Give some examples of everyday vibrating objects. Which exhibit SHMy(+vlolq6 1m+uk- o hgyl3h0g, at least approxima -ggo 0(+1ohlhlv3yyql 6ukm+tely?

Is the acceleration of a simple harmonic oscillator ever zero? If so,+.8gpy +zrx ew 1/zehk where?

Explain why the motion of3x*/z+tk4mwdbp*0 u 6brlsaw a piston in an automobile engine is approximately simple harsrwlmx/wutk+ 3ad4**b b0z6 pmonic.

Real springs have mass. Will the true period 2y* )vugln 8cpand frequency be larger or smaller than given by the equations for2n uy8l)vgp* c a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillatorak l tv rp6v0ci41l/0s-b*bo e (SHO)?

A 5.0-kg trout is attached to the hook of a veqj/-k+aqf yl2p cu,n)rtical spring scale, and then is released. Describe the scale reaq2)y,cn fp kjq-/+ luading as a function of time.

If a pendulum clock is acmp1* +fa8:9mm :q*m p6a f;fcsh ygxxmcurate at sea level, will it gain or lose time when taken to hif;+phfs:m8gx*cmq:xmy*m9 a amp 1f 6gh altitude? Why?

A tire swing hanging from a branch reaches nea6mbw d zq2 )m.tn/a (jsh ulv.qkf3w,9rly to the ground (Fig. 11–48). How could you estimate the height of the branch usinn,t 3s khu zw(q)mf.9mb 6q 2wl.d/vjag only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shak ibkra 4y; ;.hv8yn0q65- iostlfc(rne the pan at a certain frequenq.;-4fbtk0c(nli6 ;yv ior 8har5syncy?

Give several everydad*x,g9not 6hvy examples of resonance.

Is a rattle in a car ever a resonance pot uu ng r;e7)v7dl42zhenomenon? Explain.

Is the frequency of a simple periodic wave equacp:zig0p qswb b8-t57 l to the frequency of its source? Why or why 8p:cz7-qgtib ws0 5 pbnot?

Explain the difference between the speed of d7 wqmklc 0wemno;8ot. *rs/ 1a transverse wave traveling down a cord and the speed of a tiny piece 1.d;wmk8no /soq c7m*re0 twlof the cord.

Why do the strings used for the lowest-frequency notes on a piano nvvc hk;*j66xep,sw1a5 zv bi0 i mhy12ormally have wire wrappe1 wh vh1zs0pi*6x6;b cj25i kvym,vead around them?

What kind of waves do y+ 3a3bwo/o 9 wgsmhkf:ou think will travel down a horizontal metal rod if you strike its end (a) v3/hb+3wok :sgwo f 9amertically from above and (b) horizontally parallel to its length?

Since the density of air decreases w;b 4n3 pu7dpctith an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in;tc3bu7d4pn p air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as they trave m..d fin c xw*,5z9otur *ilhnn)(e6rl away fr6iie.f xt*r)z n9o (lu,.5n hc*mnwd rom the source.

Two linear waves have the same amplitude and speed, and o ju0.zt:*jwmo therwise are identical, except one has half the wavelength of the* oj:uw .jzt0m other. Which transmits more energy? By what factor?

When a sinusoidal wave crossebr 8bi;-h u0a-n1ujv z l44rpdzn*nd/s the boundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velo4-nlji zzr ubhubv*r; n-/1n pda04 8dcity do change). Explain why.

If a string is vibrating in threq93o a6z 8 zxto6me :u:o,*e a6htvwebe segments, are there any places you could touch it with a knife blade without distux8*e azh:wm e3 teo9 z,ab6u v66q:ootrbing the motion?

When a standing wave exists on a string;h plexi( tm56l *soo5po2q ,s, the vibrations of incident and reflected waves cancel p;5smp*o(qs5io2x,toh l l6 eat the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one p- n;tbm y6qs,d-dx q6 sa*zgcmv3 xc)*lace to another, how might we determine whether*--66nbmdv) ;mtd*zxgsaq 3, cxysq c the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total distance i1fl6fvao27 5 x o*bg gstzp9w9wn y5v zvh8k7(t travels in zwh25vst(l*ov7p8w65f g x7n fkba1yvz9g 9o one period?    m

  An elastic cord is 65 cm long when a weight of 75 N h ht*n7;ncci -tangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this elastic cord? -t n;itn7cch*    N/m

  The springs of a 1500-kg car compress 5.0 mm when i)a 6cl-dp3 u ;vpva ozruv:c8)te 9+ypts 68-kg driver gets into the driver’s seat. If the lpz r)3ucad;+9pvca ):yp t -8 vu6ovecar goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs fromxxmewk b74.05kvjd + fa ba(a; it. (a) What is the spring stiffness5k(km .xbwefa0a4d ;vxa7 jb+ 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 when a mass of 0.60 kgbcs wkia cn0+j(4 *o2o is hung from it. What is its frequency if only 0.380aik*(o2+ wcn bo4s cj kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–z* )uu y73 vy*bypum7h2 at times t = *uum7*yp hy 3bv u)zy70,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 wer)) r8exfuu3t b. The web vibrates predominately with a frequenu83)f )x urertcy of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency of 0.88 Hz. Whelkv2(pt 4c1rrn an additional 680-g mass is added to m, the frequencyrt(p r4 vck12l is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 x*2c(3dvy x+8czbsghh+(vq j s8pz*ztimes per second with an amplitude oh(2z bv+ *xj+8 gpzzqx (y hsdcsv83c*f 0.13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement lyr:idf;,w.jfrom equilibrium is the speed of a SHO half the maximum valuejr dwl y;i.:,f?$\approx$    A

A mass attached to the end of a spring is stretched o/7 z.ej bh)dda 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 sprind2 3ayn;kt,d*s*mc+ua. vl8 bs r tr4vg 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to rmt cvsu kav**,; ysd3n at8+ 24r.rlbdeach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attm*9 ynpwg i13iached to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it igiwim1y9n *p3s 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 popgutqx-;l+cc0t* dl,:crcaz o, xn 0.200 m to “load” ar ozlxcl a-td ,:ct0x+;c q,*c 0.180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizont zdlp s/6f(.y(/ igxafal, frictionless surface is attached to one end of a spring; the other end isyx z(ps afl (g/.f6i/d 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 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 accordnlodko;(d43hpra38b+c0r aking to the equation x = 0.45cos6.4t where x is in meters and t is in seconds. 8bo(d+aoh rr4k0 kldapn 3;3c 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 Sbk753mi m2wh.vh s)y.:c9.ospusv diHO half KE and half PEm29ssh.. ):hio iucy bms 7vkw3v 5pd.? ±    A

  If one vibration has 7.0 times the energy of a second, but their frequencie2jqbhw..yjm7zx):)ej e 9kawqs / q+is and masses are the same, whabesj)m7+xqj)y 9:qea wj/i w.kzq2 .h t is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light sprindw0.hb+kj prlm ;u1j, g once every 0., 1+l0jk b;mud.rpjhw 65 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 supported by two identical paralv04gv k4iqx5m7v ))fjk3brh c;/vhv vlel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will b vhvcjmr744vx5;qb k0iv vv)/k 3 gfh)e the frequency of vibration?

  A 300-g mass vibrates according to7bd6(kzhaisr0 x ,e(h, t )js+grjsq) the equation x = 0.38sin6.5t where x is in meters and t is in seco egbix(rzs)as6(qk7),h, sdjjh rt +0nds. 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 Bc: mvjh qyl-7:pitj+* . 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 sprfg ( ovi t6cct-s *8nmms5xi+4ing (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/ x*g5+n (fcmisc 6siv4 -mtto8s 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 stif, 310rls,z/h) ziqpptkkqd 4 yfness 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/k3z,lz4 0r p h1kq,qtyipd) s 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, with spring stiffness constanysvmc fq 7p+(y3b+r i7ts $k_1$ 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 horizontal spr/ z1 nkr 4z(-xwwbh2naing whose spring stiakwz-(4zh br/n x n12wffness 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.qygp 7t 5 ttdt.hqx t0*n.s)/d0 kg jumps 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. Calculat7 .sq*h 0pttt5/x ).gnttydqde 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. g6- vej:xgvgbk vhu ,409o9q+ bm/ist* tv f.iWhat is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is tz3g 1f:dmwt5to make exactly one swing per second? (That is, one cotd1g 5fz 3mt:wmplete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on e pt qqu.vfk7e2 3)qg2Earth. What is its period on Mars, where the acceleration of gravity is about 0.37 that on Earg 7qqf)vete32q 2p.ukth?    s

  What is the period of a/8ynvm31q8j ncvae6 n simple pendulum 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 mass of 365 +ya091gz tqt 9/6s -ac emssqqgrams, and it is released atq9sts1-gq0/m+z 9yeat c qa6 s 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 ofcwjo+. rj f+ i5yhd. c4*mdsv- 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pendulum+o.cc-rs+ dj m4hjy*i.5vfw d? shortened by    mm.

Derive a formula for tsf9f ilw5 lh**he maximum 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 oscill4b08p/ +c1vt nsm 3tjo sn6cgvates at a frequency of 2.5 Hz. At it is released from rest starting at an 4c6 1b msgptonjvv8 tn0 s/+c3angle 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 c8ca-g+kxjt 1miv9 0yg :t3ncmrests pass the bow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 mvai8c1xm:30ct- gkn9y+t gmj. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hzqc2se.dj :3sli 4)zg z and travels with a speed of 343 m/s How far apart are the wave cresdls)2c.zg s3e j iq4z:ts (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kicy.u+q x vo/7 ey ds0sc4(mrk-lohertz) and travel with a speed m-ukcyo /ery. vd 0c(x+qs74sof $ 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 t3j z56rk o;-vi p ;szakrq::klongitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the 5m:t04z*a txa ptrqgv z-7/y7rg drz )same elastic modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be greatet4gmra : y5/a*z-zgz dr)tr07xp7vq tr, and by what factor?   

  A cord of mass 0.65 kg is str*3kia8 :ue85r yuxlj yetched between two supports 28 m apart. If the tension i83uxa8 y5e:ik jyur l*n the cord is 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected togffv,8 +i79kysnzq4 dyipo+(q3vmp1 the 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 its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that i7v i f1y+opyn4(8f q 3z ds,i+mqvgpk9t 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 ju73)wc / r3vna3iwc hgzst below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s l)ri333h/vwzwgc 7na cater. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and this differenco ik)scl 7yw b+4f.4bxe helps in locating the earthquake “epicenter” (where the distkxbl)iyw4s.bcf +7o4urbance 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 4/dr 1-)jpcfk*+apu- wzzsz hsinusoidal transverse wave. / *- k-u pj)+1z4shcwd zparzfAssuming a frequency of 0.50 Hz (typical of earthquakes, which actually include 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)zt; a o073cuzcu a0vr4dqof0+ the intensities, and (b) the amplitudes, of an earthquake P wave passing a ud oof 4urcctz0 ;70qv0z+3athrough the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through7g5v o)d.+u a2qfpbdy the Earth is measured to be guvd2 od7) pfq yb.a+5$ 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 wavesa5 k,i0lvqjk( of the same frequency travel through the same portion of the Earth, but one k5ikl j,qav0( 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 sam6w,k ( 8 vbb mjeyqg-7.q+znvme frequency, but one transports three times the power of the other. What is the ratio of the amplitudes of the te (nqk,g vwbmz.7-+6mb8vqy jwo waves?   

  A bug on the surface of a pond is obsery 8*kf xldozam x:)5:eved to move up and down a total vertical distance of 6.0 cm, from the lowest to the high )xxf kyad l:z8*5moe:est point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) Sketch the.mni eo;li7u5 rt74*7jsjidv 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 pulses pass each other, the string is straight. What has happened to the energy at thi 7osvti i5i7* jem.rnlu 7dj4;s moment?

  If a violin string vibrates at 440 Hz as its fundamental frequt:m kk48(p 7b:bkxegs ency, what are the frequencies of the :es m4kt:pkgbkb(x7 8 first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz w4rja 1q7:4 b i9(sor,rogwiewhen unfingered. At what 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 :7aowgr1 ( ,q4b4rsiio ejr9w vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz. Namewrxp*o+-s 2 qj at least three other frequencies at which it will resonate.xjqs- o2r* wp+ $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequen8;) w4hxk btczcy of standing waves is 475 Hz, how far apart are two adjacent node8t ckxw;bhz)4s?   m

  If two successive overtone 6uho;uo9k74blur : aes of a vibrating string are 280 Hz and 350 Hz, what is the frequency of tl;oau:o 47r k e6uhub9he fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. Th:hg;yiq45wee1u//j r:3mzpi bf*cbq/ c s4 sfe distance from the bridge to the support post is L = 62cm and the strf1p b* :sw ebi/qijy/ 5 gqfu;434cmrehc/: szing is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is measu 0,h hx* d*ehnge88hoored to vibrate at 205 Hz. By what percent should gohhoendhe,*hx 088* the tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vm8mr ;qf jf/+0n **eelt8wldm ibrate 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? decrear+ f8l;*8tqjnemfle/ m*0 mdwsed by    %

  One end of a horizontal string is attached to a small-amplitude mecf 9l;6yn n*jtxhanical 60-Hz vibrator. The string’s mass per uninjt*6n ;9 yxflt 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 lengthus j (y .aubwxluf470)y74fj 2ma6dq r of the string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m4x.6 uyb7f)duj0 j wrusla y72aq(4fm?   

  When you slosh the water back and forth in a tub at just the right frn.zg6ck3 tch0equency, the water alternately rises and ft6 c0nc3.zkhg alls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boubn 75 cipd2r oz,/o8rkndary within the Earth between two kinds of 5/o2 zirckdp7b8r,on material. If it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velociv 5uwpi:80vh mty changes from 2.8 m/s to 2.1 m/s If th wv:mvi hp0u58e incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when 2+:lp9 :gq8 0 lf8xnjfl 8fc h-ggjdnk-wuq o0it hits a layer of cold, dense air. If the sound wave hits the cold air interface at an angle of0hng-f qd8 p9j+fo: 20k-:fxcg8ug njlw8qll 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary between two types bqeb)mq;2y o( 4h/huqof rock at a 38m bqq/h()u2yb e4ho ;q $^{\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 d;rws1r8je8ie/ f +r psc 2db6zlrz95giameter. According to the user’s manual, the dish has to be pointe;6wzci rz9 sdlgr2rfe 8 /+8sp r5jbe1d 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 travo: k79an8/uxgk(7 uanwulxf 3els across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approkuxwua: un/ax9 n( ko 78f37lgximately 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 *8 d,x.gnp8v;w qxmn(7 aps vgcar bumper has a spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, cp.qxv*mn8 sd7; 8,axwpvgg n (ollides 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 mxv,vkpyq5.+-uh u) k18 m below, which stretches the net 1.1 m. Assume that the net behaves like auh5 pmk-,v vq.ukx+)y 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 pleddhm mk0ll :b0c-:/ daced on the end of a freely hanging spring. The mass then falls 33 cm blhd :cm0-0b/d: led kmefore it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), compress2j3kz.ott q40gy x5wb ing the spring 5.0 m. (a) What is the spring stiffness constant of the spring?5toktjb3 wg y4xz.02q    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 w. w:*uyeodq0hy2nm 0b ax3;1u+hvih coffee (diameter 8 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 top (Fig. 11–55). Estimate the speed yhnwd3uo;2a *yxqi .1vhu +m0w0:hebof waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the centedoatg eb -y*gmaz h ;t-34*n ks,(hw1cr of a 33-rpm phonograph record have a wavelength of t*o;1- cgkt bh4syne3wzagmda *(-h,1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7di(uoz t,2.; d.rrw lo.40t where x is in meters and t in seconds. Detezd ;l (,wo. r.uotr2dirmine
(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 frequencphibtgm)i:k7 is m14o.4 u w5py if it accelerates at 0.50g (a) upwardtp m:i 4k)7u1b.hsiipm4 go5w ,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a dp t k619bn6em75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he s6ebkmd p19n t6teps 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 (Gscu-/kf /( ipc) and 440 Hz (A). ui/-ks p/fcc(
(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–a r4u6ao(ryuo8ns+ -9 h kyn7c33. 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?) ( +r9 k6 ono8a(as4rcy7 yunuh-c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency obtn;:gh9 b xm.f 264 Hz, and the tip of each prong moves 1.8 m.;9 b:thngxmb m to either side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of frequvuh4: /s 1r0spb83 qjhbj qlfjv o97q8ency 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 (Fig. 11–56) will not lose contact with th v 0rshjpb83j4/s9qov fq7lu1:hb8jqe board during the oscillation?

A string can have a “free” end if that end is attached to a ring that can slid4g d02im l(1 llyqqhvyz 86ib7e without frictiob7lg mz4ll01vqyq i(6 8y2ihd n on a vertical 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 2.000q9,;;t7vnvmc pl z6gv s — each one-way swing takes nqmcv; ptl96vg 7v ,;z1.000 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 ; ;phz /g;nxbkugwyr5x /qe /-a iny72-.kifithe vertical direction or can swing as a pendulum of small amplitya5-i/ e-.2 /xr7;uk i ngb qxhpg;z; n/fwykiude, but not both 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 stretched under a tension8hsj5d ugs*q ( of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Whe (gh5 du*qs8jsre will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring 6:i44 8c 9enkusmpgs hwith spring stiffness constant k. A penny of mass m is placed on top of the block. What is the max68nkpsehsgi4m c: 9u4imum 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. The2d)4dr8go/ oqxjd j lqai,a+ (94pg t)sbqwx. steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]aojd4j)lr / qibt d wqg ,)4 dxog9.(spq2+xa8    s

  A block of jello rests on a plate anvqrg /p5s7/f s shown in Fig. 11–58 (which also gives the dimensions of the block). You pnp gq7f// s5vrush 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 (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz