Give some examples of everyday vibrating u7 5k0yx:uvcsweda gc.5. *m vobjects. Which exhibit SHM, at least ape ykx*aw c:..05v5cuv sg 7umdproximately?

Is the acceleration of a simple harmonic osjtdjg2 6 ck4nm;ll:2x)kn2 xocillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approx(.vhevn 7v,vg imately simple harenv7v gv,v h(.monic.

Real springs have mass. Will the true period and frequency be larger or was5z;-jht-jn ggn1mj4v8 ,s: zwil7smaller than given by the equations for a mass oscillating on the end of an idealized massless spring? Explalh1 zwg, 8w 5-n :;jn-a4s mjvig7jsztin.

How could you double the maximum speed of a simple harmofmx9yduz0m ;rmln xw5 h*m5ulm+67o6nic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and t)1 )9xw2a/vrgdf sx vlhen is released. Describe the scale reading as a function of time.l2 wdxs)/ vgvaf9x1r)

If a pendulum clock is accurate at sea levesvfz 1qg- m1(:bd-kb3p0qutvl, will it gain or lose time when taken to high altitudeqg b uk:v f3(-1 t0qpvm1zs-bd? Why?

A tire swing hanging from a branch reaches nearly to the groundel9;el))v o f nsq21xlv -8szd (Fig. 11–48). How could yo;sfl 8ox 9lqldvv2-)zn ees1) u estimate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth innvwq,py,) /n;.h n/t oap:jkl a pan only if you shake the pan at a certain,nvtpj q/kp ,n.oly;wn )ha :/ frequency?

Give several everyday examples o a/rkk3 7ujx/sf resonance.

Is a rattle in a car ever a resonancei7ux 3wwm 76bg phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of:s7 tu a(lh8bp kbsl5l 3)xanu9) t2dw its source? Why orbsa ulnds: tl8h)lwb9 )xt 5p2 7a3(uk why not?

Explain the difference between the speed of a transverse wave travel de.fs 5boxfk;qbe- w.vas8l(w) 7v9ling down a cord and the speed of a tiny piecef. ;bk5s.w e)(v7wfv 8ea do9sbqxl-l of the cord.

Why do the strings used for the lowest-frequency notess:gq4(jst jz ozm/zk2q8 )*sv5itm/ qexn .h6 on a piano normally have wire wrapped around the i6 qhz4o gmtksz5 sz(:nqev2jm8q*j/s)xt /.m?

What kind of waves do you think will travel down a horizontav 4a)jh(bs;ucl metal rod if you strike its end (a) vertically from above and (b) horizontally parallel to its length)acj h( s;b4uv?

Since the density of air decreases with an increase in temperature, b+( zbtm0lta 64/f) f /g2bvesyzt9ruv ut the bulk modulus B is nearly independent of temperaturebg9b)s vvt (zt6ra zm ey +0//2fufl4t, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrbu yljj+t9 r-+2kd)z8 k:afxbease in amplitude as they travel away from the sourc9 +ad8u+jrkt 2x-: y )bzkljbfe.

Two linear waves havtzbal(zv ,3 g04ksehe34vt7l t,a g 5we the same amplitude and speed, and otherwise are identical, except one has half the wavelength of the other. Whi tvalgawevg0 34 s3eh,bt z7 (l45k,tzch transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary betwep(g4kv2s(4r5 uiak0fp lenj gc6 f28zen two sections of cord as in Fig. 11–33, the frequency does not change (although4(2rlufzs 2pe4kcg fig6p (kna58vj 0 the wavelength and velocity do change). Explain why.

If a string is vibratingjimwj1kkuq0 5y0. 2l itn;v3b in three segments, are there any places you could touch it 0kqn w;b1mt. 2ui0jv j3kyil 5with a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incidl1)ci :y epqe9ent and reflected waves cancel at the nodes. Does this mean that energy was destroyed? 9 qee1l:py c)iExplain.

If we knew that energy was - kg-db/d:dvwfj 5 c+ubeing transmitted from one place to another, how might we determine b5wdk dj/fvc:- +-ugdwhether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM wp0 33r xrj 7*p;nfxhedi;x zn8ith amplitude 0.18 m, what is the total distance it travels in one pid3he0xpjnnz*fx ;7; 3p rrx8 eriod?    m

  An elastic cord is 65 cm long when a weight of 75 k,0 1n mvatnm/1u *dxntct7h6N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k /60cvm*1an1u7tmtnt d,kxn h of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68m*pl h3(bh )jg3b rxg;-kg driver gets into the driver’;xl3(pbr ghmj*3gb h) s seat. If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3 ze/ij3l,zm2u.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffness cons,zzu/ je2 li3mtant $\approx$    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 mahmm p.ukgn655oq0en 7ss of 0.60 kg is hung from it. What is its n5p57umomg e .k60nqh frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x c 0) p2qd0lvmeof the mass in Fig. 11–2 at times t = 0 q 00vd2p)lmce,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 pia*y*ogcg 9. k 1sjg+tredominately with a frequency j+a* c i9.stggo1 gk*yof 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 frequency0n;-l0fxviw8bzn t9 1 t1gvou of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 01buw -nx9otvn 8;00vfg zi1tl.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the en f/ 4jkj99anend of a spring vibrates 3.0 times per second with an amplitude of 0.13 m. Determin jkeafn/99n4j e
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed of a SHO hal8+ n*b tj7xzjy uly)j,f the maximum valu8b7+t,zlyj)jn uxj* y e?$\approx$    A

A mass attached to tisd036js d,f she 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 vertical spring 0.8wybr r uc67n5 i+ 57vig),u6wqldhsc315 m. If the spring is stretched an additional 0.130 m and released, how long does it take 76)6dv q8nh 5is7r ulb,cgcw5y +iuwr to reach the (new) equilibrium position again?    s

  An object with mass wm u hezz7)gh6r ht,5j: wi793w c9hmc3.0 kg is attached to a spring with spring stiffness constant k = 280 N/m and is executing 9mz7tjhw:hme5)h7gcwu 6ci zh3 , 9wrsimple 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 comqxb+dk*5x* m,k nxm(qpress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what (5+x qbk*mnx d mk*qx,speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless kk/t4 dlrut)woy*m8ek4.a8v surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum aek 8w/y8.lo 44mkr)adtvu kt*cceleration 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 = 0.45co n6p ros7fs* j0osjq84s6.4t where x is in meters and t is in seco47 nofssjq sp86jr*0onds. 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 and ha+xi;x2f86 de1vifigbyr7 nz4 lf PE?gfz7i+b 641vxifdix;yer 28 n ±    A

  If one vibration has 7p1dpg6 5-65elia0d)j48yi bus io uiu.g* mxl.0 times the energy of a second, but their frequencies and masses are the same,sadu5um.j gye pp54-6i du)io10glii x6*b l8 what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hangie0o6iu 0j* mheng light spring once every 0.0j60ou ee i*mh65 s.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is sc8e naq-pzfk3lng n4 ,n(+ m7uupported by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibran e7um(c pn8l n3kan+,-z4fgqtion?

  A 300-g mass vibrates according to the 03by. wpbx :dgequation x = 0.38sin6.5t where x is in meters and t is in y:3b0gwx.d bpseconds. 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 exsy8g/g /rrc5 vamples of SHM, labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal spring (k = 124 N/m) is strv2;gfoud8b8q szb(b2* vqt5 wuck by a hammer, which gives the mass an2( s wuq;b2dvq *o8z f5vt8bbg 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 stiffne9qft*k*bvz8(vqk ww ( ss 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 ve qz v8*w9vb(kk*w(t qflocity 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 spr5wfc mxs+9 *yiings, 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 horizon oi tc8ctzp (q pn(/9yu3u6sqc5 bq47ptal spring whose spring stiffness c9uiny5pb((c /qc7 6 tp8z tupqq4c3 osonstant 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 jumxk nfe eimb,*0e50rt s.o3jx5ps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness con5fte xmjxk.0*r o,e 30i5nbesstant 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. Whatr ,ost (ziuc,8 is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple p8uk9royq))z yir0 bc;*h uy5dendulum be if it is to make exactly one swing per second? (That is, one complete vibration takes exactl khbd*y5)ycq yu09uzro) 8ri;y 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, wherea8qztpa8 ul zyev*74z 8 w6ndj* h37lh the accelere3zv*al*8t74p qha wjuyh76 zl 88 zdnation of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pe )aws: op-ldq8yb/h7gx* cqc 8ndulum 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 bob has a mv2)jy bzo aj11ass of 365 grams, and it isa1b)jj 12 vyzo 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 pe 1(wpwup2e l-j)h)swxndulum has a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the penduw e-sh(j1l w2x)puw )plum? shortened by    mm.

Derive a formula for the maxz8lrl4 yr/v78*derz z imum 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 released from ra56k vo1-uxefest starting at an x f5ov 6ku-1aeangle 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 t;;jd c 3c:1z 9kxhvgpfhat wave crests pass the bow of his anchored boat every 3.0 s. He measures the d; 9d hpvf13gzkc:xc;jistance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels withre.hgt6-0r3x qk*p- x zafjx t2uw41h a speed of 343 m/s How far apart are the wave crests qh. whk0g-2jxtx -t u*z6xp f3ea4r1r(compressions)?    m

  (a) AM radio signals have y,eong3s0 b (yix.m4u frequencies between 550 kHz and 1600 kHz (kilohertz) and trav nyeo3,u0 i(xg4b my.sel 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 wave(qu 3 2uvb0)gt.mjq ;oy+rncbs in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is tl5lhyf 29ke;b )f,ff3tqaj c 4wice as dense as the other. In which rod will thf;)lq 5yh k24ae9fcjfl, 3ftb e speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched betzc-sp30 ua yju2u/ 7hlween two supports 28 m apart. If the tension in the cord is 150 N, how lonc7a/phl0zu3y uu-s2 jg will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable ofky sfy. 70dmk/8b qh8h length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observedq0kkhbm h/ y78fdy8.s 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. He m8zo2e8ksaf 3-0dl d rhears the echo of the wave reflected from tzl2r8ead 0kf mo3sd -8he ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at difff( )a1 wxnu8cb q8sv5lerent speeds, and this difference helps in locating the earthqc1w8b5xu fl vnaq8 ()suake “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 dajsmxb,8bw- k xdo, f)r+8(wtransverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objer(wxf,x )-b,d kd8a 8moj+ bwscts begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intetfl)(h5p +4nx+n ao) 6hsvi mwnsities, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km fromn w +46hx+vhsfp )lmnto) (i5a the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured to bcm,l+i x;e iss7z*ptt3q. n( de zi*qp.etm 7( s,3si+t nlx;cd$ 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 same portion o*cy(brw9ay0 5wso+o5st/j c mijy 4;h f the Earth, but one is carrying twice the energy. What is the ratio of the amplitudtw irysj*;90o 5bcyoaj5s wh( myc /+4es of the two waves?   

  Two waves traveling along a stretched string have the same frequency, but one ; +rvpugaz,qvv;t) /b transports three times the power of the other. What is the ratio;,v uztb/g qv+apv)r; of the amplitudes of the two waves?   

  A bug on the surface of hajd2 i2b2 os4a pond is observed to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what fac i2a2bojds4 h2tor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) Sketc tw9uq p8 xzmcep8u(8,x*f2zch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the stxmx zp c( 8,epct8*uf2uz9q8wring 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 44d zg*b,3q0k .kpu g4qm0 Hz as its fundamental frequency, what are the *u,0 p. zgqqk4d3 kbmgfrequencies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At ww pt ;cdpe.zv ba3(;ducmh x2g,)4j,p hat frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wavp ebvp;.uz(xw2d 3, ha t;4ccjp)g,mde.)    Hz

  A particular string resonates in four loops at a frequ8h:2k-/cdschis f fi7 ency of 280 Hz. Name at least three otheckdi7 hh2 f8cs-sf :/ir 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 frequen/ gcid o9 xtt,uzd1)4ccy of standing waves is 475 Hz, how far ai1 4,d9xtcdc zgut)o/part are two adjacent nodes?   m

  If two successive overtones of a vibrating s2 dp(jhk; -dfg, :.jvuagikd 5tring are 280 Hz and 350 Hz, what is the frequency of the fundamd5(g;vkuh:, jk-2fp gajidd. ental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance frop 6+zpka wko15m the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the f51w zpopa+k 6krequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hn2b3z3tphz9 f xwq 2.iz, but it is measured to vibrate at 205 Hz. By what percent should the tension in33z2qz txn9 fpiwhb.2 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 su*a i-;, ytv2ad 74txyt5wsi ippposed to vibrate at 200 Hz, but it is measured to vibrate at 205ys yv*2 wpa; txi5tta id4-i,7 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 atw ,a/hsdg8tl/4 pku/m: m*ts small-amplitude mechanical 60-Hz vibrator. The string’s mass per unit length itswgm: /ml8ukt s,t a* phd//4s $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be adjusted by moving th+ /u57tu1tzmkj,j qpne pulley. If the hanging mass m is fixed at 0.080 kg, how many different standj1 ttpjm z5u+u,k 7n/qing 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 rigim spdg;x9ti0-yhe b4p 2)am3 iet5k-ht frequency, the water alternately rises and falls at each end, remaining relatively calm at th piem 5m h tg-)bpx0e-ds4iy 9k;a23tie center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a bouf qhavp,*g6y*ndary within the Earth between two kinds of materia gf*vq ph*a6,yl. 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 underwat:x,2a 3n rs:h wgca3gyqw h xog6:r/ 0qfc7b8der “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incb8goyx:w r 2 3,c3qd0/ 7awgncr:s6hq: fxaghident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is travely7htx 343ts7/ psai rling in warm air when it hits a layer of cold, dense air. If the sound wave hits the cold air in /stis r 4p73xy3ah7tlterface 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 sf4.d zpikbl ;,3wst w8cpji82;-aerl trikes a boundary between two types of rock at a 3-idpla8 j; , wzk83wif ;ecp2s4lr.bt 8 $^{\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 0v.g1e63 rz sjy( e y8juonxto4e+1b+b.5 m in diameter. According to the user’s manual, the dishy8sb.3(6z1ye1+be 4g jox+jto ne ruv has to be pointed in the direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 km/h travels across the Pacifi8mo n5jl3fg +qc 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 shofjq538+m l ngore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper hax9ui714riq 7zesc)ma s a spring stiffness constant of 550 kN/m Find the maxiz cu7ir si4x1aqm9 e7)mum 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 conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18xw1ix3u ptc16*b z 6wy65such rjcxtc vs.05+ m below, which stretches the net 1 jxt1.1hvp3 6uwzbctx5si r+ u60c5cy*scx 6w .1 m. Assume that the net behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hanging spring. Theu hqv 8of::3xtex) :fz6:sgnt mass then falls 33 cm before it stops and begins to o)et8vs:f6 x hgxq t:fn3z::u rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speedxw, .a650gob:an hzdcwe y; 1m of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness g z;manoadc1 ,w5 eh: .bwx6y0constant 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 ol9i y rkvkilf)1i *yij3 1eth- c/rqm7ute7/ 3f about 1 step per second, the coffee sloshes more and more until eventually it starts to spill */ul3-tcrjhfe9e1i7kl v 7yqii tm kr)1/ y3iover the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groovec+.:he *9djfmbz ti6s 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What whejbzs * 9d.c+f:it6 mill be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40tce8 9paf. bh6aboe85dm fr n1. where x is in meters and t in seconds. Det9rfcea8 .ea oh5f6p8b m.n1bdermine
(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 it acc/xpn 44+c(a e* mcugxrelerataxc (/rge*4nu +cxp 4mes at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats18r/)m+vi y np1izhn t on a lake. When a 75-kg man stands on the raft, it srm+i p1t)nihy/1nzv 8inks 4.0 cm 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) and 44n62* 0dzq kavb0 Hz (A). za*v6d nqkb02
(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-part cord of Fig. 11–33-aejvc 8co5fzw +fkvrq (xfa(f 90f( ). 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) I+8oaz(acef )vwcvx0 ffq(ff5-( 9jk rs the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264dostf a2 ldr1j8/)m/q ;ghn 8o Hz, and the tip of each prong moves 1.8 mm tg1rqadd s;)ho/8tln8m/ j2f oo 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 simp*-f-a uu jox0p9.ki1snac (eile harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fpkc *aj.1n i- us- eu9i(0oxafig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “fre ds0ve wx)9m6hj:nga 3e” end if that end is attached to a ring that can slide without friction on a vxe gh 936m: nswvd0)ajertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.n( (8cuhy3avy000 s — each one-way swing takes 1.000 n(ah(yyc 3uv8s.
(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 oscillatexhktzl/nz0.qj 5 5qq(xl 9u-n 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 period of the horizqx z( k.htxzq/- nllj5q5n90uontal 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 massd( spl/c*i,r egdm6e* 123 g is stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is gec de,e/ip l6drg *m(s*nerated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a sp, k2jna0dzd-j5i 6v laring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations n 5lji-djz,2dav0ka6 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 the junkyard. The steeld12nou1b gtw/ho6c*h +xrob,z c i*h+ 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 bouo bhztodhuoi**c12h,/ g rc b6+xn+1wncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on r6qy6 lxe)pux 6d)*jea plate as shown 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 shear modulus ()6xe j uy6* exrp)6ldqSection 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz