Give some examples of everyday vibrating objects. .f7hy lvq**j dWhich exhibit SHM, at least appf.vdy * 7h*jlqroximately?

Is the acceleration of a simple harmonic oscig9/cy 3n5b 9bevq9ju kllator ever zero? If so, where?

Explain why the motion of a piston in an 81xz*,f kk du(otd 1ncautomobile engine is approximately simpdzk ,fn1t1uk(x *c8odle harmonic.

Real springs have mass. W ;mr sq fl qwe+5x 5zuv69xy4uu;mjx2)ill the true period and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized massless spring?x425;mxw ml z5jvr+9 x)qfu;6 uyuseq Explain.

How could you double the maximum speed of a n.dv9z z vh( ad)hdd gno*i+tr9;y+a:simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical +p:5plig,d*v 1keor2aax3zc,lt lk )spring scale, and then is rel+vraip, xt lo zpd153: 2lk *,el)gcakeased. Describe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or ynodvi-(5qb1 lose time when taken to high albiqd5-yv(o1 n titude? Why?

A tire swing hanging from a branci5fleh6b4ydsetmta/ykug) 0f )(;/t h reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the br;k /eysy5 am0)bgtfthu(d6 i 4lt/)e fanch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake theec3d bpc i7,+b pan at a certain frequb+bd3,e cci7p ency?

Give several everyday examples of r.zyan4i )n*wvb.f* vxf19vioesonance.

Is a rattle in a car evvtdz.ip h( 2 hq3ntt(gp +)-pfer a resonance phenomenon? Explain.

Is the frequency of a simple periodic wave51rmd7 )vghkd equal to the frequency of its source? m 5dd rv17kh)gWhy or why not?

Explain the difference bet0fh 53-ag*c xf*yhyhl9 j,vvq ween the speed of a transverse wave traveling down a cord and the speed of a tia 9*v*h05-fvcflyx 3q,ghyjh ny piece of the cord.

Why do the strings used for the lowest-frequency notezmq*tz+() w ,i0n0zk h y.tdsks on a piano normally have q00k)tizwtyz* . (md,zknh + swire wrapped around them?

What kind of waves do you think will travel down a horizontal metal rod i38 r -ifwnq,wyf you strike its end (a) vertically from above and (b) horizontallyr3,nfi q8yw-w parallel to its length?

Since the density of air decreases with an increase in temm )c t/k rp6nif.u/oxp5o1p g1perature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound wavep5o/o6fmkp/uxcng)rp i1 t1.s in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as th0;jyydt +uu i(ey travel away from the sourc; y0(ud iuy+tje.

Two linear waves have the same amplitude and speed;thl4j hac ://ck lmk0, and otherwise are identical, except one has half the wavelength of the otth lcc/ /lhk4aj:km;0her. Which transmits more energy? By what factor?

When a sinusoidal wave -tp o0n1 bqoow;1t)hg crosses the boundary between two sections of cord as in Fig. 11–33, the frequency does not change (although th 1tg ob0h);n1w-poqtoe wavelength and velocity do change). Explain why.

If a string is vibrat1 76ricoiy e)ling in three segments, are there any places you could touch it wit iey7rilo6c1) h a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrati kj vx63+ /,ftq6v xk3ha(qepmons of incident and reflected waves cancel at the nodes. Does this mean that energy was destroyed? Explain/jx pafx6qvh+ kq,m3v36 k(et.

If we knew that energy was being .pl6/mfg nbec:m0 *f ttransmitted from one place to another, how might we determ n:mpbfgtlf0em6c /*.ine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.186+u1d)+eqp o ajqo)tb m, what is the total distance it travels ia)1q)bj+ 6eudotqop + n one period?    m

  An elastic cord is 65 cm long when az0: ,euxfpth* tkt2+v (x y0xq weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “* t u02x h +:0ptvzf(qxet,kyxspring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-k+s wk43tb bdjoe10kn; fzf:-m tznb b)pt13* hg driver gets into the driver’s seat. If the car goes over a d +4 o)k1 -t3bnp0 t*fn3tf ewkzjmbhb:;bz1sbump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs txfs6r* 0 : dh(ujut; zqpe:;gfrom it. (a) What is the sp;qtd(zsrj:hu :;u *6gt0pf exring 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 freq n.cwrmjk) nkn; a93s(t.h lv0uency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its fr. tajcnrs.m;hk9v0kn3()wn l equency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 1klxo1*+ rak0b1–2 at times t = 0,0+l*arkkbx1o 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’rf-m:, lf+p fgs web. The web vibrates predominately with a frequency of pfgf:f+-mr ,l4.0 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 04jsztu1u r hf h.fn2u):jfd.with a frequency of 0.88 Hz. When an additional 68. : uhjt1.jf)f4z f0suhu r2dn0-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 vibrates 3.0 times per skdd;5 m( y.xff73 rley6zjs)yecond with an amplitude of 0.13 m. Det6s zk;r7de5 jm3dyy( f)fly.x ermine
(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 displacement7igqr/2j 2vpf from equilibrium is the speed of a SHO half the maximum valjfv2rqi7 p2/g ue?$\approx$    A

A mass attached to the endcj *u pg(ry(d/ 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 spr-hs6 nary4a a3 0rkz*jing is stretched an additional 0.130 m and released, how long does it take to reaza- arr a*s jhk460ny3ch the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spr9b,fix6ytezg,5jkg 1a*pvlmb o h54,ing stiffness constant k = 280 N/m and is executing simple harmonic motion. When thg, l mia4pt6 1jg zkfoeh,b,5b*v59xye object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a toy popgun 0.200mrp48n j e/a; 1kny.4weqs8 ll m to “load” a 0.180-kg ball. With what nla.r8k484mej/sp l1qw ey;nspeed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to xu: gnrv7kh 9;+r h:p-u .zpscone end of a spring; the other end .n-ur+p h:rc;xgus z9vkh:7p is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum 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 i-k/6w p9aujyi n meters and t is in secondsij/p6k ya uw-9. 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 2brj3cuik 86d KE and half PE?ib6k3 d28ru jc ±    A

  If one vibration has 7.0 times the energy of a second, but their frequencies andu8m-:,vly b4a9gcj 4 vs,zl fe masses are the same, what-:l4fjzc48s ,mev vgaluy,b 9 is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vert1dndesu;p9uht3 l.uv.r2 em6ically hanging light spring once every 0.65 sm. u9sun1 ud6hd eve;2prt.3l.
(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,j4riruy7d lxldogq ,;750 y)vyu d11s each with spring stiffness constant lolrdyi7y5x01drjgvu su ,; yd7q 41)k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates accordi 6evf*.fvg/t;x .tew dng to the equation x = 0.38sin6.5t where x is in meters and t is in seconds. ve/ge.ftt6 fvw;d. x*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, what isw u zl:wkd dh579avw/y9i:;zn+ wsg d6
(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 horizo-r3zlgzb6etgp.rd *7 ntal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.e*gzb 3- rr.d67pzgtl96m/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 stiffnese 1qd17fsi): ysck a43hq -vtmrl4wt1s constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The m)1qtwm y4-4 :1hcsa1l rqe7vdsitfk 3 ass 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,yx n/ej (n)wq0 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 attached to a fixed horizontal spring ai z6rutpk)mtn)30e;ftnl60 whose)tm ;utlr0 f)naptnk636z i0e spring stiffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.08cjx, vfu:c(m8v ijv3 kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below mjj 8cucv3xv,(i: 8vf 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 vg o.1jcw.orfj w6pbql0h783r ibrations in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum * q-/cx3 h5o ww e.eg.pr*s4ogoymzq.be if it is to make exactly one swing per second? (That is, o-x3p cym..gge /*hqqooe 5z .*sw4orw ne complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earthx dytdtm4 )u)lk6b.w5lw-46u+f gv my . What is its period on Mars, where the acceleration oflw4gt4)-mk)t lvu 6d6wx 5uy +. dfbym gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm *xz3hisqzs; 5tzid21 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 ha t(yrg +3c(/hpfiqcds.xm3s9 s a mass of 365 grams, and if39 /srt.hqcg3sxcydpi(+m( t 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 len czw88z; a1bmngth of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pza 81cm wnbz8;endulum? shortened by    mm.

Derive a formula for the maximumm ft2s7gi i/1u speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At it is released from r/avlot; ht u4kx hoy(i 1f 9dzres-9(w9:0tymest starti t0sv xw(zy-t(4h d/u r ty1l9k9i:; 9mafehoong 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 anch15hjr /7)v4ds 4dfysyav 1us9xdc(sj ored boat every 3.0 s. He measur45hva/71s(d fx sj)v 4 russj cdyd19yes 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 a x mdlo;fk 1dt2nz5z f*0x :gt)speed of 343 m/s How far dfz 1zgk5tx ;) md 0t2*lf:oxnapart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencie gsoww 4,jb*v.tq., hus between 550 kHz and 1600 kHz (kilohertz) and tu.hwsgbtv,qw ,. jo 4*ravel 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 oom6dca vsqmz(tl e(5 3+g/cc+f longitudinal 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 tteyqo ;sowi44bzo -e yzx8os-ajo+s 33:b 4:dense as the other. In which rod will the sp3tseozzaq4:ot+38 x owsy ye-4oi4sb-oj;: beed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. .8 z(r6lyxv1x gv.csv If the tension in the cord is 150 N..v8xvv1y (r gcls6 xz, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of owk*n5 kkc.r995y kueej +)ama 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 sends a wave pulse along the cable. It is observed that it took 16 s for the pulse kj k)oa9* k c9e55ekry+w.nmuto 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 thepgg6.rle t*-n side of his ship just below the surface of the sea. He hears the echo of the wave reflected fro*6g.g-er p ntlm the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and this diffe8qq09 rw5apmw rence helps in locating the earthquakeq59rq0p ww8ma “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 ouz ;0xd:2lycj 8r0cojm2 vzvs-iw 86 surface wave can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave conta-r: s8ijoy2wcv6 cjo8 02vuz m; 0zxldct with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of an earthqtvge6z d62x 0( j23dbm9 hakjfuake P wave passing through the Earth and detected at fa6jet3 md2zkb 2xdhv(6g09 jtwo points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is z7j1u7, twm) ey9kckkmeasured to be ,7 7 ycj t)kkkmeuw91z$ 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 saak :esv(9:aqlme frequency travel through the same portion of the Earth, but one is carqv la9:e(s:ka rying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a ib 9 d v;5f6ls76gclx l3jvq3astretched string have the same frequency, but one transports three times the power of the other. What is the ratio of the amplitudes of the vf7bx9q3sil65cj;d v 6l3 lagtwo waves?   

  A bug on the surface of a pond is observed to move up and down a total vertic ktko ,5lgy9*ew2bz. val distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the b.zykgl 2o,ek9v t*bw5ug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) Sketch t1n ;*6:b9qv ozc bwdm )sxsttdcl6x4 .he shape of the string at the moment they directly overlap. (b) Sk o xstlw;mn*4vxzb16 qb:ctc.6d d )9setch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, what are thet ;.ip y0 pjyrjnn(c9) frequencies of the fi nitp)y;pc9.y( n0jjrrst four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 2948l)z2vpb p.:x,hpxk; saxcl 5 Hz 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 as a lck5. b:p )zpxl ,v2xh s8;paxstanding wave.)    Hz

  A particular string resonates in four loops at a frequ5hlr rs3+nudk)a)g fm bm.of/ 8n*f2g ency of 280 Hz. Name at least three othefk n 8fsdfbm5n+uo/)2ag.mrh)g3rl *r 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 frequencqur9g/)p )3f rwk-8)ggk-w j bdq rkv:y of standing waves is/rgq rf:-) k-9wjkgdv)r3pgw q) bk8u 475 Hz, how far apart are two adjacent nodes?   m

  If two successive overtomq9;4 d h j,inm5q)k:b,omvqknes of a vibrating string are 280 Hz and 350 Hz, what is the frequency of the fundamentalmnib hjd9m5kqk4,q;,: vqom ) ?    Hz

  A guitar string is 90 cm long and has a mass of 3.6m/:y5or jst w( g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and fi5m j /(:wtorsyrst two overtones?    Hz

  A particular guitar stringwhey(jrh / 8t) bb*l2u is supposed to vibrate at 200 Hz, but it is measured to vhbw) j uy(*e/8lt2rbhibrate at 205 Hz. 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 . up+syigjml7z+ qie6 z*.v)t at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be *ipiqj).etzumy 7lv+gs+ z6.changed to correct the frequency? decreased by    %

  One end of a horizontal string is atcns8on,4a z3w:w t 4lqtached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass pers :l8won3zw qcn,4a4t 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 string48+rotiz i q.;ef pj .wppq.x. may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be x 8jr4ep .i q.i+ ftqp.wz.op;achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and 9.qu 0 0bhl9 zwb1ky-juiuo (c1tku j,forth in a tub at just the right frequency, the water alternateu 9 ,-o0 qw19bh tyj.iz 10culukbjku(ly 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. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary with 3hentqv lv;w 8ydvf muvv,k3v8 r2u:a(w8 2m:in the Earth between two kinds of material. If it approaches the boundary at an incident anglethnv8 u:e q wr:( ,8vvdyu2v83f w m3vl;m2avk 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” q5r. jwe)iia 0where the velocity changes from 2.8 m/s to 2.1j 5 qwaii.e)r0 m/s If the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer o 7 s0hysxalr54+)vqqx 6 c(ridf cold, dense air. If the sound wave hits the cold air interface at an angle o0ssc+q4x)5rx 6vd 7ahyirl q(f 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 earthg8 h)1z emt;usquake wave strikes a boundary between two types of rock at a)mhs1z;e8g tu 38 $^{\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 0.5r+)xfo h03ch b. x0foj.nz) yx(-lfwq m in diameter. According to the user’s manual, the dish has to be pointed in theb()xnf.hq.-j+ h0yffo0 )x lrox w3zc direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 km/h travels across 4h jt* d sip81iu c-+r9k2yvzjthe Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died ucytjvd*sk 28h 9ji4- pr1z+i 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 consta wj-,p271kq4drlri:sonkz h(u mn3 di 9/;omqnt of 550 kN/m Find the maximum compnh79wk:q41o ijku(;2l r ,zs-irqn d po 3mdm/ression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18( .b 6 gpnb se.)5exl-u/u*veaa 3saaw m below, which stretches the net 1.1 m. Assume that the net behaves like a simple sprin5sea.l6ax uea*u bsb g n/e(p3aw.v-)g, 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 pla*xb3bmc 1xyed cb -fuci.c2 1,ced on the end of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frf3,d2 uybb1m eb1ccc .c-xx*iequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed ofgo8 b1;ejiq*zwpo)r . 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is tq o1p)*z8;erbi j .gowhe spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just thw0b k*w jkyj65e right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves inkj56jw*yk b w0 the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the cenlh1iw:*v52cbxn xe i1 (-8blhq4d zpg ter of a 33-rpm phonograph record have axvhlb* dh2-(bw18ei1zgc4 x:q p i 5nl wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equ3.s .tm1h7ytbp at nr:ation x=0.650cos7.40t where x is in meters and t in seconds. Determina1:3..ynh ttprsmbt7 e
(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 frequek)(in ppigz ,+p/so2 wncy f. What is its frequency if it accelerates at 0.50g (a) upi o+,pz/pk(n) wpis 2gward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lakx rbd) k17eeih s8+in*e. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the watebsi+ ihxr) de7 18ken*r. 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 instrumx8yta)*c6 ew2.falg* m-r ngsent are tuned to play at 392 Hz (G) and 440 Hz (Axrf*.g e * c ym2slg6a-8wtan)).
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stretched two-part cord of Fig. 11–3r7ku 7b +xf)kp1wv0 eh1g8cpd6h)vx s3. Determine a formula (a) for the ratio of the speeds of the wave in the1sk xrxh) phw 6p8cv 01+u7gf7kb )dve 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 t01s4y,pj pjgp ip of each prong moves 1.8 mm to either side of ce 0 1ygsjp4j,ppnter. 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 harmosi (rldz80 g.tnic 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 (Figsr d8(it.gl0z. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” enu)x t1:ew or27ilm5s td if that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one em1s:rtw2lto5 i)7 uxend fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.0kv i(rmc y xw;9k 74iqc9mc81c00 s — each one-way swing takes 1.;9ccmm4kv (cwi1r9qcyxi78 k000 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 (vpz+5ybs ,wvthe vertical direction or can swing as a pendulum of s+(, yw5vvps bzmall 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 stretched under a tension of 255 N. A pk sz1gv7f*)2i ;h wjlhulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where wisf) lw;j12 v hki*gh7zll the two pulses first meet?    m

A block of mass M is suspended from a ceio o82om(; 1vhuagzs4ro jqi *;ling by a spring with spring 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 to just stay on top of the block? (i;g uqoj8 41mvzo;2s( oroa *hAssume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cable is 22/p pk,lvtmsbm1w18 pm lm867f m 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 bouncin1f8 mpt71bp8lm m,lw6svm / pkg? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a .ek,t-udt6gtwb16; hnel p0qplate as shown in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimgbt0q tl;e.6enk1, dwu t-ph6ate 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