Give some examples of everyday vibrating objects. Which exhib5e9gaq17bk7l,f v3f vmi ba8 bit SHM, at least approximatekaiv3bf lb 8f7a1 q7eg5,m bv9ly?

Is the acceleration of a simple harmonic +z f psru+ffao8b-.+k oscillator ever zero? If so, where?

Explain why the motion of a pi3hq ; joue;wa)i g bqhb45i,n+ston in an automobile engine is approximately simple harmon;qnabo3 u45;i hwb)h, +e igjqic.

Real springs have mass. Will the true perid3kb8)x*pq wta,/cu d od and frequency be larger or smaller than given by the equations for a mass oscillating on the etx/ qc83,pbwdua*k d)nd of an idealized massless spring? Explain.

How could you double the maximum spee n t3, eo,v4(x wsx pc;rc3 qq*g.hlq6uj*tgp(d of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertica xowbmh c3- ms by.1xgh.,r9(ll spring scale, and then is released. Describe the scale reading as a function oom3c hs .r.xm ,bl- xgb(w9yh1f time.

If a pendulum clock is acc 44q+o,onq tj+6ukzw curate at sea level, will it gain or lose time when taken to hiujn6 4+o qcz+, woqk4tgh altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground:*hklxq eij:( (Fig. 11–48). How jk x:l:qhe*i( could you estimate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan onlfak:s3)r b7k ly if you shake the pan at a certa: lskr3a7k)b fin frequency?

Give several everyday examplesq:0apx usq/2 s of resonance.

Is a rattle in a car ever a resonance phenomsdz.4fs w+sm:q4g5:lsk2xgim d 2;xhenon? Explain.

Is the frequency of a simple periodic wave equal to the fr 8c+ae4uh-zy959se i adx a)dyequency of its source? Why or why nod5d94 u+8aaeyz 9 -)sahiceyxt?

Explain the difference between the speed of a transverse wave traveling down aky ogh*nb e-9* cord and the speed of a tiny piye9 hn**o kgb-ece of the cord.

Why do the strings used for the lowest-frequency notes0e,9det)dg1i w3ctdyyb sid6h qb156 on a piano normally have wire wrapped around them? c)69b 35ywdg 1yse,0hi1 qeddtd6tib

What kind of waves do you think will travel down q x7 qeh .uq.yk.7g(mf9ds-sc a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parallel to it(dxsmh.fqqqsy 7 7k. -.eg9 cus length?

Since the density of air 1 ljs y jlu6yy9jg-7)xns)huc9y :y ;ddecreases with an increase in temperature, but the bulk modulus B is nearly independent of temperature69lun)sjc91xh: j7 y-yy dyjg)ysu;l , how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitul*szn+ 1gt+ ilde as they travel away from the sou* i1n+g ltz+lsrce.

Two linear waves have the same amplitude and speed, and otherwise are identicalelisu *m8*7j q, ejse u7q* *mi8lxcept one has half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sect6 ktdo(rq)ge (ions of cord as in Fig. 11–33, the frequency does not che 6rkd( q(ot)gange (although the wavelength and velocity do change). Explain why.

If a string is vibrating chtm5 : /)adu27trtwx ebki(5s wgs/1in three segments, are there any places you could touch it with a knife blade witaswm(g1t/t5w 2rcs5 dbuix:)t /h k7ehout disturbing the motion?

When a standing wave exists on a string, the vibraw;xx vx8ex4f +8k:4vtn6u elttions of incident and reflected waves cancel ;tv 6 t8kxve x8u4 xl:+wenx4fat the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from onefup+2 b (yc19viq;khc7oe9 . vm/ulye place to another, how might we determine whethu k29 bo1v7/pvuc.eycfhm;(i9 e +qly er the energy was being carried by particles (material bodies) or by waves?

  If a particle underge1 -hp d0lfo9;.cp bcyoes SHM with amplitude 0.18 m, what is the total distance it travels in one pcloy cd e 9bfp.h1;0-period?    m

  An elastic cord is 65 cm long when a weigh e n8ightg*x7 rjw0qo;/ j9g+ ezp1r2bt of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. Whpze98 g+rb 0nxw e7t*21jor/qgj; higat 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-k) - mozr5ybi.;4 pavpx ,sff1h/g s6dag driver gets into the driver’s seat. If the car goes over a bump, what will be the frequeaxy;/ v-a) ,.smorgbpff 41szd6i5phncy of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. ebf*m8ofk2 ybll. ghb*0( ;if (a) What is the spring stiffness b *.bllyg o hkmfie8*f0(;f b2constant $\approx$    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 ao 8c 2mcg3ggo5;-vhr q7l qly4 frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequen8oggh7 2qy-ll;q4vr c5g co3mcy if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at time; 0h ditosw2c7q (ku4es t = 0(kqu0o ;s2htd 4 wci7e,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web. The web vibrates predtz2p ;x; qrm,cominately pc2qr tm,; zx;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 0.88 Hz. When a*vt; s+i3c(9wfce lwd n additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the value of m9 w;sdve cwfc(+lt*3i?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 timestjsl + ) i ;2raumfa3cgy0 g;-ola:j9a per second with an amplitude ofsl3;a cu 90j+o2 atg-l; ai:agyjmr)f 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 equilibrwv5bioc c 2:(q hg3-fbium is the speed of a SHO half the maximum valc 3g:ibf5oqwc2v-b h(ue?$\approx$    A

A mass attached to thedf3p6m3ct3+4v wvjuv end of a spring is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a verti w95 m3wwj+3s v0vwjxzcal spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equmv035wv3 s9wx zj+jwwilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring st;e+ne; esi solp:f8g,zh l8(biffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving withsfgoe ,l;e lz88p+he:is;nb ( 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 80.8hwnhv0n 5y zhl2x)6r2e/o kf0 N to compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what spevx fn5w2o h)80yl6hz/en2k rhed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attakij0(i+ xk9 m huw r9 atxicx.512:co1xl5w zeched to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the s :u1l z5 ck0mhicxx2a5j9toi e1rww 9ix(+. xkpring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equat99ar p il;cvw2ion x = 0.45cos6.4t where x is in meters and t is in secr w p;99alvi2conds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of a SHO half KE an q rua30wc ggx.56v;gtd half PE3ug grgqt6 a0v5.;xw c? ±    A

  If one vibration has 7.0 ur 5xc (3)wgdmtimes the energy of a second, but their frequencies and massem )wugxcdr35( s are the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light s pcf9y/q-qhg f*qq -o;pring once every 0.65 s.fqcgq;*/qyphf9q-o -
(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 eyd2x h0nk)gwb:o 0j pzd1(qml(w7b1by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the fb1nqydb hk0zp(xw:o2dj )l0(g m1 e 7wrequency of vibration?

  A 300-g mass vibrates accordb 2 ;k*tdr(wckret8k+ing to the equation x = 0.38sin6.5t where x is in meters and t is in seconds. Detedw;kk2e(tk b+ t8*crrrmine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and B. For each, wha(mn416mj qs fnh r29nzt 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/mu.od.0jh987z m laxa k **taec5lpd6 hh-i6kg) is struck by a hammer, which gives the mass an initi6h hm9axjd0ik k.5u cpethd*8ga-a7l* o z.6lal speed 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 constah ) 5ktd*j. oeej-g+ ws9bg o x-ahc(g(-d3geknt 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the e*kgb- acex9 gg((wsj)h-go3dd t5k o-e h.j+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 sprixki:ezwb /n9/,h*e hqc 060ofx xb 1tings, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed h c;7:7i1i; hkti lqcevorizontal spring whose spring stiffnes:l;cec7t 1k;q v7ii his 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 a high bridge. After reaching hi;n xa 1b1/jiy6mz:s, koftyb*s lowest point, he oscillates up and down f1a/b mnyjsti *6b:o kxy,z;1, 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 vibrations in exaje46g xexhdtt .fm t620 bs55xctly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it h0kgdh k b2b)-is to make exactly one swing per second? (That is, one complete vibration takes exact)hk0-dkb bg 2hly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. Whw44 0 umds7swzat is its period on Mars, where the acceleration of gravity is about 0.37 that w 0ds4u wzsm74on Earth?    s

  What is the period of a simple pendulum 80 cm lop h -f.yo49+p;xr e1 zlci21dgqmotn7ng
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 b o5tkn+u+dlcl;gy0b/t4 0jvm, the pendulum bob has a mass of 365 grams, and it is released at54 tvdg jk+;l tc l0+ouny/bb0 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 ofgzuw3hf2l-oy us x3tk ;7/v ,n 0.9930 m. If the clock loses half a mino3 uzfskv7 t /w,nhul- x2g;y3ute per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum spewqn4n c27xs3jed $v_{max}$ 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 releay.nf -7so4vuk sed from restof y nvku74-.s starting at an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass thvs ,e47nq/ f/nh b)yqje bow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast areq/ /ybjs qn nh4,vf7)e the waves traveling?    m/s

  A sound wave in air has a frequencn( h-.e ,hi;uvf:clllhqm3u9 4jqveq )4uq m(y of 262 Hz and travels with a speed of 343 m/s How far apart are the wave crests (compres9hulmun ;3v(qf e qq4m,( )v: lcq.lehi-u4jhsions)?    m

  (a) AM radio signals have frequencies between 550 kHz and vaslw,loe 3 q+58j l8d1600 kHz (kilohertz) and trav l ,qaow +8ll8d5evs3jel 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 longitudinal waves in m83; vt(mq-c 6i7t yg p)nbkxm
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modu6 6oijlv- ess ;n0e)uklus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, and by what f 0)j-n6e6 s oe;silvukactor?   

  A cord of mass 0.65 kg is stretched between two sk4/ sroekbv7b4 5gj ow+v;ot *upports 28 m apart. If the tension in the cord is 150 N, how long will it take a pul/7e;ogsobwbjrvok* v 4t 45k+ se to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a jcz;faefxp: k+s6*t ( 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 se *cxpfa t;szk +(je:f6nds 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 aup:erob/;i: below the surface of the sea. He hears t:ur o;bip:ae /he echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an eartrr0t *eehgn r3 ;71vari0gx;lg i vlu*f(zd3:hquake travel at different speeds, and this difference helrviergl3ie a; *u137 r0(zg xv * hg:t;dnlr0fps in locating the earthquake “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 can be approximated by a sinusoidal transvey (xulgc s64e cj.*k0nrse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), wykl6 xj4gcsc*n0 (eu .hat 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) thky ibf(2cun u6k,us( ,e amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 k,( k,2sfcyk(nui6 ubum and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured to b-bx i35,n w vknjku4s.e i4n3 wbj- k,vx5uk.ns$ 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 sa:odi59x j ;iwbh c*ed/me portion of the Earth, but one is carrying twice the xd cd : b;hw*ei9oji5/energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along amaxui/:mui)( tc24wpn 2yw k- stretched string have the same frequency, but one transports three times the power of the other. What is)k/c42: i2axpmnu t-yu ( miww the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down a total ve7 uaotf0k+b(pe(r c3(jiir 6 yrtical distance of 6.0 cm, from the lowest to the h 3p o6(+i(7 (cut rejra0ifbykighest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) Sketc/ .plt uv:i34r2k/ xymjfenz;h the shape of the string at t3x2/u 4ln/ tmr jkp;veyfz. i:he 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 fura72o f7q tq(9 zdpa*dndamental frequency, what are the frequencies zqd p2f a 7d7t*r(qa9oof the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfinger8db)ad;9 n gkn4t x()im vrpg-ed. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thr;v kn-gbi(4gm8t)a 9dx)nd pirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz. Name y5wmduml6ts; rq7 ppz-)/p a9at least three other 5;r)9q-umpta7 wpsmzdp ly 6/ frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the ie5ft 5w i+ 1l e+p5a,ovjxv2v; sgf/pfrequency of standing waves is 475 Hz, how far aplfpef,5+ i/v; asw5v51xg+ v ji2 toepart are two adjacent nodes?   m

  If two successive overtones of a vibrd/ 78dc hfl2jgating string are 280 Hz and 350 Hz, what is the frequency of the fundaj2/8 cf gddl7hmental?    Hz

  A guitar string is 90 cm long and poy-.oaac.9m qrg 5/whas a mass of 3.6 g. The distance from the bridge to the sup5w amq/g c 9-oa.opry.port post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is suppose4 jvy-0j:kg .lak1yxn d to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So k1n:y. y vxk0j gj4al-the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar st. 7/ 0wz od+bqjvo:q- ;embmlxring is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed mob7+/j;xbov-e0 .:dqzlwm q to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude fy75 xr.bf:p.5+ 2e r oz*ofu9pqkzstmechanical 60-Hz vibrator. The string’s mass pe +p.rp7yo2br5uf. fo xzetfqs:k5z9*r 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 bms v2hgn0h:j8* p*rbthe string may be adjusted by moving the pulley. If thenr* sbj*h 2bh0p8:vg m hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the right fr,6r,qeakiig 2equency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the6 2kaiq,ri, ge speed of the water wave?    m/s

  An earthquake P wave tra) kqw p0hh0ws psc):2pveling at k.0 km/s strikes a boundary within the Earth between two kinds of material. If it approaches the bo0wh0p p)h2)cwp sks:qundary 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 thekk 9wnfp bq,0; velocity changes from 2.8 m/s to 2.1 m/s If q9 bfkn0kp w,;the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer of cold, : v3c;e 5iiloqdense air. If the5io qv3li;c :e sound wave hits the cold air 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 earthquake wave strikes a boundary jrmbosb85 /. tp3g ,tcdhy,d/between two types of rock at a t,dp jcmt h,3b/rsy ogbd 5.8/38 $^{\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 1g e7gktg 75bgdiameter. According to the user’s manual, the dish has to be pointed in the direction ofg7gkbe1g7g t5 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 75w1ib)woazg;n ql-b 4mpw zw f(jbk -.6/sza8,0 km/h travels across the Pacific bw )l(q4s b--w/.zw fg bz ;p6z1mwok,i j8aanOcean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died 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 constant of 550 kN/m 9xh emkx8ff7;etp- wmg1: j: yFind the maximum comppfmjfy x 7;tm:we1-ex9gk 8h:ression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 173ahrs6h )/kltu r(hg 8 m below, which stretches the net 1.1 m. Assume that the net be/ug(h3trsa rhl k7)h6 haves 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 hang ivq,2r: 9x drc3,qcmxing spring. The mass then falls 33 cm before it stops axqxr , cr:2q9mdi,v3 cnd begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring ay:g 9(2oofd gst a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring sto (gyfo dsg:29iffness 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 cl styhkw9 v55yj2.m+vcid1x.x 47 psjust the right pace of about 1 step9sc vx24ysptvjlkmc+wh. y5x 7i 5.d1 per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 106 n47my2p9lbl qqva8z.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will bz4ln2q8ma 9q7y 6p vlbe the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0j)m is:dp0s:p/ecc :p .650cos7.40t where x is in meters and t in secm i:pc:/ ss0ce d):pjponds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. What is its frequency if x;2 f e2-j:o xdotjac.f3n ba.it accelerates at 0.:.fo;.t aojnjxe2a fd32-x cb50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stan-u:d e*mn tadp6solbeq(7 .v0 ds on the raft, it sinks 4.0 c*7dv6e-t :d a.mqn 0(eubopls m 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 at 392 Hz (G)afw) glc5 o98s 4kdqm, and 440 Hz (A). )8wms5dl k9g,o4cq af
(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 p5zsckagus.9 d1: 6jk-part cord of Fig. 11–33. Determine a ak95. g61zkpjucss d: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 heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of each prong mf5.: uao)o7f ycn b h(nl h:b(j2omej)oves 1.8 cbjholn(.oe)5ufy:jf: bn72 )ho(mamm to either 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 frequenxvn,kq1g 4j-r cy 1.5 cycles per second. What is the maximum amplijv,qkrx n-14g tude 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 attached to a ring that c22pfgkx2e1l )u7p qqtan slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations q7qulpp2 12f)k2txeg of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2 3oezgm)b m2j:.000 s — each one-way swing takes 1.000:jz2e mm3g)bo 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 swiikjnb7t3 6j;dl(lk -) gbc-ykng as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or t; 3n7li-jbkydl(c6-jg bkk) 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 stretche cmug4 x jfs+(k9ddk.(oh s,b1d under a tension of 255 N. A pulse is generb gx94,hs.sddfkju+c ok( (m1ated 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 spring with spring stiffna7d34 (/mdfx f,tvrnr ess constant k. A penny of mass m is placed on top of the b7rdf rdv,m3/ 4xatf(nlock. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at t 4+/mcunqlkx 11wmmq*;y6 mzihe junkyard. The steel crane cable is 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 Tablcmwmi 14 yxq;6+u* nm1qm /zkle 9–1.]    s

  A block of jello rests on a plate as show3a 9stng: ux(c) 9gyfkn in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the f9ufa 3g)ktcgnsx ( y9:requency 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