Give some examples of everyday vibrating objects. Which exhibit SHM, +amwb ) ;i +muhl-,cycat least approximat)a-,+lwh;immc +cuby ely?

Is the acceleration of a simple harmonic oscillator uvfa-v9f r-b7c:a9pr)y7 w pvever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approximately si wf6*q1q9(owxltdagj+ n(7c implwl(1* 6j qfd9(oqtciwg 7nax+ e harmonic.

Real springs have mass. Will the true period and frequency be larger or smaller kh3f/z +1 +i5x fgtshethan given /ft3 5h1s+i+ghex zfkby the equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the + k;n d1mkmkfk-dkh;/ maximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to th8w,ad kcyn3a+ e hook of a vertical spring scale, and then is released. Describe the snway3da ,+8ck cale reading as a function of time.

If a pendulum clock is accurate at sea level, will it g:c p bokrp8;:aain or lose time when taken to high altitc b: op:;krp8aude? Why?

A tire swing hanging from ai: 1on pu7p306vnyfar branch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the avn 0n3y 67uifop 1:prbranch using only a stopwatch?

Why can you make water slosh bacgvpb, 6-ap )nsk and forth in a pan only if you shake the pan at as6bpg ) pn-v,a certain frequency?

Give several everyday examples 8gas ,a upe7:lof resonance.

Is a rattle in a car ever a resonance phenomenon? Expla-ub9rn fsr2:bh 2liv :in.

Is the frequency of a3g:9ie av qz;p)ehe 08mhbp0j simple periodic wave equal to the frequency of its source? Why or why not0zpqm3:e jp8h g ia9 h;eb0ve)?

Explain the difference between the speed f; ehtds 4;l*tof a transverse wave traveling down a cord and the speed of a tiny piece of the corde ;4s;*ht lftd.

Why do the strings used for the lowest-frequency notes on a piano normally/xijk+/3cvc t ,1+bubhp,d lv have wire wrappedv/ /x ,+3,ld bkccj ivpb1+uth around them?

What kind of waves do you think will travelmjhue(z :tatr( 7ov6) down a horizontal metal rod if you strike its end (a) vertically from above aah:jztv ((m ) r67etuond (b) horizontally parallel to its length?

Since the density of air dey yf,,nzqc3 f-creases with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary wi ,yf,z3 cfn-qyth temperature?

Give two reasons why circular water waves decrease in amplitude as they travelcja: o87k;zsp4nag -p-5 tgkp away from the sonsaoj;ac g 47p-tpgk 8z:k5-p urce.

Two linear waves have the same amplitude and speed, and otherwise are4hy+6mth9wpo o .9 s5s2u qsvw identical, except one has half the wavelength of ho w26uspyo9v.qtssm 4hw5+9the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sectioha4b 2* ols j/pw9e)wsns of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Explain why. wao9)ls*h/j bs 4wp e2

If a string is vibrating in three segments, are there any places you could towjs8vxf1x f(: uch (8 xw f1jvf:sxit with a knife blade without disturbing the motion?

When a standing wave exirwz e2gh *0u)y99urwasts on a string, the vibrations of incident and reflected waves canuar2 g09uwzr ye9w*) hcel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transf4 ql2rrj /y2kro5 jn nt;qu7.mitted from one place to another, how might wertq2/l yqrfu k onn.2 j574;jr 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 the totf1zeec )utm74g9 lztk;ehv; 1al distance it traveltzvm e9h lut1; )7g;c4ke1e zfs in one period?    m

  An elastic cord is 65 cm long when a we i uu we d3lj /1yhp/+/qnc:eje6q+:z4s) tpqxight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is thepues)3ypdn:je x41 +z :l+h/w/uqc tiq/ej6 q “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 6+c cmbw8yh2g 47dht,z8-kg driver gets into the driver’sy7t,+ md4 hg8bw hzcc2 seat. If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangsvbe.zkytu; g 0x42o :*anj*km from it. (a) What is the spring stiffness c 420jn;g* xykot: ubemv*kza.onstant $\approx$    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 v, ox1uj0ir1q kg is hung from it. What is its frequency if only 0.38 kg hangs from it? r1,1 qio0vuxj   Hz

Construct a Table indicating the positx e i+9pu+c-4lymxxz6u; ij;pion x of the mass in Fig. 11–2 at times t =xixxjm;6ceu; uip y -9lz 4p++ 0,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a4okzq,ig2ab5b 5 1jec spider’s web. The web vibrates predominatelyez,ajqo g5i142bbk 5 c with a frequency 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 0-6 z914sl+nc n+o 4 akmnzchy*jrw6cp.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the value of1-jszykw4 hmor9n6p nzcc6l 4 +c+ n*a m?    kg

  A 0.60-kg mass at the ebnw0 kh(v(/fesb0y6n nd of a spring vibrates 3.0 times per second with an amplitude of 0.13 m. Determi( nknhw00b6evy(s/f b ne
(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 spe)u0 n o0wuiaht rpk603tm6 ml1ed of a SHO half the maximum valueh luip0r0 6mot3)t0kw6mu 1an?$\approx$    A

A mass attached to the end of a spring is stretched aj9y w il)6nx gbf9b;k- 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 stret4 ,0 yu3nd gvpf4u rin8*3lmbjches a vertical spring 0.315 m. If the spring is stretched an additional 0.130 m and relea8 udflb3r3 4 g0m4iynnu *vjp,sed, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with sprin 9 k1k(7hlbntpg stiffness constant k = 280 N/m and is executing simple hk17lt9 bhpn(k armonic 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 popgun 0.200 m to e ;;6fglehp 6xt9x wloz4;*wb“load” a 0.180-kg ball. With what speed will the ball lelo;l; x 46t whx;*gz ew6b9pefave the gun?    m/s

  A mass sitting on a horizontal, frictionless surffc )bq qepu :ps9;v41qace 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 experienceqb1 ppqqu:9)e vs f;c4s a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x = 0.45cos6.4t where x is in. r* pyxunl-o:xo;5 sd t0s,sj metersrsxo*y,x : ldus 0-o.jnp5;ts and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement fks ci+s q+3j3( cqo4cyrom equilibrium is the energy of a SHO half KE and half PE? 3( qsck3c4ic+ ojsq y+±    A

  If one vibration has 7.0 ti2 h7it1lou+dv qs+8.u ax-d :cq1fiximes the energy of a second, but their frequencies and masses are the same, what is the ratio of theiauu xl:-io . 1v+ 2q8 h+1qcfdtsidx7ir amplitudes?   

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

A block of mass m is supported by two identical para/ 6gz-ahjvt39cmbn90mtb c j8 llel vertical springs, each with sprinjm ncgzt6/jb98c a-0 9b3vhm tg stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to tvoabmwi6v .z47x -xek.m(s za q;e*.fhe equation x = 0.38sin6.5t where x is in meters av ..oz a74s;e -vmax( be mkw6x.i*zqfnd 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, lablf.r,sme4 jh7 eled 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 = 1ittkns ajev,4kss* u607hb8+ 24 N/m) is struck by a hammer, which gives the mass an initial speed of *bans68k+4 7eih0 ku,sv ts jt2.96m/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 s6yq,djnv,* egpring stiffness constant 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 positive veeyvn jq6,,*gd locity 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 co6eugingx5 i, dz(5 thnd7higr 51fb),nstants $k_1$ 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 attachedl4svnp n-wa-8 to a fixed horizontal spring who vnw8 sap--nl4se spring stiffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps fmk2 *uig*( f+)ymrjo grom a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25mio*+*y(gg r2) kumjf .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. Whj v(u(nn4/vgy6 w v4mmat is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is t(i)v9rum 9nh :z1 afeto make exactly one swing per second? (That is, one complete vibration takes exacv9ze:tn h1)imu 9r(fatly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What i.j vnrk*u;0 ofs its period on Mars, where the acceleration of gravity is about 0.3jofn. ;0rvuk *7 that on Earth?    s

  What is the period of a simple pen b3,1ae7:nsh;mbj*hh yw lhw.dulum 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 brk fsij+k (jv fl;lazz0a.303ob has a mass of 365 grajs0 0(.llaa+zk33v;k jr fi fzms, and it 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 length of 0.9930 m. If th75x.ha s e9tis7) lwy.b v)odmzb8 sz3e clock loses half a minute per day, how svzz yws osdm7. 3t)9 axh5e.7ls)8 bibhould you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the max2bli8hpp)e 0013p jys8e c ttoimum speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At it is releasevknbs0-sn dnja991 r n zy8;:jd from rest starting at an angn9y-bsra8 jn0:; k n9zvsdjn 1le 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 hi8amc -ssb+bp o (-dn-ls anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the waves travenma-pd l -+ b8-osb(csling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed of 34wrwy;5e zm (ki*hy*)m l y5z*i3 m/s How far apah(;z*5wmey)mlrwyzy *ii 5 k* rt are the wave crests (compressions)?    m

  (a) AM radio signals have frs28 b5pyxw9k*oolps,equencies between 550 kHz and 1600 kHz (kilohertz) and travel with a speed obs5ywsp*ko 9,lpo x82 f $ 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 longitudin6ac4 kb o-vf(hal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one i070j zk obgpo2ajaq7kfx am129a4( d es twice as dense as the other. In which rod will the speed of longitudinal wabk4a (m7x2 0opafgae q1j0d9 2akz7ojves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two suppor nn(e7mw(() jnz yaeo*ts 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from on(zwne( jmo)(7ney*a n e support to the other?    s

  A ski gondola is connected to the top of a qmyl95l+c9 be 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 +9ceb9yqll m 5the 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 surfa7-j v+h) l1x/(ivsu40opizmvfo b :u*re ni 2qce of the sea. He hears the echo of the wave reflected from the ocean floov 4 pu 2bvs(l7*o)nim:-u0oeijx ivrzq1hf+/r 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 dctz ik,9 qpv;7ifference helps in locating the earthquake “epicenter” (whe;zq c,i p9ktv7re 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 can be approximatt eta46vqo1x gv*1lo*nq5c p,ed by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually inclu1tt*6 ol4oc qg5* n,eqv 1vapxde 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 intensitie;on.g ;//nfxtgi ds8hs, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two point;/ oxtgi/8hndf .sn; gs 10 km and 20 km from the source?(a)    (b)   

  The intensity of an eeuh i:mu4 ri+(arthquake wave passing through the Earth is measured to be 4im(h:e+ uriu$ 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 trav;a9q s g )q4syt2vix5nel through the same portion of the )xna qs;yvq9sgt 25i 4Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string ha2d) o)g)batcxve the same frequency, but one transports three times the power of the other. What is the rattba)2)c)x od gio of the amplitudes of the two waves?   

  A bug on the surface of a pond iu:3mt 1xf w 6sp;zknm1s observed to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, asf ;u3 tskpn:w1m1mx6z 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 othe**a 6 53kzvlvb9bxxfxr. (a) Sketch the svxx zk 9fa3bx *vbl5*6hape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequencg +lgoop/3mb6 w 7hb)qwv,8dgy, what are the frequencies of the first lg 7 6 oh+b,p dgoww/)qbv83mgfour harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency will i2cc4 (tj,i 6dbl- yoza nz)wc;tk ao, c,1ut9it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the strin o tz,a 6c;b-wy1l ikc(i2) tnjad ,otc,cz49ug vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz. Name aajwfe- 7c.jy 2t least three othefe.yj27j-cwa r frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves obex/z /vuepu3a7 v y;9n a string is 92m/s If the frequency of standing waves is 475 Hz, how far apart are two adjacz3v ;/a p7xu/ ybv9eeuent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hzs 6xxpw zlc2 hel8*ljv(56q5b, what is the f5lh(lqvesp *z8x52 x6bl6c wjrequency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass 5otr:vx gi:z90w fuwso o73-u of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is un5oi:7uo0 x 3zs wvu- ofgwrt9:der a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is sl.1bg,4pxd md* kb1izzjea( 7(q f3 aqupposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent sho7q3q1 k.djz(1,dl fgibap *4ea m(bxzuld the tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is s.qbd)h ld9jdj h74gkan)(b2 g upposed to vibrate at 200 Hz, but it is measured to vibrate bd q k(d)jdlnhg94h7b ag.)j2at 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 to a small-amplitude mechanical 60-fi n;*u2g(i vsHz vibrator. The string’s mass perni ;f g*ui2(vs 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 on +mvb(z5bz.oksp( 3mnjailp 4+d+p- f the string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kgzb j3+pp . bi+ +-s4nmn5kapld om(vz(, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water bb in5f*3:uc70 *ryncttgl v r-ack and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose -bg rcuni 7vlft3:* ry5t*n0cthe frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary within the E; tns 3kq6/4ri/ jnwylarth between two kinds of matl k6/;yn wi j3/4sqntrerial. 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 chang4u(j;l aykd9sr4fu2 t es from 2.8 m/s to 2.1 m/s If the incident wave crests make atad4k lj(sfur9y;2 u 4 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 la2s 1m ho:)(aues7jpr1v )khlnyer of cold, dense air. If the sound wave hits the cold airn1aphv7ljs: sm))u h(1kr2 o e interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthsnz9hv( )j ,:qe:bbj tquake wave strikes a boundary between two types of rock at a jjb,:)v bezts(:h q 9n38 $^{\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 ind ,x-4mxt1d zq diameter. According to the user’s manual, the dish has td d4xt, 1-zxqmo 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 velocity 750 kpo,03,1uo( s pzwwv-7c1e 4)gfsfe0elyesy vm/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an un3 1y-ops vl, egyp)oec7e(f,0sfe4 w z 1uw0vsusual 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 + vm3 fki9g6nfconstant of 550 kN/m Find the maximum compressv3+im6kf 9ngf ion of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from9ll9u;-z r2;x;3cy xufv czba a window to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a simple spring, andvlzu ucb9;y f2;-c3l ;9xarzx
(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 enoibh d6cxb2)x-ex10 n d of a freely hanging spring. The mass then falls 33 cm before it stops and bbnxb 06- o)ie h21xdxcegins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge sd27 7oqp6y u.uyqtwqy* fa(4apring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spro 6auyuy7.ay7 w qf2pdtq4( q*ing stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just the right pace ofw+qon f1xl od0u ;opi:6x 2;jy about 1 step per secoj:;d ofo+l6 x p12x0n ;iuwyqond, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a cernd84p.m yt m2htain groove 10.8 cm from the center of a 33-rpm phonograph record have a wavelengt hmnymd4p 8.2th of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x is iq1k9u kd6rj :m1vxh;gn meters an6hvukg1r:d9jm x1;qk d t in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates wpmnw+ 67 ow3owith frequency f. What is its frequency if it accelerates at 0.50g (a) wno6w3o m+pw7upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man standz5w yrij z*;t;s on the raft, it sinks 4.0 cwyj ;5*z;z tirm deeper 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 play e4oru3-rfndnzkkp;mpo0* 6q :33g eyat 392 Hz (G) and 440 Hz (A).yrmf*6g3r:p dqu;k33n e k4npooe0 -z
(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 travelingql8 3lye) 5(yd7n:fyn eq)e vj down the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section vers lyy vd5n(7y8) 3jf enl)q:eqeus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibratlenw+xf ./;kroxc)r. ik 3v8hes at a frequency of 264 Hz, and the tip of each prong moves 1.8 mm to eitr.c.k ;lki x x/)feo8nv+whr3her side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of frequency 1.5 cycleslcypxb6:/y z- per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board durin/byz6 ly p:cx-g the oscillation?

A string can have a “free” end if that end is attachzvfw+e4 gezci3rj69 : ed to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of4e 6:je+i93 rgwfzzcv the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swing thl 2wfo95it4sgup 51f akes 1.0001i5f5 lu9fost ph2w4g 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 :t0jy .j tu:iuq)a +ipa spring can oscillate in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the periopt:i)uat0u.yj+ q i j:d 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 nf13vfngqr+ *255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two p3+1 nfrgv q*nfulses first meet?    m

A block of mass M is suspended from a ceiling by a spri 0b f(ss51 m5q(q.z 5fzg5alrje4 itpnng with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of tm5 n.5 451fbqzsftrp (ze0al5gjisq( he block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. k-e a38,7x hnaj nt2ekThe steel crane cable is 22 m long and has a diamete xa e3a8-ketjn,k2hn7 r of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which also givesrdbxx- or419y uji8h5 the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. jx u5i1h-9yxdrr b48oIn 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