Give some examples of everyday vibrating objects. Which exhibit SHM, at least a8 tl*s5o,gto- wocu4 bp4ogtt5owco su ,b-l8*proximately?

Is the acceleration of a simple harmonic oscillator ever zero? If so, w2v*e mx+rvl.1ibc nj (here?

Explain why the motion of a piston in an autjck 9;xxl3o;sw . a9toomobile engine is approximately simple ;lcja9 ;39oos twxx .kharmonic.

Real springs have mass. Will the true period and frequency up( oa95tq*kzs8uu 3wi7q ao8 be larger or smaller than given by the equationsk iaz37u 8uqwoo(*su5qt9a8p for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the dqump xck7(p6v c,5)u maximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to6u b) enptwf)/ the hook of a vertical spring scale, and then is released. Describe the scalenwtp)/ e)6b fu reading as a function of time.

If a pendulum clock is accurate at sea level, will itxp)s7;qgmqq6(- e:v.dc mzhv gain or lose time when taken to high altitu)zmq.p (e;m:6 7vvhq scxgdq -de? Why?

A tire swing hanging from a branch reaches nea th 8q0si ih85 lvfgcuhvy0.s*s2d3r(rly to the ground (Fig. 11–48). How could you estimate the height of the branchd.3tlhhs*0vfc(v 0uy588 q2g ir sihs using only a stopwatch?

Why can you make water slosh back and forth in a pan o(l0r v0o4;axi t lg cgpul+dj)5af0t6nly if you shake the pan at ad +oj)pcal x0 ;(aglr0 t5v4gfi0t6lu certain frequency?

Give several everyday examples of resonx e5pcy7x:g3 jance.

Is a rattle in a car ever a resonance phenome 0i abcqzrkfi c1k 4p8:2x49ajnon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of i sfj x19gu1,yfh9ncz o)6l qi5ts source? hjnzf)5iu sx1o9gcq6 l1,9fyWhy or why not?

Explain the difference between the speed of a tz va z.9,tcdf*ransverse wave traveling down a cord and the speed of a tiny piece ofvd f zat,9*.zc the cord.

Why do the strings used for the lowest-frequency note2 cr1hr*p zp5ws on a piano normally have wire wrapped around them hrw *c2p15rpz?

What kind of waves do you think will:-5/xzw+- o ncu svrkq travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parallel to5 s-x:/uv+-wz cqrnok its length?

Since the density of air decreases with an increase in temperature, but the jtz-w)3sy hag+- zufnt,0m)p,a o,tb bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary wigb0,ty, )ofz,ha m-+utns 3japz - tw)th temperature?

Give two reasons why circular water wave5(pswwaeytpr.bt:wp08 thgz38k x4 d* om1n2s decrease in amplitude as they travel away from the source.orw 5 8h2gbdpt3 . pwa 01nz*sxmwe (:yt8k4tp

Two linear waves have the same amplitude and speed, anxkkh w;w w (k1/6hs(lxd otherwise are identical, except ohs 6w;klk (hx1k ww/x(ne has half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections oc)qs nt 3v) ixhpffidsgeg 3t.)(. +j4f cord as in Fig. 11–33, the frequency dnx c )3qpsg)dtsv .tjh)+(fei34gfi.oes not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in th i3 +bs pln j7/ vfxyob0nmd9y..xc/8free segments, are there any places you could touch it with a knifey.bv8p3 yl ./dbonim7+ 9xscx jf/0 nf blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incident and re 3rfwp1n3) adp5c tisi3 *jr+kflected waves cancel at the nodes. Does th pjk 5iswt+p*racdf)i3 r133nis mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to v50oam qacl *yw:)wattq1kui e- a7u79w-5kz another, how might we determine whether the energy was being carried by particles (mwyaak)-vcew0lmo7 q :u1t5a9tziuqka* 7w -5 aterial bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total distance i -lj. bw 5hvbvuye78uam; ,u7lt travels in oj,lue.au;8l-uhw775 mbvyb v ne period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but is 85 cm 0uqgde1 ta9pkkrtj+05q wp6 *long when a weight of 180 N hangs from it. What iswp +pr*01 j5gq0u q tka9t6ekd the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg dji12n6rhn +xzdh.-gu t,7f e(m+azieriver gets into the driver’s seat. If the car goes ozj1ae,x+zhg7- m.d2eutirn+6 h (nf iver a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3z+3tv :upg pd..6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffnes pzgup+t:.3vds constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz whe ilor (hbjfq0j)9. bg-n a mass of 0.60 kg is hung from it. What h(b)bjrq9go . f-jli0 is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indhzh7 or x19zo6icating the position x of the mass in Fig. 11–2 at times t = 0,16o hzohr9 z7xt = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 60)yj zgzl ify 5v9:vg+4mh 1sakr*r uspider’s web. The web vibrates predominakz*vr fz 9vs65g4 )ghamy iyr0l ju:1+tely 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 vii(tv i1u*.me qbrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the value m (ei*tiu.q1 vof m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second t0-y*bmd1ezph6*fxo with an amplitude of 0.13 m. Determine -zeho **ftdb6yx0m1 p
(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 speeg ,lm)(zd f/l;ykwu lx((1z mfd of a SHO half the maximum valuey)xumz,z/ 1w((( mdgk flll; f?$\approx$    A

A mass attached to the end of a spring is stretched a dim(w 6.g *bzayfs;uy .ostance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. If the springd;g9 xmns)/.uoqbm8 t is stretched an additional 0.130 m and released, how long does it ta9mno;g dmx /.u)tsq b8ke to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached twup; b6 o 6ejxoyh-gx.xu5c4:o a spring with spring stiffness constant k = 28begu o;65:xxu6 cwp.y4oxj -h0 N/m and is 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 rh5o6szif4l,xy x 58opopgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave the gun 8iyr5o4xlof 6zh,sx5 ?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to onkq(bchh g3m7hw8z *n0e end of a spring; the other end is fixed to a wa0hq873 w(* zgcbhnkmhll. 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 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 accordir3ec 2n5w(nb sng to the equation x = 0.45cos6.4t where x is in m2s(3rcnb w5e neters and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of a SHO half KE andjzk4:db6 bs0, ;gr oyz4bh1r(0 xosfn half PE? ±rr460ghnskfd0yz;bso :1o4(x j , bz b    A

  If one vibration has 7.0 times the energy d5ul(r); d mpsof a second, but their frequencies and masses are the same, what is the ratio of their ampp) us5l(;rmddlitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring oncbqvw1tf7jizsz e -r2*u7 d1 9re every 0.65 s. 2e-z*w r7bsqvfziu 9jr 171dt
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallel mv4iw*/j3xp m1 .t,uuk ld9gezh*re8vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of el d4pv 391g r*mitu8*ukjwx h./zme,vibration?

  A 300-g mass vibrates accordinji td4vu b8v2a9l85mr( vikru2d .s gzo/5wj +g to the equation x = 0.38sin6.5t where x is in mete25m8iwb 9o 4z jrs(urat /u8v dgvi5vlk.2dj +rs and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and B. For xvdr:)8 okw s6each, 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 en1: mu ih qn+cz6jkga75d of a horizontal spring (k = 124 N/m) is struck by a hamm5agkn mu7qzc6 i h+j:1er, which 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 stiffnewy+0l ub(z m(sss 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 velocity at wzl 0s+ m((uby
(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 tz7a*9xjlcz z 1o8 suo+ lb:5pmwo springs, 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+b*yie5euqixj t3r1 c ;q*0g 1z *etvl to a fixed horizontal spring whose spring stiffness constanti1qig5 1 3y*eltrjz*;0 +ecx qb*e vut 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 juevr bwib4yc d3q6 ,bb-w7w -9rmps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low7 b-v3wi,-w c6 ybdqreb9b wr4 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. What is itsz0irq1r tsp- kr(d2:p
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pen.z el c o(8ah0,s.jupbdulum be if it is to make exactly one swing per second? (That is, j hzu opc,s0b.l(e8a.one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Ma-pzycxr7 (.qauie 9h0g 4cpaoo l3x)) rs, where the acceleration of gravity is abo04cplq) y(ca7uzogp 3i- ho)xx9.ea rut 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm long *fsdz yj;0jyi)*2gln
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simp.xl;: h09lv wvcrosr)le pendulum is 0.760 m, the pendulum bob has a mass of 365 grams, and it is released at awlxo;)slv:r9 0rh.v cn 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 clocci. o0 c t63.yl/j/uix9 vwgjdk loses half a minute per day, how should you adjust the length of the pendulum?x.i/ug cy ow39cd jli tv/0j.6 shortened by    mm.

Derive a formula for the maximum . jv sxma044 0(tzsrr8r jh/kbspeed $v_{max}$ 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,izo0(z 1uc79 xyc uezkgc2k; released from rest start9 u kcxye2czi0c;1 zugk7z(,oing 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 the bow of his a jn)g ,)q6otvcnchored boat every 3.0 s. He measures the distance between two crests to o)j q vc6)n,tgbe 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 speed of 3:2 w-sgg0w su5 k mww*(qok+fj43 m/s How far apart are the wave crests (c:s(*jsukmf 2 w5ggkww owq-0+ompressions)?    m

  (a) AM radio signals have fre9vb,rl7(a thyx0,y l fquencies between 550 kHz and 1600 kHz (kilohertz) and travabhxr 9lly f7 yv0(,,tel 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 longizh2z77i.mvud tudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one1(bow *n c,ser is twice as dense as the other. In which rod will the spe1nrb,e so(*c wed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports .fq0v65soyug30qnud a 0o8mr 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one support ty6s ouogdm.n 5a uv0q03q 08fro the other?    s

  A ski gondola is connected to the x8hz;k uijzx9 kae2 1x*tym9/top of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of i2zej8 y m;/*z k9uka ihx9x1txts run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his shi:6esw j,w8nxj p just below the surface of the sea. He hears the echo of the wave reflected from the oce:8 s,jewjx6wn an 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 different speeds, and this difofy 42v8xauc-ference helps in locating the earthquake “epicenter” (whereox2-4y8ucv af 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-producgp5jj aij:) tcw6+t7ced surface wave can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually itj wgc:aip56) +7jtjcnclude a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of an earodgw 2yo oe6x,1t:u4kthquake P wave passing through the2dw:o ,kut4 ygoo16xe Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquj ap: 6m)nyasa0 )vz9xake wave passing through the Earth is measured to be mjv9 z x0n:ayp aas))6$ 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 sa,1ky ihzjxnb/ muo8nsz0 bh df:: u7-5me frequency travel through the same portion of the Earth, but one is carrying twice the energy. What is the rath yuh07unk /:5bdfzi,8smo:bj1z n-x io of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same fr* l ; f6a-rlwpa,mqth2equency, but one transports three times the power of the other. What is the ratio of twml;hp2lf-,aar qt6*he amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down a total vertical kr6ib+xwz0 zggoyd3vb+i -. -distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, b3gb.g+0zxzkoi6w id- y+v -rby what factor does the bug’s maximum KE change?   

The two pulses shown in Fi2/ e/lzg7x*crv ek6hbz +jg: yxe 9mg6g. 11–52 are moving toward each other. (a) Sketch the shap g g7lymb9hj6:rkc // *ez+evz62e xgxe of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequencywp;mg/8n u3u a, what are the frea8wmgu3 ;unp/quencies 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 what frequ )o oe0tmwrf 0(2-nqgmency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string q mo(wf-0t 0o men2g)rvibrates as a standing wave.)    Hz

  A particular string rpf7 21yh+f4y g;f 3noubg-(sf xy7x/x mgilw)esonates in four loops at a frequency of 280 Hz. Name at least three other frequencies at which it will reso4y1(pf;) xm gulfx2nw y- g3bffs7 go/ixh+ y7nate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a k 1xol0lx5w/ vstring is 92m/s If the frequency of standing waves is 475 Hz, how far apart are two adjacent 1ow5xx/ v0l klnodes?   m

  If two successive overtones of a vibrating st g*hv+1 fjni gen5 0fi(w 9oc8i30zvefring are 280 Hz and 350 Hz, what is the frequency of the fundamental9i8iwn5+f* o0ngeh(z ijvff 3cg01ev?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distan 6eji ; cij;7wy2ruo80m )vdnyce from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. mow6 id0vr87;j cneiu) y; j2yWhat are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 2ip0 yu 76ch 7iw w5 gj0h6h;eiiz,nsi+00 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 the three frequencjuh7w6 i;,h iwzi0i+7 gh60iep s5nc yies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed twqq7ix)h be1h,jf. 5. 4qswcj8y 3idmo vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be cs78qj.q w34hh jdqxmcf,i1i.w 5) ebyhanged to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amp*gww43mjyqc4n2 z8nm 5mwn sso5/ ak 3litude mechanical 60-Hz vibrator. The string’s massksnjqon 2y/4 zm8g w*a5 m3wwm5 3cns4 per 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 the string may be adjusted by ikp-1fta 4.wp3vo8r lmoving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achiev31alp- p8 4ovtrwk.if ed by varying L between 10 cm and 1.5 m?   

  When you slosh the water ev; knv3lg5h0 ,6uzeqback and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standin6g5vnvk,3qe el0z u; hg 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/8:io )6lqgu2jy g wh(ps strikes a boundary within the Earth between two kinds of material. If it approaches the boundi: )po(gh8 6w j2lguqyary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the veloci1z x*o zgdq sym-f*s07ty changes from 2.8 m/s to 2.1 m/s If the incident wave crests make as-xy0z1*ms q dfg7zo* 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, dense 1 f*2 yxz/blapr.2vufair. If the sound wave hits the cold air interface at an angle of 2y2 f* z ur12vlbpa.xf/5$^{\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 wavecv rh)yat72 s8 strikes a boundary between two types of rock at a 388r7va 2cth) sy $^{\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’-+ pdg62 nalpms manual, theln +m-p6agp2d dish 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 ande(tkr c98. oce hz;1lk velocity 750 km/h travels across the Pacific Ocean. As it ap1kle8kcte9(hr z c .o;proaches 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 ca 10r(gueh2r0 p s0trhsr bumper has a spring stiffness constant of 550 kN/m Find the maximum comprethp0srs1e2 hr0( gu 0rssion 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 18 m below, which stretcgw 2-* .ztfdv8znd)n,z1k v-)fd5p zvuiq s1thes the net 1.1 m. Assume that the nkdznpigzzutd v,v)s2n.5 zq8-)v wt fd*1f-1 et 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 hanz)9st2i 6( heeo /qrhcging spring. The mass then falls 33 cm before it stops and begins to rise. What is the freq 2rth oe) qsz9(6h/eicuency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 miq/ k42 hkmc2d/s (Fig. 11–54), compressing th km2 c/kq2d4hie spring 5.0 m. (a) What is the spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8a lior0,1 pzz;.zeken-if3 /v cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the to0e.pa iv/ kzf nl31-roizz,e;p (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33 zfh1 t).f( w6ybnjxw:-rpm phonograph record have a wavelength of 1.70 mm. Whatt:6nw1fy.bz)f ( x whj will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equ y* xh gvll91nwrt)wp1+p0f;fation x=0.650cos7.40t where x is in meters and t in seconds. Determine lth;01f+ lrpw*x)gvy f w1n p9
(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-xr tuk n( unyj4hb *3;/,jauy frequency f. What is its frequency if it accelerates at 0.50g (ja;jt(4uxn3* b/y,r uuk h-nya) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lar 4)yy g*:g(n rdnpzp9ke. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrynrn dp4 z(9r :*ygg)pates 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 Hzqj*g yh; ,gv1rrc3nw * (G) and 440 Hz (A). gr1c;w*gv *y 3hrjn, q
(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 th*r gu6w2s2: kca kcr9pe 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 sec*ua2r 2 w:scp9 gkrk6ctions. (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,( xsk +oq .l5-(szmqar and the tip of each prong moves 1.8 mm to either side of center. Caas(x roql.+ qs(mzk -5lculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates wwmlg- tls 58 ;6ug2x0cz2 iilaith simple 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 a2t zci-0gwl 5usl26;m ilxg8pebble 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 thatg(iy so o2n3+d can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibration2d+s3oniogy( s of such a string with one end fixed and the other free.

  A “seconds” pendulum has7/k4v:cc6ircz +kztsgq(m;x ge,2nr a period of exactly 2.000 s — each one-way swing takes 1.000 s. ,kgc2c4z vrx7gi zq k nsmr:/c+6et(;
(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 canw* h-6f5ajm uzs8)w mu swing as a pendulum of small amplitude, but not bot wjwfa*s )zm8-hmu5 u6h at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [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 st 9sf:;- wdfvbyretched under a tension of 255 N. A pulse is generatedvs db;wfy-:9f 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 sb: 3y(ko1osu a jo pc9)sp6kvl8b.i t,tiffness constant k. A penny of mass m is placed on top of3kapbjoc9syolo 6i:8v, k ()bt spu .1 the block. 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 the junkyard. The steel crane cabll(rh g7.v4/tk-*odw ltrsti 7e is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the ctg( ks. llr/vw o*4i7d 7t-hrtable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which:d erb0rs +rr9 also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello re9 : +rdr0rsbsprings back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz