Give some examples of everyday vibratinnd(y+p)kgl( fg objects. Which exhibit SHM, at least approgf+p) ndl(ky( ximately?

Is the acceleration of a simple harmonic oscillator ev3 q/tq*hg9zlj er zero? If so, where?

Explain why the motion of a piston in xwyif2 4(uj d -s;mwh*an automobile engine is approximately simple harmon(-s;2j*iywdfm hw u x4ic.

Real springs have mass. Will the true period and frequency bg9cnp0 9rj*+ tib, d iazlgkw3 fb9)t7e larger or smaller than given by the equations for a mass oscillatinlnt zwr0kd3 i79+fca9g*, bj t9pbg )ig on the end of an idealized massless spring? Explain.

How could you double the maximwls0 0ftur1 .gum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring s hxgkosp:22o+6sl-m6d,uug su 8z wo:cale, and then is released. Descrss k6 g-6xplzd+hmguws uo2 8:oou2: ,ibe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or beusy )p;h p)7cp*y8elose time when taken to high altit*pe7p u)c ;e)yb8phy sude? Why?

A tire swing hanging from a branch reaches near +rj y0p)-qmbro::4xbso )uxw ly to the ground (Fig. 11–48). How could you estimate the height of the branch using only a stopwatchom)sjwrop+x -4 ): u0yqr:bbx?

Why can you make water slosh ba/lpefg4eee, - ck and forth in a pan only if you shake the pan at a certain frequency?e/gee, -f le4p

Give several everyday examples of resonaubn;qx-b70wad 2yc6 ynce.

Is a rattle in a car ever a resonanslz9hjm6a ld j*r-j3,ce phenomenon? Explain.

Is the frequency of a simple periodic wave equal to k/ab 13e )px:(cdcukvthe frequency of its source? Whypku/ cke3:1dv xc a(b) or why not?

Explain the difference between the speed of a transverse wave traveling down ad no04)z*4namoi+ py rm;yr*p cpn** zyd ioo r0m;p+a4 )mrny4ord and the speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a prc4 ls ztm64zm9 .1dpuiano normally have wire wrapped alpc6t4srz um 4d91. zmround them?

What kind of waves do you think will travel down a horizofc5;pr w j xgt9ad(4(ys)ek):4cnljwv) wv3c ntal metal rod if you strike its end (a) vertically from abov xlvjpc)e(tsv j4) 3a;dnrcc4 w): 9wgy(fkw5e and (b) horizontally parallel to its length?

Since the density of air decreases with an eotrxq2r bt(8c8 +r7j increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound (t8rq rc+7 b8xtej r2owaves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as they travel 4/j. ln(jxa : pmmi 0wmwb7j,tv+t*ol away from the so:m ,m74*tmb+n0 ax/lwv wo t(ijp.jljurce.

Two linear waves have s pf**b+5 c9:mhtob64ewb wj gthe same amplitude and speed, and otherwise are identical, except one has half pb: f649tjh w5be*+mc w*sobgthe wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary betu +-jxq;utn:-5fffc6qvu+r go 8f f2oween two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). vr 6 2fu;u- nxf8q g:qfojut c+5f-of+Explain why.

If a string is vibrating in three segments, are there anyx f a/ k,k4:2fyr5vwzs places you could touch it with a knife blade without disturbing the r/ a zkwk yv2xsf45f:,motion?

When a standing wave exists on a string, the vibrations of i 3no l :ghi2lgbz9 9eonik83u u6fuc71ncident and reflected waves cancel at the nodes. Does this mean thatl6f inu21bi u7 h9une: o9l38 gogc3kz energy was destroyed? Explain.

If we knew that energy was being transmitted from one placch md +kg+p/2 y)b* m8cei;ntse to another, how mighcs2k c/ y;+)nhd8t+mg mpi*eb t 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, wht cy:)x( 54h20bx8anxvekmlh7 ikax2at is the total distance itahn:)ehyv 4ak( x 72lxcxm825i t0xbk travels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs froyme;yox5:jlc2t/ +dpd,v ;2easp5xxm it but is 85 cm long when a weight of 180 N hangs from+y/m 2o5: 2 py; e5exdxvat,xsdcjl; p it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver gets i zer rpb9l7.w-: 4hocjnto the driver’s sea.-jroph w4l zr:c7 eb9t. If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (a) Wha1+x ) s,6ff3-nopvdg5f aydy vt is the fnx+)f 6yado1 3p vg,fsd-5vyspring 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 frequency of 3.0 Hz when a masrvb /:st3f.rq)ejf hm0sls ) -s of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangq m 0jsv/3)r.se-h l)rfbft:ss from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 1(i6z6kc4;gdq0 vm 4sximwq/m1–2 at times t = 0,t k0s ; c g(x6 /wmivm64imqzdq4= $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s w d1or-d.16 v8 ;gikeox9rl4ytlcosf :eb. The web vibrates predominately with a frequd-vx;8:of r1y1lc6 rtdlksog i9.4eoency 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 tqq7tv-uj d2 ;an additional 680-g mass is added to m, the frequency is 7t;ujqt- q2d v0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 tid(hqnbb p: tg*)x,0yj6kgy 6z mes per second with an amplituden:kpd*tyxh6b gq,( zg)0b6y j 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 isyso, cp0arqy* b/ js5dbe1i:; the speed of a SHO half the maximum valueciydsjq *sb ;: 1b yp/oar5e0,?$\approx$    A

A mass attached to the end of a spring is stretched d-qslh2lbik. e*6k,w 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)h7)) w t obli2w/gvlt m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium position a litbgthv)7/2) )o wwlgain?    s

  An object with mass 3.0 kg is attached tof44i:qv 1l+ xyq*rjmr a spring with spring stiffness constant k = 280 N/m and is exeq v1j*x4y+m qr:f 4lricuting 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 a toy po9n zf nfe)gsn: )p5i2ypgun 0.200 m to “load” a 0.180-kg ball. With what speed will t nff 25)yie pzgsn9:)nhe ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is atxx 4f e+9;y5 7hgrofpptached 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 expexfg54r9x; +7hyepo p friences 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 aj)) 37hgcviwo3*eozc dog w,6s:yux ;wua8 . qccording to the equation x = 0.45cos6.4t where x is in meters and t is in seconds. Determi coo wxgg7u,3:dzoh8a) .v y6w) uwjc*i sq;3ene
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of a SHO half KE and halfrl1/ysd8t*t e*.u yrn PE?y/n ld.r sy*tr 8u1e*t ±    A

  If one vibration has 7.0 times the energy of a,nljcvw4 kd-(;)gql c second, but their frequencies and masses are the same, what is the ratio (; qn ccdvkl-,l )jgw4of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light scijt pp)53 j0fpring once every 0.6 5tj if0c3)pjp5 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 idefzulw4y20 y:kuyf j ,-txdds u8us;/7ntical parallel vertical springs, each with spring stif4zuwl,udux; s /y -72 kuy8:0tsfjfdy fness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates a(zn 0nfkgw +6px9oc 4lccording to the equation x = 0.38sin6.5t where x is in meters and t iz(n+npx90o4wg6l ck f s 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 examplebhr+z8q kski8gb tzw1; 6n ,q7s of SHM, labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal spring (k = 124 N/m) is str pafj/*ru) vp p55q b.oj*kvq:uck by a hammer, which gives the mass an initial f5 jq upkj*b .5*pqpr:)/v ovaspeed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constants igojo rc3tpnz9u*(4bo1 : g6 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from itbtuj9c6 *p (i3so:1oron g4gz. The mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring an;8, ndz kj1 qe8cll,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 attachmx.v y32bqeoz d13z5sq3j)9 )izrmfqed to a fixed horizontal spring whose springs593o )m.mj vzzxd3q31yiqzef 2b)qr stiffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from aohqx8w /3uixz/blh .4c9ao,u,mw36uzysz8 k high bridge. After reaching his lowest point, he uzq8wlmuzy h/ x zc/4ix. w9,,3a86b k3ohsuooscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibgtmstman15(--p )vx.o natb . rations in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swing pwzu9 * qonjd /h 7ub0yw3,gwe,er second? b/joz*, h ,wuww70 g3yeundq9 (That is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its pegy/6r:;d*o 1 alau cdariod on Mars, where the acceleratyar1ud;g d*6coal /a :ion of gravity is about 0.37 that on Earth?    s

  What is the period of a sim;q2smesa lz1g 3 g)u7hzsv ;x3ple pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the 0w. ibtdy1)ywpendulum bob has a mass of 365 grams, and yt yb0.)1 widwit 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 length3 br)2swpr.uetzw, 2pb;e 3ng of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pendulneszr 2r3;2,b3gwb.utp )ewp um? shortened by    mm.

Derive a formula for the maximum speeyk2p6 hc i;-xnvynp +z+m;8und $v_{max}$ 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. 6 2o)qlozuj,-fkps 9m. ux cl1 )gil(tAt it is released from rest starting at an angle of 151 j6)zgt,plqum- u2ckfio( 9los)l x. $^{\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 an q-k0gr tkss, wfm2)v2chored boat every 3.0 s. He measures the distance between two crests to be 6.gktvwms )2 0,frs2qk-5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with os7 lknb8.oju5ss**x a speed of 343 m/s How far apart are the wave crests (compressiookbu **s8on s5sx 7.ljns)?    m

  (a) AM radio signals have frequencies h6j2 thko v)c4between 550 kHz and 1600 kHz (kilohertz) and travel with4)hcov6kj t 2h a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal m aiqnc;:m81 e:celv5waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elk1qhy,/1ixi(7h kc e uastic modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be gr y i1x7 hik,chk1(/euqeater, and by what factor?   

  A cord of mass 0.65 kg is stretched be* i+ti xyq))p8i qqyrlb)e //htween two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one support to t8i+rq) yq lq )ebixyh*p/i/t )he other?    s

  A ski gondola is connected to the top of a hill by a steel cable of leocy c9+;mdj0tfyst de ;r4w.-ycl,y - ngth 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into thdw0mc4f c;y;-,e .ctry-sl+tyd joy9e terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the mtq993t2t mo tsurface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep m92to3tqtm 9tis the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and thg3-kgfbv4tj8+oqqu/is j-o1 q)kx-h is difference helps in locating the earthquake “epicenter” (where the dixoi+bq8h3ok -4f /j s-j tq-gvkq)1 gusturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be apprzll17y /vt d(:-; q2iprbqwcpoximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include aqic/z: r ylq(dpl-p; 7vtw2b1 mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of an earthqu 0nvpdvj3 2yi5ake P wave passing through the Earth and detected at two points 10 km and 20 km from the sou vvjdn 02y5pi3rce?(a)    (b)   

  The intensity of an earthq47 .2zurgho ptuake wave passing through the Earth is measured to be 2.o7uhgt zpr 4$ 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 sametjq; sj. 4m5xg frequency travel through the same portion of the Earth, but one is carrying twice the energy. What is x;5st jmg4jq .the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched stuyry3bqs,6 m -l5o3 akring have the same frequency, but one transports three times the power of the other. What is the ratio of the am3ka ms5oq-3 y6ur,l byplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down a total verti fw*1.dmbe r94j:n aj wgf*knfu 983qfcal distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm3u:j*nm 89.9a fkqwfj1e*fn 4 fgrw bd, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) Ske(*2y nowozr nwh 2qp:/tch 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 z/ whrypo n(2q2:ow*n 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 fus t9uk/dkewkm2)v o/ 9ndamental frequency, what are the frequedk/ /twksk2u 9o9em)vncies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. 0xd lue .xq5 eq.)plp-At what frequency will it vibrate if it is fingered one-third of th5l )e.pp .- q0quxledxe way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a freqfjiqf + :1xka5jk7p:zu q7d/a uency of 280 Hz. Name at least three other frequencies at which it d:k+f7ui/qa5a:f7kq 1z pxjj will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of standhjk:gljif- r 26n jcq2n)sp07ing waves is 475 Hz, how far apart are two adjacent nik:7hfjj s 2c2jpgl r)q 60n-nodes?   m

  If two successive overtones of a vibrating string x ;uk(njwsy+2 are 280 Hz and 350 Hz, what isnuy+ (w2x ;kjs the frequency of the fundamental?    Hz

  A guitar string is 90 cmg;xi0tjjr: ,ez*4-ad lx/xa )rwdra .g */arj long 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 are the frequencies oax g),**l0 j4d rx gdaz.;xjtrrr/ :-a wa/eijf the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is me-0or8- gqnxxf j5 nnrnj 9)g*easured to vibrate at 205 Hz. By what percent should the tensq8* nrno5 j0en rx9gg-n) xf-jion 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 supposy.dojed-mw83) +jxwe y):/ qn cn6haped to vibrate at 200 Hz, but it is measured to vibrate ane o3: d/why)myqwde .6 8-jpnc+ )jxat 205 Hz. 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 tr2 u qdzfp31r5o a small-amplitude mechanical 60-Hz vibrator. The string’s mass 35ufrz1qp rd2per 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 the1xl6ez0 cgtj7kzn1.b string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many difxb z kclj167 .0g1neztferent standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tu jugqtuo/ a9wl.9ej46b at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center.o/weaj.69gq luj u 94t 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 t42:xjdxi,ni0 n 2cbtmon9 hw- raveling at k.0 km/s strikes a boundary within the Earth between two kinds of material. If it approaches the boundary njt owbn:nxx h,0m 2 icdi942-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 changeson,so.n,o a4 qu(4zog from 2.8 m/s ozns. oq, a,gouon(44to 2.1 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 i aa(ke3j *q:ujuakl8 1u*e;lzt hits a layer of cold, dense air. If the sound wave hits the cold air interface at an angle of 25ja 1*klaj:*aq 3ue;8eu u zk(l$^{\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 boundar k/k1fke. w5ehyc 2:1vy naeh2y between two types of rock at a: 512ekae.1cwnhvy key2 f h/k 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 0.5 m in diameter. According to the user’s manual,g0 6apy lr74y-of6nqs ximo18 the dish has to be pointed in the direction of the satellite, but an e 8 npg1a x4mq0l6yo76-y iofrsrror 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 travelso q/awi-/(ato r*;jls across the Pacific Ocean. As it approaches Hawaii,/ soiajal t/(*; qwo-r 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 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 c quojx6vygb(; czn).r)0 0+3nulzjgu onstant 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 2.2 m/s (appro+ jjx)lg( 0ynqvg;uoz0nrz)u 3ub c6.ximately 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 stretchesp07 u/roq56nafe bx4n the net 1.1 m. Assume that the net behber p67q/anox0f 4 nu5aves 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 s xxh.poo ywqh 12.5gx,pring. The mass then falls 33 cm before it stops and begins to rise. What ipgx2,oqw.x x1yhoh. 5 s the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), comsatv0e*k+ g. 8pd-wj(a64qzm9t rpdjpressing the spring 5.0 m. (a) What is the spring stiffness constant of sajj*d9tz0 mrpw.d4p+t(qk-68 ga e vthe 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 (dia / tj631ks(ka/k;sqp mg3tvlj meter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it s3mkasj3s1t(k p/kvq/t;l gj6tarts 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.epgfis dp: txd 1v; *l.ng;9(j8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sound emi(dpp *gn vild.;j91g:f txe;s tted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650c;.s w0pzp meqd) q(2zcos7.40t where x is in meters and t in se 0. q)pq(c2;dpwe zszmconds. 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 osc gayh 5.a*u4lr izp:x8illates with frequency f. What is its frequency if it accelerates at 0.50g (5 .uy4rh*la:apzix8 g a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stfu 4h-j8f aq ,pnvg-7iands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates foq,pjh8f-4n 7 fviag- ur 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 instrumen 6tj.; 7s,yiinytc hi*t are tuned to play at 392 Hz (G) and 440 Hz (*ytnc t7,h .i;ysiji6A).
(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 tm)c,,c0o4m4vuq0ndy+symx wwo-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 greater in the nc c +4xqsdy0vm0,4, oy )mmuwheavier section of cord or the lighter?

  A tuning fork vibrates at a frequency okd)b d-li+ jop. ;c:yof 264 Hz, and the tip of each prong moves 1.8 mm to either side of center. Calcdc:joko-by+d. )li; pulate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of frequency 1.5 cj n85u xde2,g0 mcpbnic2 qh/,ycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble gq/852e x0d c iuhjpm2 c,bn,nplaced 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,xz5p)+dx/ em t2w fo4zckky5no3 p d2 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 the other k)t cnp3zo52 z2/4 m,e5ydkpo f xd+wxfree.

  A “seconds” pendulum has n .qcyxn) jmm7g95o6oa period of exactly 2.000 s — each one-way swing takes 1.000j g6om)n oyq5 79xmn.c 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 vertical direction or can s7t;lww-ftx n26n*/ x4 vp* rqakh1gdrwing 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 swings, and by what amount? x*g/l6q r 1 tw*2pdv-4kr7ax nthwnf;[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 12 +;7fb edmz0cqj3utm93 g is stretched under a tension of 255 N. A pulse is generated at one end, and 203 7umm+cq;b9et dfj0z.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 fromebyr 7ybk69)pa*ck/cx ka +i4 a ceiling 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 yba *7x49 cbeyrk+a6ipkc/k)on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cable is d,ql6vd f333, xvfg;xmxyw 9p.sl+zx 22 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 bouncing? [Hint: Refer to Table x;l 3,sd3pxfzmlv3,w x 6fxv9yd+q. g9–1.]    s

  A block of jello rests on a plate as shown yj msjgf(skk wu;a:: kv:23i8 in Fig. 11–58 (which also gives the dimensions of the block). You push it sidew;k jkis8 3v jkgm(a:wysuf2::ays as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz