Give some examples of everyday vibrating objects. Which exhibit SHj/dj te;v9r o8M, at least app9dvt r o;e8jj/roximately?

Is the acceleration of a simple harmonic oscillator eb 92:q 8qsh ,4mafp/b lha2fktver zero? If so, where?

Explain why the motion of ajtbwxa 7**7e2 i3v vq.t 2kjbg piston in an automobile engine is approximately simple harmo73 v2q* t* avtie b7w2jbg.kxjnic.

Real springs have mass. Will the true peri-/p+ b gn.fycwod and frequency be larger or smaller than given by the equations for a-cfnbpwgy ./+ mass oscillating on the end of an idealized massless spring? Explain.

How could you double theh/m jw0,/d, bw9d4av q w; fwulj7lmw; maximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale,z ,vc 9.2joxzj, bju-mpoa ,+a and then is released. Describe the zup9a,m2azjo-jo. xj+vc b,,scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it tl/huiqz:tk 4i,)*nve r0t 4pgv ,+btgain or lose time when taken to high altituttt/ni*vpb l4vr,:)zet q ,i+kg 4h0 ude? Why?

A tire swing hanging from a branch reaches nearly to the grounqgn+u9gc rey;g9p67t+f/kd ed (Fig. 11–48). How could you estimate the height of the branch using only a cdg ;96uf+gr7 n/peq y9tekg+stopwatch?

Why can you make water slosh back and forth in a pan only if you shake the py /1 dd2da(thkan at a certain frequencta d2d/ d(khy1y?

Give several everyday examples of resola t (7,koeef-qj/9xpa wa2/wnance.

Is a rattle in a car ever a ren/ynx j2m w:e+2ef b -ot0pfm(sonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequenc7: +n-uclbj qzy of its source? Why or why not? qbulj c+-n:z7

Explain the difference between the speed of a transvwlyrt-142 l9rjz -zxlerse wave traveling down a cord and the speed of a tinyjt-rw4lrlzz2 xy 1l9- piece of the cord.

Why do the strings used for the lowest-frequency noteahb4 f4a 4ino1+w:xtes on a piano normally have wire wrapped a:nh w1efi bo+4t44xa around them?

What kind of waves do you think will travel down a horizontal metal rozt xx qozc3a8 kt,8zn 34+phs5d if you strike its end (a) vertically qt4px5zxz 88+s3zkn3hotac , from above and (b) horizontally parallel to its length?

Since the density of air decrrpis/ b6 ra/9reases with an increase in temperature, but the bulk modulus B is r9i6 pb sr//ranearly 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 ampg/:- jsc1lisn litude as they travel away from tnis1/ j:glsc -he source.

Two linear waves have the same amplitude and speed, and o-k60 j grccsf3therwise are identical, except one has half the wavelength of the other. Which transmits more enj3 s0ck-gfc6rergy? By what factor?

When a sinusoidal wave crosses the boundary between tf 3cv2,qmwes)l 1 hxf4ou ).uawo sections of cord as in Fig. 11–33, the frequency c v. )eh,3s4 wmu1xq)ulffa2 odoes not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, arq dah/q50 d.zke there any places you could touch it with a knife blade witho5 0a/zdhk. qqdut disturbing the motion?

When a standing wave exists on a string, the v20s8m 3 qo 19/ ffi17pivroehkql 6foayqt0x5ibrations of incident and reflected waves cancel at the nodes. Does this mean that energy waaiqv9x08e7y0 mihf3k 26 1tp ql/ r5ooffo1sqs destroyed? Explain.

If we knew that energy was being transmitted from one place to another, how mb.+t-hh j-zpnts;q lo1su5b qm9:u e6ighl9:-qtpt 1n+ sbe5 ob6hhsu;mq .-uzjt we determine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is thqc8uy/pnse-mf8m l nkfg m/t3 * 05uk.e total distance it travels in0*u3fs5fy 8-.q klut8 n cm/ekg n/mmp one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but is 85 cm v dnvk;7.4kpt4g)l 1 ok0 jhwulong when a weight of 180 N hangs from it. What is the “spring” ku4kk;j4 plv dtowh 70v).gn 1constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mqk 7jp2-2nue :gqwkx8m when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequency of :2e kj gk7nqp8-2wuxqvibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish h /jzuu zi.:7xlangs from it. (a) What is the szu .:xzu7jl/ ipring 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 w u j )zu-mnk4r6rj+ p/t4rmiz8ith a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs from it? mpr t/ku)-jrmn6i4 rj zzu+48   Hz

