Give some examples of everyday vibratingy+rk/uy3v.hy c- j/jed 0*mj k objects. Which exhibit SHM, at least approximatv3 yyhk e+ c*/0r-u/ kjdjj.ymely?

Is the acceleration oz:7 e8g kv2y6 jy+m.b e mku/ux*hhq;ef a simple harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in ani gwjnrl7b e1n9(3 v9l automobile engine is approximately simple ha3 vw1jel7(nl g9r9nb irmonic.

Real springs have mass. Will the true period and frequency be larger or smal5 9v09tmptm3 8g bcdchler than given by the equation5mmgdtp 0 8bt9c9h3c vs for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple har dm nwl3iqrc dw/y30; rh(jix3mf k225monic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical sprin xwch4 -0 *u7c;oftezng scale, and then is relcxwtz4 ;0eunoc- 7h*feased. Describe the scale reading as a function of time.

If a pendulum clock is accurh4o;dgr 9/e fdate at sea level, will it gain or lose time when taken to high al/4hr;f9 g dodetitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–48). Ho (kbuq 1:70 rm ngay;+w+enldmw could you estimate mnkd1wql+7r0:gb(+;any e muthe height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake the rl -5kwi(:c0xa-mhbb pan at a certain frequckb-i-r w0 xhm:al5( bency?

Give several everyday examples of resonanz81 7hq:; hv1qaoz zufce.

Is a rattle in a car ever a resonance phenomenon?a y xb jvf+/7.4u2ln0 5qzkt6op9xuiq Explain.

Is the frequency of a simple periodic wave equal to the freqdo,ala g-/e .suency of its source? Why or ,/dg aa .-oelswhy not?

Explain the difference between the speed of a transverse wave traveling ry 96s/y8 vxikdown a cord and the speed of a tiny piece of the co v9iysk8 6x/yrrd.

Why do the strings used for the lowest-frequency notes on awqo.0j1d 8 +a zwu:av::fqbox piano normally have wire wrapped around:w z1:.aqa b0owxuov8fq:d j+ them?

What kind of waves do you think will tryc+08 q,s.x/ io3ynhyii 7spoavel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally pa/ 3.i ih s,qo+iypycny0xs7o8 rallel to its length?

Since the density of air decreases with an increase in temperature, but the bulkj 73hptu6z,k a modulus B is neara pu 67,jkz3thly independent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water wa*: g0i uckp95eomt6m zves decrease in amplitude as they travel away from the6iemt o z cum0g:p9*k5 source.

Two linear waves have the same amplitude and sw6 79zt ,h fplmjig5j8peed, and otherwise are identical, except one has half th 6 5jtlip7fmgw8h,j9z e wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sectionym fbzn3l 2u;(s of cord as in Fig. 11–33, the frequency does not change (yn3 (zmul; f2balthough the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are0j3gmdb+ (wry2fr*2n-xlop/ v+ eyz y there any places you could touch it with a knife blade without d2+ved(3 +o flrj2/ *- 0 yzbmrpywngxyisturbing the motion?

When a standing wave exists on a string, the vibrations of incidentt ;cf;ebgn5e3 and reflected waves cancel at the nodes. Does this mean that energ5;cneetb fg; 3y was destroyed? Explain.

If we knew that energy was being transmitted from one place to another, h7uyu k4r8 9ptrow might we determine whether the t 7y9krup48ru energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total dista :3xt7,d9gj. x ktrupence it travels in one period? 9r3k ,teu .xjd:tgpx7   m

  An elastic cord is 65 cm long when a weight of 75 N hang: r/on8cz bh9d6f+ )d*svn 8olbvj0jrs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this 6hv*df nb90bc jno:+rolvj s r8d /z8)elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when itsz02bn m wo5+lk0zw8yf 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be twkb20n lwf085 +yzzo mhe frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs b jv zg-;* 6hb9k/ftdcig7ga7from it. (a) What is the spring stif*d/6g7gcb a t9fi7vg;hkj b-zfness 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 frequencdgy14acv fb88y of 3.0 Hz when a mass of 0.60 kg is hub8v41 agydf8c ng from it. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicatirf.*i + qbz;snng the position x of the mass in Fig. 11–2 at times t = 0,t biqs+.z fnr;*= $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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/l a,lk bap92a; 8z3er5wywfn .25 g is caught in a spider’s web. The web vibrates predominater3 p ewwa8/f9;nlly,b 5za 2akly 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,r 9a54fjd;z,wzry,xxc.gau spring vibrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. zd yxx.59gj,zu4f rw; r,caa ,What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibratel cyhae j36+5bs 3.0 times per second with an amplitude of 0.13 m. Detec6l3ha bj5e+y rmine
(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 frouidwq5 2k9d2lq: h6cwm equilibrium is the speed of a SHO half the maximum valudww:q 56c9qk2u li2dh e?$\approx$    A

A mass attached to the end of a spring iwpl(4c d/pv ;a;l 9kj6npp 0ejs stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spriniv ;iv+x4+ywqr v fo77g 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium position agaf7 yov qxrvw7 vii;+4+in?    s

  An object with mass 3.0 kg is attached to a spring with spring stivq281s o7 k,xm oztch(ffness constant k = 280 N/m and iz qok xt c27,8v1ohs(ms executing 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 popgunru1 .3trl./ght ttcqao/. l,r 0.200 m to “load” a 0.180-kg ball. With what sp.t .gtcloq/u.3/ra1r ttrl,heed will the ball leave the gun?    m/s

  A mass sitting on a hor gviud0m eh)h;wfw (6.0ejf+rizontal, frictionless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the masdm;u frhf0vhwe(ew)g i0 .6+js is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x = 0.45cos6.4t where x 1s3-ezgp2iyc ;2vmzn z:2q1 pdjef9 c is in meters and t is in 2 mfccz3-gs2qzdv y9nz;211 ppee :jiseconds. 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 equili22faio;w0h3r rx ) 04 edextgabrium is the energy of a SHO half KE and half PE? ±aethd;43r g20f wxr0e)i o a2x    A

  If one vibration has 7.0 times the energy of a second, but theai2hhws 3y 2 g a(ovp(wh,4yi*ir frequencies and masses are the same, what is the ratio of thih4*, hp a v(2 o2wiw(sg3yhyaeir amplitudes?   

  A 2.00-kg pumpkin oscillates from an,. b /cvfsc :ui(5s4svp3ch9sw2z so vertically hanging light spring once every 0.65 s. 3i .: w9 24sv5ssu n/(vzfphc so,scbc
(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 bh1ha plmq-5x 9)hy m- *fr6cdyy two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequencc1 9qhh)*mya5hr y6-f-lpd xm y of vibration?

  A 300-g mass vibrates accor3qz .qrg7n +s k7s/aixding to the equation x = 0.38sin6.5t where x is in meters and t is ins+x zk nag77qq3/is .r 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 twywlz(ci)ze3o7g z/jm,if *. so examples 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 hoxyf*ix-z )i+ i3vfrn7rizontal spring (k = 124 N/m) is struck by a hammer, whichirnfi *xi3vf7y -z +)x gives the mass an initial 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 constantu m05vy /alv+n 305 N/m vibrates with an amplitude of 28.0 cm w/la5 nv +mu0vyhen 0.260 kg hangs from it. 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, withy)c j1) kt8qau3ij jfjd414q ;vz2qyy 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 hormkpxn 8(- v+jhizontal spring whose spring stiffnessvmk ( jn+px8-h 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 j 76rpsubtgq//z2h +qf umps from a high bridge. After reaching his lowest point, he oscillates up and do7hrf+/ spz utbg 26/qqwn, 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 exactly 60 s. Whl9no2wu) j 5mmzee/- gat is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if itmm 4+yodas85 sqr-t.+q tz8kh is to make exactly one swing per second? (That is, one4.-o8tak tqdymzs8rms +5+hq complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. mb,m;guzbxq ev6: 5xbwc):j. qw.z/ik8,avc What is its period on Mars, where the acceleration o cj5:a i w,z kqgv,e.xu8/z6bcxvm;:mb)w.bqf gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendu hpf 4:xj;aaozwo986s5awu-pf8y mg( lum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum ii)mj3jguiud bc / 4g i,ua6ltp2694lss 0.760 m, the pendulum bob has a mass of 365 grams, and du il3g4l9) jgipit/jm,bc4 u6au2 s6 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 the clock losesw d9vtz:tvw ne mt*e-..j66u l half a minute per day, how should you adjust the length of the pendulum? sh ew u.tt9tv-lw.*m:dj6nz6e vortened by    mm.

Derive a formula for the maxim9wegayn .2cg -um 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. 6yq1b 8 q f(3ai9ub;p jbdq,jfAt it is released from rest starting at an af,yi6uqp(1qda q bj89 f j3b;bngle 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 thalhadf 6r1/cl5du,3 eqes0.i b t wave crests pass the bow of his anchored boat every 3.0 s. He measures the distance between two cresc3 e5fbrl0au q .eh, 61lds/idts to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speyp:p7e0m 7s l,3cjg mdmw,a+ ied of 343 m/s How far apart are the wave crests (m m 7 : 7mp,aj0ipgsec3dlwy+,compressions)?    m

  (a) AM radio signals have fre12, mwu xzi)ugztq,r( quencies between 550 kHz and 1600 kHz (kilohertz) andtxz(2rg,m ,wiu uq) 1z travel 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 long1 s2a5/kgmnyfg:o o8l itudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same ela)x+obqg6 ;wl 3o+gxpystic modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, and by what fact+ +qp;wgl) gx ob3ox6yor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If the ts g050kero1 cwnph+h 0ension in the cord is 150 N, how long will it take a pulse to tra p00o5 0kwshhn re+g1cvel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable ) n6b81e ye6nd zksgy+of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable.egd1nyb)6nsk 6 +ey8z 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 surface of the sea. Hem z : -nv61 keg+ts(hn4h tds1;whi;wm hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. sz-mth:w+ e64 i(1 smk;g1 tdh nwhn;vHow deep is the ocean at this point?    m

  P and S waves from anau/up5 tx,) qc)bto:b earthquake travel at different speeds, and this difference helps in locating theu)p)b : xot/qbauct5 , 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 trangap3) d v4a1hfsverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is n )aaf4vhd 1pg3eeded 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 earthas0/ zwm.kfk p/:b:qp quake P wave passing through the Ekpk/q .pf:w/0 azb sm:arth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measurez fjikobg5h.q2696+qs ch v r6d to be ch.v h56j9zq bs2+fiq6ko 6rg$ 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 fopl;l fc4 nqyh3d9a re6q4lo6 5/g:whrequency travel through the same portion of the qpqgldof3wr6ly9 e4l/: hh5c;6na4o Earth, 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 have the s;ytjy 7t5t/e a:mfr9bt(r ,fdame frequency, but one transports three times the power of the other. What is the ratio of5a deb:t fyyt7(rr; ,mftt/9 j the amplitudes of the two waves?   

  A bug on the surface of a po2 ,oenk;n nj )qqmdo;8g2kj3 ql*i.ou sz. /rlnd is observed to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum,u;i.qjdnsz.8oqe2m n /)l;* 3 2ojrgkoqkn l KE change?   

The two pulses shown in Fig. 11–52 are b2md4okex, 4bfd); uumoving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulse d ,2b4muku) f4;dxbeos pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrac 2j s 2os1b5op,yir0etes at 440 Hz as its fundamental frequency, what are the frequencies bci yojs1 p,0s 2oe2r5of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 9:)4n vgthol7 u dxnz9294 Hz when unfingered. At what frequency will it vibrate if it is fingered one-third oz9 )4l7godvhx9nu tn :f the 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 frequency xyl+an:q*uj ayw7g 86of 280 Hz. Name at least three other frequencies at which it will re wxg*l +u 7yn:qjaay68sonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of standing waves yix*tsex/kw s+3s; -jdgm7ci* xa3g 2 is 475 Hz, how far apart are two adjacent nodes?*iksgm3x3 ;st*s+wx/yi7c-dga j e2 x    m

  If two successive overtones of3w)niegqk,cyiz.sd*079 t eia 4b v w: a vibrating string are 280 Hz and 350 Hz, what is the frequiiy : bt)9dweekwgn.s73 ,vz c0qia4*ency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.gwp rh)mtc,7(xg *xhaeig9 bb2,w+ 1v 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 t vb9a( x*hbg,mgw hicgr 2xpw +17et,)he frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is mez,xhw 8uh x u7n4skg(;asured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequencies a78xg hs4 hu n;zwuk(x,re,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibraall vvr 5, ,utip+e12+h q:7ft3 vvfryte 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? decre v3rfflr:1a t+ly5ihuqvt ev,2p7v +,ased by    %

  One end of a horizontal string is attached to+vtc xyow,7 vzh:gw1 2gg d2j. a small-amplitude mechanical 60-Hz vibrator. The string’s mass per unit lengthw:wg1d z2+vxy7,j.gtvo2c gh is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be adjusted by movingag t+t xm/-ioxz261 3 ycjxb3 )tvmxh6 the pulley. If the hanging mass m is fixed at 0.080 kg, how many different stand -x)mg6 z 31b6ttxxmh/v+ ct xjoia32ying 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 freqz zukxwfu+1lim m69g * er,7o7uency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce z o6m7u ux*gwz+f,9 7keml1ri 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 aow gwe85nltje,3.7 gy boundary within the Earth between two kinds of material. If it approaches the boundary aejg 85ow,g.y el3w7tn t 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 velxdvmq( szgbb- 6iud4/mzn/ (1ocity changes from 2.8 m/s tobz14/vidgd s/mbu( mn-zxq(6 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 ware/zh0gxle zl j.e 4i()m air when it hits a layer of cold, dense air. If the sound wave hits the cold air interface at 0zezh/jg)x( e.li 4elan 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 earthsyqa9:u 0h3wjs9lun8 quake wave strikes a boundary between two types of rock at a 38n0wyq :a9lsh38s 9juu $^{\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, tb 5b9dss0uks59vbp/q 9q9 grthe dish has to be pointed in the direction of the satellit p gkdq599bbv09 5bqss ru/s9te, 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 k/3nhp6 i1p w+bf p:7. frnuctr2h po*lm and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time 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 boat1btr3 c2+6.l:fhihfp nw7rpponp/ u *s.)    min

  An energy-absorbing car bumper has a s3md5i6e2 qra uj3l s3wpring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use consae53mrsw iu33l 6q2d jervation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m r3 u6iw-zg)zrbelow, which stretches the net 1.1 m. Assume that the net behaves like a simple spring, a uz-r)w i3z6rgnd
(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 pu/wivf/v5yw 7 83( 7soq itnzqlaced on the end of a freely hanging spring. The mass then falls 33 cm before it5/ z vntw y73qu7v/wsi8io q(f stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speedvc 17qdmz- wl9 of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constantw9d7-l qc 1vzm 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 7vkgmmw0; nmz +atpw7d1+7znpace of about 1 ste1dw7nmgn;m v0t +zw +k z7pam7p 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 certhojkc* 7et7+1 qy l,so3 9ryzad bz94eain groove 10.8 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 emittea4*9+ yze 1l7kyzoetj o,hqc37dsb r9d?    Hz

  A 2.00-kg mass vibrates according to the equationeyj0epk6g)r 3nv im8zr. bp4(-it pl) x=0.650cos7.40t where x is in meters and t in seconds. Determi b.-rm6ivkzi3rp8j4p)ntp(e eyl g )0ne
(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 frequencyp./b c v2-nh01rtcuhi if it accelerath.n2 but1icc/p0 rh-ves at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a )fctgvzv) 5t:q2- fag ) v 4yzcf4tc9tc+/tss75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates fost9t cfgq4t)avzgy-ts2 :c v z4)5t)cvfc f /+r 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 5 bz.rp :jxae a-q:4lzat 392 Hz (G) and 440 Hz (A). zjpzqax 4lrb.:a :5e -
(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 tzwvtdsgk )-ne.3,vgm 0+e x8 rhe 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 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 gv.m+x8 kg)sd -,g0e3tz wer nvreater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of each prongnmg:8i9d/ 7xsency8l moves 1.8 mm to eige:mn dy9is87 /clx n8ther 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 kxzv t hr,c7y. 35s,zfharmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which thervc.3 zf5 sykt x,z,7h 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 tha+rbpo:0q o oj7t 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:7qro+p o0bj o and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s1bms*g eh5m3 f — each one-way swing takes 1.0*mb me g5f31sh00 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 can28 owz. lh-qvx swing as a pendulum of small amplitude, but not both at the same time. Which one is lonxv8o.h2 z w-qlger, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mas 2c/4*7whzodzebc)qwyi/ ex2s 123 g is stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulsw7/)2 zd cebx4woh/c2* qzieye is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ce skq4vdd k44y:iling 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 on top ksv44ddy qk4:of the block? (Assume $m \ll M$)

  A crane has hoisted .z cggcnvsjsqbr7 )51o( 4v 5ba 1200-kg car at the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze startbvn 1q c.sb5zggv7)4 r jos5c(s 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 swx bs sfdh,,j;u,qx6+25kfzj5kadc* v1a a2mhown 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 frequency of this vibration, given that the sheajsz aj k*1fwx6v2da2; ,h5,b qcxs m+ufd5ak ,r modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz