Give some examples of everyday vibrating objects. Which exhibit Sl7j t npyp976eHM, at least approxima6 ltp9pynj7 e7tely?

Is the acceleration of a simple harmonic oscillator ever ze le 1e)/ev4iwsro? If so, where?

Explain why the motion of a pi5oi,zmb 8 w.qz:d.zi qston in an automobile engine is approximately simpleo.qzqzi8 b, :wd.i5mz harmonic.

Real springs have mass. Willa60 ittp y8tr1 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? Explai a t1860rtyptin.

How could you double the maximum speed of a simple harmonic oscillatorlot7 0t 6mp,c3r:dj fr (SHO)?

A 5.0-kg trout is attacho:cq13qsz 5jh k o 58sh22bjbfzpv.j3ed to the hook of a vertical spring scale, and then is released. Describe the scale re5bo18.sjjv2hhpcf s2oz jk5qq zb3:3 ading as a function of time.

If a pendulum clock is accurate at sea level 2t tvck5m/uc:, will it gain or lose time when taken to h :u mcc25tv/tkigh altitude? Why?

A tire swing hanging from a branch r;sh (0xjwv8zy nlm a./eaches nearly to the ground (Fig. 11–48). How could yhs wz;m.(v8n 0 xaylj/ou estimate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only job br(dc/77h1ypd7 o if you shake the pan at a certai7b d717p b(c ho/dojyrn frequency?

Give several everyday examples of akya .j:;d,ak resonance.

Is a rattle in a car ever a resonance phenomenon? ax;3 k6mc2ksz ;7 sfwjExplain.

Is the frequency of a simple periodic wave equal to the frfihk:wlq7 m( b 9pz8 -+ham/ygouj54requency of its source? Why or :g h5a pofmm(98k4 ir-hw/ql+b7ujzy why not?

Explain the difference between the speed of a transveh4e;j(7jpd tt,:i8x xi zs jc1rse wave traveling down a cord and the speed of a tiny piece of the cor x4 izjics,:7xdph1(;et jj8td.

Why do the strings used f8o6j64x/ jmtp9u*7m 7cqbp)f ,hy0lpt itk jqor the lowest-frequency notes on a piano normally have wire wrapped around them,u7m6* 4m/70bjtp)6 pq8tj jhfl qx py 9cikot?

What kind of waves do you think will travel down a horizotzhkxp*:k 5umb mk6:7 ntal metal rod if you strike its end (a) vertically from above and (b) horizontally parallel to its lengb6 m khu:k*xk mtpz75:th?

Since the density of air decreases with an increase in t1l5..5p+ lgco(v(zdp kg6 p+gtitil*yj+ ick emperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waz* g.(5+d lt+i5ccyppg6+ (ikio tgklv1l.pj ves in air to vary with temperature?

Give two reasons why circular water waves decrease in axw olg u4:;s5zmplitude as they travel away;lw:4z sx o5gu from the source.

Two linear waves have the same amplnsll l3q u8)lob;e1x.itude and speed, and otherwise are identical, except one has half the wavelength of the othel3b8l;u ) ls.olen1xqr. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary beh43yqy dpm i+p is8bj 42db)i(tween two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Exhqi i(2bd)s8m+b jpd3iy4py 4plain why.

If a string is vibrating in three segments, are thpkiu7q.0s a t6ere any places you could touch 0aukt .7psqi 6it with a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrat qrot w6f9grp:ckl )x15f;s;rby2 e;kions of incident and reflected waves cancel at the nodes. Does this mean that energy was rgp 6r2)sefy;;rfxlqw9k;5tkoc1 :b destroyed? Explain.

If we knew that energy was being transmitted from one place to anothblesv;c 1k. 67;ieu cber, how might we determine whether the energycluv 7e;bie6kc;b 1.s was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what i-n+bhkz/ 4l 7 d,s)-ddzw f 5s(aqfrnv8h,dmls the total distance it travels in one 5n(k)fdbdhf8sr +dh dm-n lz/q4vw7sa -z, l, period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but is 85 cm51lv1*iaf: +0 on. kkzhcf q t*qcv1ve long when a weight of 180 N hangs from it. What lvc1ffvk1*eqz avqi 0 :*+5.1kch ton is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 m;gn60wgy *(b jhlqu -xm when its 68-kg driver gets into the driver’s seat. If the car goes over a bumg-*xjlwyh(u;b0 6 gqnp, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale strelwy+,hro; 7 ufv+ 1g y7*odlzktches 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stkgo,o 7v;lrdzhyy1 7*ul w++ fiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mass of 0.60 kg istucm a3-2cfc* hung from it. What is its frequency if only 0.38 kg hangs frocfc2uta *-m3 cm it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at ti/ty(dfu:sb 8m mes t = 0yu8bdm /s f:(t,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 t 5t(ygyq . n)uj-zg9 *n(vrphg is caught in a spider’s web. The web vibrates predominately with a frequency of g9( *t tnqpzj vug5-(yry .n)h4.0 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 frequencyi mkc5p /22rcg of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hzpc2c gkim2 /r5. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second dn)e6 h ova-cyf 8y(s(with an amplitude of 0.13hn8eo- y6c)( vfy(d as 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 frd2go+ hfi3ak z*:;3pbe pw7 lkom equilibrium is the speed of a SHO half the maximum valu3od2pp a;:klzb f7g +eh3*wike?$\approx$    A

A mass attached to the en5il)1.w.z b0jq q gbcud 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 springb9e,w.w j4 6lavyym1z is stretched an additional 0.130 m and released, how long does it take to reach the (new) equili z y w.mvy6ebl91,wj4abrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffness kk3fss1- gxqdx9,-*pu qni 4k:y s qi4constant k = 280 N/m and is execut4i-q3fy n9k u:- x iksqq1*s g4dxs,kping 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 80.0 N to compress the spring of (nktt9l-)fasr 8e8 h6t+gow; mp) qqw a toy popgun 0.200 m to “load” a 0.180-kg)n 8r- go)f tae wsm;tl9(q8hq wtpk+6 ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, w0u (h3 bych;efrictionless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the sprin3we h;uyc(0 hbg 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 = 05f wwd6 i,cx n6jhlj3xvf,3) vx) 0jot.45cos6.4t where x is in meters and t is in seconds. Determine ,,i 3jfj n lvwcd0fjwhxo3x))x5 t6v6
(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 eqm.zq++sy z h8kuilibrium is the energy of a SHO half KE and half PE?z.+yhkz q8+ ms ±    A

  If one vibration has 7.0 times the e 388 u,falhnlbua+r/ rnergy of a second, but their frequencies and masses are the same, what i nah8a,f/ l3u8r+blrus the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscilla6pj33kueen ah4mb-+m+q* bf ctes from a vertically hanging light spring once every 0.+jf3e*b+nk me6c3uhb4aqmp-65 s.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two idenb-qeh l t1er -,7h sp;,xyvdg.tical parallel vertical springs, each with spring sty--b.xr se, ldghqpt7, v1;heiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equa5/b(mksbp( 8 zex4ci ation x = 0.38sin6.5t where x is in meters and t is in seconds. Detek b4cap 8miz(/ (exb5srmine
(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 SH /bsg wj9,y0fyib(6t hM, 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 q 5p c8kah;nxsemx/65 of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed 5cm6s/ xkp e8q5xh na;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 withkf. ua,n 1o.6v.slif v spring stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes thr 6ai.kfv s.vlon1,f.uough 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 t4mo,z +ysf**uky at.iwo springs, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed horizola 9ffzv*z d;q al/t37ntal spring whose spring sa f l*9fvd/ q;t7zaz3ltiffness 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 jumhx1)mev nk 9.pps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point )mv.en1kp9x h eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations ine) jip (9 1m7co3my*ij jal,cw exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if l6)s*1e vdrawit is to make exactly one swing per second? (That is, one complete vibratse 61r)d *walvion takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is 2,lxn1o)*gafr:su )s4xq wfj its period on Mars, where the acceleration of gravity is ab wjs4r, qx)1ufx 2lao fgn:)s*out 0.37 that on Earth?    s

  What is the period of a simple pendulfp )9yru3wt: kum 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 bob hac r0;* nthf3crs a mass of 365 grams, and i ;0hcc*r3frtnt 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 ) ujv/itkcvh1u*amye*,c/s: pendulum has a length of 0.9930 m. If the clock loses half a minute per day, how shou)/ hj*,kcvtavu1 *usm:y i/ec ld you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the vqmlad (4 t7 2eo+ur-amaximum 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.dmi:wo3- yx32xy9 tlb5 Hz. At it is released from rest starting at an an9t2mxyxy3l3 d bo: i-wgle 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 ev(n,,1iugf 6r un *j-sugj/j w) urh7vpery 3.0 s. He measures the distance between two crests to be 6. 6)rigjpu*j ,ngu-unv1uj/hs,r 7w (f5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a +mtn7 ;oxoh0cb u oqa-o13te,o5qh +jfrequency of 262 Hz and travels with a speed of 343 m/s Howo+t a1h; bo xq,ot- m57o+uj3 chnoeq0 far apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilohertz) e(s+jv:(ig3 vm zt2jmt; y (sdand jst (s;j :d+e(im vzt g2vym(3travel 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 oub2 *uxssve6:9t:)ofj bk6o n 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 d-rzskb w.qa69( w-.gwd,xojlh) v n-nense as the other. In which rod will the speed of longitudinal waves be greater, and by what facr-a.)vgsxkwjwo ndq( -9z.b ,n6-w hltor?   

  A cord of mass 0.65 kg iswjvzfpk* +utezsg+ed-7 3p1 cjn; 3(s stretched between two supports 28 m apart. If the tension in the cord is 150 N, how long wi+f cez;suk- tj7dg jn( s*z+pep 3w1v3ll it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of len8g p+5s: lnaiwgth 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 theal:ws 8g +ipn5 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 jus tqkzmv+vcga4c67cr);h yb 33t below the surface of the sea. He hears the echo of the wave reflected f63vyb+m t ;q74z)gacrcv3c k hrom 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 differenczpyr*74zb gj *+j.o1,z xuz(ad uli2ve helps in locating the earthquake “epicenter” (wh bz4 zxj+z7 2, *ildgy.jupour z1(a*vere 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 wala7 o*m1crkf/ ve can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz ol*fm/ a rk17c(typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intee 9y ,qbk/ac a2n+rnp,nsities, and (b) the amplitudes, of an earthquake P wave passing through the Earth and deteqe ,yr2kpa+ a/n 9nc,bcted at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measw (a kar7e: pi0nf8,bv1quj9 dured to be v8uknqj:e a b19(0ipd7aw r,f$ 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 frequency2u/t+yoprmxz 9mb/s 2 pz/d-w travel through the same portion of the Earth, but one is carrying twice z29/zr p2/-/ sdy+ upbx mwmotthe energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, but -koh m 739 gbdz-q 2jk/:isfznone transports three times the power of the other. What is7dg-b32zifo9 j/snq-k kmh:z the ratio of the amplitudes of the two waves?   

  A bug on the surface ofd gabxm/37nw gojv gweg x5/,h,:-sw. a pond is observed to move up and down a total vertical distanceobx 3g7wsjwhgg:// ne a5v-mwxd ., g, 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 bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) Sketch l dlnwtzv 5,:v/ s0mue +3+ejrthe shape of the string at the moment they directly overlap. (b) Sketch the shape , e d+jmvw5:+30r/ts zv unellof 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, whil.hh j6*:dc.jx m8 jyat are the frequenc:8hjhjim6y.d cx. lj *ies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at acpvil4p -* mqu u za:t;3h7-xuu:2fj 294 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 st7uu:pztf; juc3v4-upl 2a: *i-h mxaqring vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz. Name at lefuu0sbjo 8 4r(i ):o 4bo0mntzast three 0)b8 jt4(:uomb4uzoi0 rn sfoother 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 4t37g bp 9oj7 cerfi4tw6yg5u If the frequency of standing waves is 475 Hz, u445gc9w ijg 3rbe 7tfyp67othow far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz ads3:e 6p2 epfhd)kq n5nd 350 Hz, what is :qndfe p352 h)sdkp e6the frequency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance from gqi 2xu3.sm1xthe 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 first two ovequ1 mgi. 2x3sxrtones?    Hz

  A particular guitar string is supposed to 5cfq.dep v*m v- 8g4awo8m)wbvibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the threvm8* 8bw4 c-5.pwvefam )ogdqe frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed tovt3hlly5kq: f8q4,l mbx 6 ,lpz65lg v vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the fre vg4665t8pl k lmq:,xlv,yzqbhl lf35quency? decreased by    %

  One end of a horizontal string is attached to a smaloh o+ aozsxx5lr+(9p2)foo 5kl-amplitude mechanical 60-Hz vibrator. The string’s mass px ( r + )zo9koofap5shlo2xo+5er 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 by movin zi1lasn, dphj :/2kfs:qt 6l3g 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 between 10 cm and 1.5 m? q, 2dj:lk6nl zi afh1:stsp/3   

  When you slosh the water back and forth in a tub jv+8yl77z -cdtq1x xealv8s3at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed o+ejlyx x-3dzctvaq78l v18 7sf the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a bo3umtu iuz i 4.6eh(6leundary within the Earth between two kinds of material. If it appro u(4t3hez 6.iliu em6uaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” wher ik3m;za ,7a blsvjx81e the velocity changes from 2.8 m/s to 2.1 m/s If tkm8sav,;3bja1 7lix zhe 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 layeiad5jl(ajo u1*z /r*pr of cold, dense air. If the sound wave hits the cold air interface at an angli d5 p1 *ojra/u*lajz(e 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 .xcg+ 4jq r5ybbetween two types of rock at a 38 jy.cbrgx+54 q$^{\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 ux zj86r9sayd7h bx3hxz(pn;/ser’s manual, the dish has to bezx3jxbadh(z8y shprnx7 6 /;9 pointed in the direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength5b,5orbvd 5fv5c pc 2aa-xl 3j 250 km and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do55vap2o3 -c jrx5,vc fab5dl b 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 sprii54t z4a4 thb nv-6x fbfc*cr,ng 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 2,6hbv*-tzn4xa r f c4bi 4cft5.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps frze:/ :j9k7i/d wseotpn4c4 zqom a window to a fire net 18 m below, which stretches the net 1.1 m. A4c wz id:tn qz47/:po kje9/sessume that the net behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the l3bn;3 alevq1end of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the freqalve3bl 3n;1 quency of the oscillation?    Hz

  A 950-kg car strikes ati7zzp/cb.yvqo4a *d cq *-j: huge spring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffnes*:o7 zcq tdi.ybpj qzacv*/4-s 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 the right pace 175 kj3q: jkfb5fep/q m) tsxfof about 1 step per second, the coffee sloshes more and more until eventuallyjkqf 7 qes x/jf3:m5k5t1f)pb 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 the center of a 33-*/fdydi8pcvu6.yc2 1 ne.1ps)waz fjrpm phonograph record have a wavelength of 1.70 mm. What w.w c*p 6u.i 2fvp/scjzy )n11 ya8feddill be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to tht; d5d (lz35hjyx o5lfe equation x=0.650cos7.40t where x is in meters and t ind55 lohx3;t j5flydz( 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 freque kf6k ssrnjkp,1wz a; f5p-5v+ncy f. What is its frequency if it accelerates at 0.50w kk;a,npp 1 jss6 v5rffk-5z+g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands bf9nlmbvz7;crnr4ny *dfxdv ,3a,je+ 3 9lf ( on the raft, it sinks 4.0 cm deepem 7f+x , l;d fj4c vl(e3db99zb*ra,nnfvrny3 r into the 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 hk sgq;xt31 i,play at 392 Hz (G) and 440 Hz (A).th,3 ki1 x;qgs
(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 co savdu+p.ojjm q -c:909demz8rd 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 secps-vj0u o8zcjmq9 d 9m :ed+a.tion, 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 frequencyldk - 0p-f8qcy of 264 Hz, and the tip of each prong moves 1.8 mm to either side of centery-8lq-df p0 ck. 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 simpo 6v qmqg2ru-hv1 :gx//q/p ggle harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the bpuggvqvg 1r q-xg6/o2h /m/ q:oard can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a ring thaiz/ 9b5 nw3jheb,c pc,t can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a strine/c3j b,hzw9n ip,bc 5g with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swinm;wgc q.6) ala +h3xkxg takes 1.l kw6);xqa ac 3m+.gxh000 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 verti:f jhaky-j6t6fk1z 0xcal 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 of the horizontal swingskth10fjj fk - z:66ayx, 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 12omdhi3 7td4x (+lsaa/vw9o -x 3 g is stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is9iwh a3+lxasmod/txd(- o 47v 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 sp5l8 nw25tp 6ilpoh*kjring 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 wil h6 *lkwlt2jp oni85p5l 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 nv5y/k uzyyaxgi w249 )ps7*q steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze star) 4q57gys*z/ay2v9 ik p xunwyts 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 alm nu .5pp8cj:dso gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello :c 8j5pdnm .upsprings 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