Construct a Table indicating the position x of the mass in Fig. 113/).gx e5tjw3vh nae(nf cfp)–2 at times t = 0,t = j 3 fx(e/5).eatn)3vhgw cpn f$\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 b,,h +dq;06d6pop b6,dnsjb a lmxa6ij,uz2h in a spider’s web. The web vibrates predominately with a frequencobj u6jdbap hi ,,6a,,s q0+;hlzxmdp b6d2n 6y of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency of 0.88 Hz. When a sl 1i+kch4ax5y,q zqa y,d25in additional 680-g mass is adds4ck+ ihqyaa,,55i2 z d q1yxled to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end off)*gg1zt(x byg- na+ 4qa ra;y a spring vibrates 3.0 times per second with an amplitua y4 )* a;agybt(g1grf+x n-zqde of 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 half the max +-c)gc *n2yuerq9.k7:gu7wdbny ztaimum valu un*2ryczbet-g 7c +u7yqg :a.wd)9kne?$\approx$    A

A mass attached to the end of a spring is stretched a n td+*t,3:* mnuii 3dqr6bg xudistance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. If the spring is str k:4bg)r ;peam rlpdk3j89/4 ggqz1mxetched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium poekqlkbjga zgrrp; 8 9x1m4:d )g pm4/3sition again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffness con36 om ;sdc*bvzstant k = 280 N/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 0.55b v z6scom3;d* 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.o 7jeinl2q :t.200 m to “load” a 0.180-kg ball. With whj7e :lqtin2o. at speed will the ball leave the gun?    m/s

  A mass sitting on a horizonta7 h mg()s,jzonduyt8u0(ta p2l, frictionless 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 spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experienc0dshomtn7 gy ,2taj(z 8u)(u pes 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 = 0.45cos6.4tn *t): /rtnzpt where x is in meters and t is in seconds. Determinetp* rn/t tn:z)
(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 ayytq:xab;vxi y;0 q6k13pd i7nd half PE? ±xy: iqd x vqky31y06;b ;tiap7    A

  If one vibration has 7.0 times the energy of a second, but their frequencies anl kisb63q 2hy3z1y v34r /0xmj ;*r*twndpzh ud masses are the same, what is the ratio of their ampliy3 l2vdjwrm4z *nb60k*3s;31hh ituz qr/yp x tudes?   

  A 2.00-kg pumpkin oscilla-rc9,ie x/c4bxh4ja** tprm btes from a vertically hanging light spring once every 0.65 s. 4em ixa*c,-c9tb rp*hx/jb4r
(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 tx( o.3fl q zdu;)bjjw5wo identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will b. q(5 xfuzj; d3lw)ojbe the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x is ing0 3.n ijgpr(ldr-iq,n)+kao meterl+dingaj- ,q i 0p3.rogr(kn)s and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and Beetmbb3s 6*r3. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal spring (k3*wlpkr /+t7hhu 9xjv = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s 73r wv/lhjk tu 9h*+pxDetermine
(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 cop+y9l ce lqxx8+dms* (shs41q nstant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with posi 4(cq+lh1xssd8 9xle+m*q ypstive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring stiffness constantf zay+,-g-x:8g hwji 6r3wvuys $k_1$ 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 attacn 0bb7tzy *lv2hed to a fixed horizontal spring whose spring stiffness constln* 20bv7 bzytant 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 m2w6hk6 :s eoe flezs7 :rf35ijass 65.0 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 fif ss l2w ee76z3o :r:5keijf6hnally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 60 s. Whah(v 4h m8l0md rxnf9e4t is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendufmq he1ne 9)r2ta, ib(lum be if it is to make exactly one swing per second? (That is, one complete vibration takes exactly 2)2i(q9ae brh n temf,1.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its p/nho s)rsl9uw3a(wz-wd/ c l 5eriod on Mars, where the acceleration of gr/w)ls9oc hasdn 5-r lwuz3/ (wavity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm long 9 ns;v:sk(qs;z(w e5z jg4 ivf
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulumg0t 9ue/ vk2q ls:xpj7 is 0.760 m, the pendulum bob has a mass of 365 grams, and it is released at an angle of 12.0 eq7sktpj9v2x / u0gl:$^{\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 pe+7s.bj xkvd(harb7: yndulum has a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of7dx( syb7:+.kar hvjb the pendulum? shortened by    mm.

Derive a formula for the rpu .re.)hlk0ab*v 6jk .k2ppmaximum 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 H.k k9 qu:gs dzsymj-zh1nc64) z. At it is released from rest starting at an angle of.jc4 zyk k1u -9qgmh)zs:6dns 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 thatos p :8 xufqp9x/4cc0t wave crests pass the bow of his anchored boat every 3.0 s. He measures tc: 0pc9 xto/ 4q8fxpsuhe 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 1(vwpy**x;9ridrggq,l e ,s mand travels with a speed of 343 m/s How fali; 9s x,1*qm e,rvypgd* rgw(r apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHzz4g9idw )h)wwedz4ou,)9kdi and 1600 kHz (kilohertz) and traz4wd)we dz9iu),94hi)ogk d wvel 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 lonzyj /1nqvbjw 9s3.xv)gitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, :dueqig9 r+jli0v -; kbut one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, and by what factor? ii+gqe udrl ;9-:0vkj  

  A cord of mass 0.65 kg is stretched between two supports 28 m apa,g hmrkj+a8rsy1x ru1z t-6:ort. If the tension in the cord is 150 N, how long will it take a pulse to travel frohu1-zrj86 : 1k saxm+yg r,rtom one support to the other?    s

  A ski gondola is connected to the tomffh5t roo )ig7)lc(2p of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observedh7m2 fg5 o)coil )tf(r 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 94y:ry vv ,bwi( zjc/vthe surface of the sea. He hears the echo of the wave reflected v c v(r,j9:vz4/w yibyfrom 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 diffe opdff5xz: ziu2a- x 4evx 05byrb3k*-rence helps in locating the earthquakebfervzu4*2ki-o 5 xz0x5x-b3yfa:pd “epicenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave cafd xgmx:101 e1xsud g;n 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 sdg01d1 x ;u1esm: gfxxo that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of an0m2 3is f2mzby,o-vic earthquamfb 0yimc2 oz,vis 3-2ke P wave 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 through the Earth is measured to bbz-d7c 2.dvghe d27dhz -g. vbc$ 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 sameoj/ rmp78/tf f portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of the two ot/f7pmf /8jr waves?   

  Two waves traveling along a strvivhn ,:+ty ;wetched string have the same frequency, but one transports three times the power of the other. What is the ratio of thevwh ,:v +;ntiy amplitudes of the two waves?   

  A bug on the surface ofrm15x+o e1:wfn-ri 8wcxrg se pk5q,/ a pond is observed to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cmrige,5k8 5sw+ enmr1-:xwoqprxc/f 1 , by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a)p :7.o s,xrpxgzj;l a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straixso:).xrpa p7 ,;jl gzght. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its ot0t(y ek+7z4d9 w*kybul7/ c di/uqlfundamental frequency, what are the frequencies of the first four harmonics?klkz wey ubd*u( t9cdl7 q7+it /0yo4/$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency will if8w s* x9+1hhvtsv, d d0)qzuc6yx tv/t vibrate if it is fingered one-third of the way down from the end? (That is, only two-thcfhv8*+s 0dqyv, su/wz9xhd)v tt 1 x6irds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four l yg(5dlyxu 6h/oops at a frequency of 280 Hz. Name at least three other frequencies at which it will resox yd(6/5hl ygunate. $f_1$ =    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 waves ,-xnb pjru2l.is 475 Hz, how fa u2lj.px,r-n br apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 3501qtoyux p wc)2um49pb.,y ml* Hz, what is the frequency of the fundamelc* pwtu x2 mby9uy)m.q,op14ntal?    Hz

  A guitar string is 90 cm lkwefxy eb( / gjup82tjo3l n q9)010iba .x.nzong and has a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What atfqb2ku w1i)e/e9jzxp.l0 n g(n a0.yxb 38jore the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is oauza-f2+8s 6wmo g2omeasured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequencies are zu+gasooo62am -2fw 8,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibn*oh7o5q bik8) 2lv lurate at 200 Hz, but it is measured to vibrate at 205 2)*iq7lv8o bnkou5h lHz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude me f g:n9ycxm9q4chanical 60-Hz vibrator. The string’s mass per unit9c4xf:my n9 gq 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 moving the pulley3 dwh w6 bfa002zftvt7o zbv3*. 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 mz th3 tv7ad 0*vbfo3 06wwfzb2?   

  When you slosh the water back and forth in a unjyb6 +3uxi nex::s /tub at 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 Hzujunsn yxx:+e36bi:/ . What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary within the Earhi j9narq1/mxyd d 76,th between twrxi 7 ajndyd6 q,91/hmo kinds of material. If it approaches 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” where the velocity changclmi :j pb/8u+es from 2.8 m/s to 2.1 m/s If:c8+iupjl b/ m 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 lay(/2fyol2tk k zer of cold, dense air. If the sound wave hits the cold air interface at an angle l yz2kk 2f/t(oof 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 strip :9cabf ii-k7q)cmn4kes a boundary between two types of rock at a 38-i7 9kqc f4ci: ap)nbm $^{\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 thezy9n cxr.hc xfqd 02,5 user’s manual, thexr . 2f0d95hqnxzcc ,y dish has to be 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 wavelength 250 km and velozufhp h1o6x5x.cm5 p8city 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in x.x5 zhpmp56hc18 ufo the 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 sprin:5qvk1h hl/s.s +z snjg stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 1l.5 h +nvsssz:h/qj kkg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which stret; vloyxpp(f7 ,ches the net 7vppo,l( y;xf1.1 m. Assume 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 end of a freely hanging spring. The mass kqr.yv w/ 4s na*eqcp5 5n2pr9then falls 33 cm before it stops and begins to rirp knr en2q /ywpv945a5qs.c* se. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge sprinl9k+8cbhdtmh-8y ,e gg at a speed of 22 m/s (Fig. 11–54), compressing8yde9b-mh gt clh8+k, the spring 5.0 m. (a) What is the 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 j d lla83ms8a83 irp)6zmov2d fust the 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 wavesdf)3alis 8 la 6r3pomdz288v m in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from thrnu7- n u (eh,a;vw(lltc- e+me center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the fre un,l-em( wa7; t(-euh+rvnlcquency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to -c *n8oog;:fpy3 nmqamqu ;l0e ,mae 4the equation x=0.650cos7.40t where x is in meters and t in seconds. ;uo8mn;l:,p3ny gae0*4mqc o mafe-qDetermine
(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.ocs,z5; nb /hw What is its frequency if it accelerates at 0.50g (a) upwarchw5 no, /sb;zd,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on th d 9g kklg0klf24gd7sa v79ewao,tb+3e raft, it sinks 4.0 cm deeper into the wadw k43sgkf b, dl tol9v20 g7ea7a+k9gter. 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 a pvrf 5sgyj01(t 392 Hz (G) and 440 Hz (A). g 51r0(jvs pyf
(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-g:nk242jbpk+ 3e+pl y-mchb x 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 wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength gk-nlkmbg3+y bjp e+c4: hx p22reater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip wlwhs)n/ 7:tnu7 )er(pcwln, of each prong moves 1.8 mm to either side of chnsl/ n()p7u)ew:l twwr c,7n enter. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates we-t(t omb6u,8pb*w xfith simple harmonic motion of frequency 1.5 cycles per seconbu bt f8wp(mtx*-6e,od. 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 oscillation?

A string can have a “free” end if that end is atta . gry),3hy;dkwiga* pdb u1urco)d)7 io0sg6ched 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 end fixed and tbpar6c)u ho7 *k)i 1 .3rgsuwydg y,0) d;odgihe other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swing u+ 8v8c/1(mpb(m uab :anavvjtakes 1.000 s. +8u: v p8 m nabaau1(mcbv(vj/
(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 vertical5+hh boovuh.0 cj6/xr direction or can swing as a pendul+ uhh r.oj vb0x6c5/houm of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched under a tension of 255x5d j b1(uhmtx8p +qzl -4nw*q N. A pulse is genera(54 xnqwqjp1* mx buz8tl- +hdted at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spnmz,qvbirci a4i-sq+.r,2.t4 pbd u 4ring 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 jus+4bidt 4-n2, ,acui i sv.. bprmqrz4qt stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at+jms; :ghlttx23 i .v* zm(zls the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouh vgt(lj3im:2zts ;z+ .l *smxncing 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 (whic / h+mene1 .4/na( 1dymfyuhtvh also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello f11d.( /hyn/yen av+4eumthm 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