.w, 7ve dxoc7jw mt 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 to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The stwltblg bk k/bl882+tnq.. 7 jfeel crane cable is 22 m b.lj kf+.l2gw8l/t7n kqtb8b long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which 5cglge be-/t2also gives the dimensions of the blo gt/c-b25gl eeck). 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 (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz