Give some examples of398qi k4pey bms1)ss p everyday vibrating objects. Which exhibit SHM, at least approxieb983i) k 1syms p4qspmately?

Is the acceleration of a simple harmonic oscillator ever zer/,axjp(kqrl2 o? If so, where?

Explain why the motion of a pmvmsc4vf.tr wp3*9f -kzv)t : iston in an automobile engine is approximately simple harmonic.w):p4fmc-rvk9 zm*v.f t3vs t

Real springs have mass. Will the true period and frequency be larger qe *iwue8tja3da0- 6bor smaller than given by the-uaw0e 8diqb*a3j6t e equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscills+e.s-p)m i9 (qrrmu +s)x5garpw i,yator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical sprikt2u tkbk7* b,n3kqg7 fsry,6ng scale, and then is released. Describe the scale reading as a functk k,buqg r*n2 637ykt,tf7bksion of time.

If a pendulum clock i l0hq )8)l3 -mkx(lk)bx*z;xdnriuoqs accurate at sea level, will it gain or lose time when taken )-kr zxux ( o8nmdlx3lhlbqi)qk ;0*)to high altitude? Why?

A tire swing hanging from a branch reaches nearly to the groco 2 e(q+jq)6l9hnnaaund (Fig. 11–48). How could you estimate the height of the branch using only a st) qnq6je +9oc2lha na(opwatch?

Why can you make water slosh back and i 6xi9 tl0sb,xtld:*m) *vk5tswst*mforth in a pan only if you shake the pan at a certain fres*isit*bsxtwt md95)*v 6 , 0xktml:lquency?

Give several everyday sd b10mw6dw07hnqp 7cexamples of resonance.

Is a rattle in a car ever a resonance phenomenfp lt 3op .:srq84jo1fon? Explain.

Is the frequency of a simple fdiadezpy4 t 2),m7yc)c5cn,periodic wave equal to the frequency of its source?d4z)2fytpam,cy decc5)ni , 7 Why or why not?

Explain the difference between the speed of a transvvt 5t5rs9 eze9+pr*e6 ah m6s;, offnwerse wave traveling down a cord and the speed of a tiny piece of the r v96ht m*s5a6nfwr esto;59e e zp,f+cord.

Why do the strings used for the lowest-frequen*kmn,/s7kj yqs-j2 bzmg /d s)cy notes on a piano normally have wire wrk- q)*s7 2mns/mbjy,jd ks z/gapped around them?

What kind of waves do you think will travel down a hc i9g.by1fj ah9b57 ieorizontal metal rod if you strike its ey99e1.bj gfii5c7 h band (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in di5l0jfrmou(rpo( i9c+. ar/:wex )vtemperature, but the bulk modulus B is nearly independent of temperature) u5i:rjdo (fwc/ ( olrv9eia +.xpm0r, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as they avkspl d+ 6.36gs;ad gtravel away from the sog36+vd ss;p.agld k6 aurce.

Two linear waves have thg6 g(v. l,)2 rf.r,b tkumtxzre same amplitude and speed, and otherwise are identical, except one has half the wavelength of the other. Which tra2b.g.rztkgl6rm r(,)uxf ,vtnsmits more energy? By what factor?

When a sinusoidal wave crosses the boundary 1dmv y /tsbq:cc76/rsbetween two sections of cord as in Fig. 11–33, tcq7y1d c6tv:r/ ss /mbhe frequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segm zjl*:vat 72ei5 ve8ueo* y0bnents, are there any places you could touch it with a knife bladee02 * eievyt lnuv7 o:j5bza*8 without disturbing the motion?

When a standing wave exists on a string, the vibratiorj3dfmqqm ws6w c7ruh ;2,62rns of incident and reflected waves cancel at the nodes. Does this mean that sd ;2uw6 q cfq7rrjw3 m,6h2mrenergy was destroyed? Explain.

If we knew that energy was being transmitted from one place to anothnt cp3c4f *,pl or/y:her, how might 3c*lh/f pny,:cr4t op we determine whether 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 nx5o z:q,8jxyyz, bq i73pv 2vtotal distance it tr2n73zxqbzo, :vy,yqx8 j5i p vavels in one period?    m

  An elastic cord is 65 cm long when mvfp5- qn:/ui;t3 x taa weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from -a ttf xmuv;/qi: 35npit. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driverjtf8blk-o hf,jf. m jz(0;gc+ gets into the driver’s sz.hj o(8cfkfgjt+- l mj,fb0 ;eat. If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm 4yp ++ s1ig0n;f nj- m*/whk7vuuykh gwhen a 2.7-kg fish hangs from it. (a) What is the spring stiffness cofsnmupig0 -khj4+w7 yy*;n u/vg1 + khnstant $\approx$    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 oztq.z9z.;+ /lwoqw p (zm:ung f 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frep.nmzuwo+z9l qzt .(g /w z;:qquency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fkgoqbnf-9; g+)gt o y0ig. 11–2 at times t = 0,t = -+09 tggfq ;gby)oon k$\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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.r44pmv z gumj x5*f8j.g3gx7v 25 g is caught in a spider’s web. The web vibrates predomimg4jxf z5. gg 8r7pjm3x*4uv vnately with a frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency of 0.88 Hz. When an6ah6imj;j4vn- f6 m ap additional 680-g mass is added to m, the freinm-j ; av6fh6pa4m6 jquency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at thrltoj+* p9sl:4d3 fli e end of a spring vibrates 3.0 times per second with an amplitude of 0.13 mf:di+rlp9sl3t 4 ljo* . Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed of a SHOkuk ,qt: tq8(n half the maximum valuetkt ku,(qn: 8q?$\approx$    A

A mass attached to the end of a spring is stretch )muqnlh *;c.2kwuxl,ed 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 vert9s: h/glg cali :5uw8xical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does itsxh9 u c5a8:/wligg:l take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is ydwjmy*0* h2 oattached to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 mhm wo0y* yd*j2 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 springvl g(ih++yy d+ of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what spee+ ++vy hdiy(gld will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to ; 8.6dtbnpy vkone 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 acceleration of;k6by.n v8ptd 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 vibratesxu(t5 kkch7ny6 dt x1) according to the equation x = 0.45cos6.4t where x is in meters and t is in d(nkhcyxt)x6 75u1ktseconds. 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 d /x28oxq l7c;*yitf4rk7w:vd2 hmqd energy of a SHO half KE and half PE? qtody2m7rx2i;:dcdq4wf7 vh * l8/xk±    A

  If one vibration has 7.0 times the energy of a second, but their freqqutp5 x30t1ro-,x qxk)9 wg xu-hn z/suencies and masses are the same, what is the ratio of tho)sx3-nq rxuug105x ktw/, q9pzh-t xeir amplitudes?   

  A 2.00-kg pumpkin osc1yl9dsk5;pgr f.l0jy wst m7:illates from a vertically hanging light spring once every 0.65 kl;rs.gyt j5 7 mf:d0s9ywp1 ls.
(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 h)o i;t5 rd.l8wz;bf)fqz fl0 supported by two identical parallel vertical springs, each with spring stiffness conf8bfzlt.zo ih0 ;d l)fr;5) qwstant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x iss;dzb 9 4kvkl0 in metz sd;b9l0kv 4kers 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 each, whaqc,g/ d+rn( 20fk mqwpt 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+a.d l(eftf(n)m5yl;u9gf u6i 3bdqyc 3 uy-d = 124 N/m) is strydfi ymud6q5u.b+u((3ffd39cn at;e-l )gly uck by a hammer, 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 stiffness constant 305 N/m vibrates with an amplitw u/cbcmz .3;tude of 28.0 cm when 0.260z. ubtm;3c w/c kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring stiffnesswpu r9zb )c;)c 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 strikesn833+b zf,hebelv 1k w a 0.600-kg block attached to a fixed horizontal spring whose spring stiffne+13hkeb 38zwblf v,ness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high bridge. Afte/nb cyf wpsy i .7,7lgi(e,eqq-w e:9yr reaching his lowest point, he oscillates up and down, hc.i(l,fwyeyy/:qp sqb 7 ei97gwn-,eitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 6 f yso ,gume u4i+pc;)wmd.*+t0 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendrh p*.g5rlv;s+ph; nrulum be if it is to make exactly one swing per second? (That is, one complete vibration takes exacn5hr+ph;gsv l; p.rr *tly 2.0 s.)    m

  A pendulum has a period of ,4wobesrcot29ntl1x u*k ;bhgi:4 a 40.80 s on Earth. What is its period on Mars, where theonu44b;k2,4h: t1oles bxt rwica9*g acceleration of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 kubl+ut0a;-w yd;i lb p-pd)7cm 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 36t0,rnvm(vu q9e(m bol9i 8t7l5 grams, and it (qllmobru7ntiev8 9t(v m9,0is released at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a7/9eo s)v tatpwke/2,tbckb8 length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pendu ots) t bvw8b7k,2/c pket9ea/lum? shortened by    mm.

Derive a formula for the iajrj ej4sj (2i3n67t 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 oscillates at a frequency of 2.5 Hz. At it+1fwirtpix,zu( u(63sn7 0vzio68 up /j avu h is released from rest starting at 6fz1ii 7, tp+rj68nsiuxph3u 0vo((wuuva/ z 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 bowtnd6m rs9cv/5* qe fk./tppu, of his anchored boat every 3.0 s. He measuresv/u /rtq5t * fm9ks dp,n6ep.c the distance 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 kkwg98 w9 dn 8c+edpy8and travels with a speed of 343 m/s How far a8de 98wkknc9gw+ydp8part are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilgnz1p:x pcvx d3)x 6,;fa/ ec ml-+yzaohertz) and 3+m-,f; ez cydga cp:xa/xvzl1x)6p n travel with a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of lon3km9ebtmvqma d306l/ gitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as dens1luso eltbw, r+)j)n3e as the other. In which rod will the speed of longitudinal waves be greater, a1ts j,b))e urnl+o3 wlnd by what factor?   

  A cord of mass 0.65 kg is )nez(kd1g3y;n,ha q rstretched between two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one suppoez( hdn)nr3,k ya1 ;gqrt to the other?    s

  A ski gondola is connected to the top of a hill by a steel ca4q 7rpyrmgf 8z jw0;,xble 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 07zq4mrrgw f 8,pyx;jpulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the surface of+ 9dj-b5qbmc+ vdqq:n the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this point? v-+ b9:jqq +dcbqm5nd    m

  P and S waves from an earthquake travel at differeni ;cxk elq. ;2xiz3p:v37 xckrt speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbance toxc7z 3;k 3pq2i iel x.vkrx:;cok 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 u*ub0 j :c8rulsinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needecr lu8u*j0:u bd so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensitim5(wzelol;ulnan;h8be bo ,qwb6- 0 ( es, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected 6b(l5hmn8euqe; w 0w,ozl; -an(lbobat two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wav1o t9,*tg klc,0kn iyue passing through the Earth is measured to be kygt90i,t, 1kn*uoc l $ 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 throamrb1p:r7s 4 xugh the same portion of the Earth, but one is carrying twice the energy. W r14 7mpxbrs:ahat is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretche*6y nog/ sinpq k8 38rhmm,gb5d string have the same frequency, but one transports three times the power ofgq i/88p ,bn s3ghm*ro5kyn6 m the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down a total vet2n ); bqs3sc5 jrw6i :b7losm803q+zbenbz vrtical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, bzzw s3l)0bv2en7;mt o8 q5bq3+bc s:6irsj nby what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving 7/*cow1dff90/ gtp)vfu day l toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each olf )wddfp/f9ta /07*gcuv o 1yther, the string is straight. What has happened to the energy at this moment?

  If a violin string vibra xcf6+v,jj*wu ls p04ctes at 440 Hz as its fundamental frequency, what are the frequencies of the firu4v ,w *ljf+pj 0cc6sxst 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 frequency willo5,6+k hybx)lypeq/;(uxx cy 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 by e5 xc;6youqp/h)x l,x (+kystanding wave.)    Hz

  A particular string resonates in four loops at a frequency of1*x 7ft51hbhy2lcfb g;c 0myc teh71n 280 Hz. Name at least three other1 cmbt*fy0h 11y 2ec7hcbx ;h5lt ng7f 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 frequ yv)s59+3 a xtf)vfhjnx p,:xcency of standing waves is 475 Hz, how hv +:j)sa5 pxf9f)x yn cxtv,3far apart are two adjacent nodes?   m

  If two successive overtonx+yxq 0t(ix(t s6h d*tej8fviul5 i0,es of a vibrating string are 280 Hz and 350 Hz, what is the *jfdth,xi0(v8(tyi ux5xis+e l qt60 frequency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance n 9r rvvyym3yd 9x7r5h9g/ zgfiti6)1from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. rx999) n5vvg7yyh /i3iy1rzdgr fm 6tWhat are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is suppos +u fs(s+ofr )b+3xrdyed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent shouf ux+ds)+( sofr 3ybr+ld 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 vibracn57sx6 n1zwyr 2f++yl/ s twljj*.slte at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in thel+j w2fll67n c.s /jswrtzs1* nxy5+y string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplrof5i28/rdmag0j/y l :e3jnw e;ivv2itude mechanical 60-Hz vibrator. The string’sf/;i2 o i28nre /mvj dyjl3er0:wv5ag mass 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 7v0rjag 7 jec8 zhmi9,may be adjusted by moving the pulley. If the hanging mass m is fixedz i gvjmr0e,ca 8j7h79 at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub av3u;c2b3)f2fcc d tg pt just the right frequency, the wate33)gc2; bduc pvcff2tr alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k/v/js;eqd :9qn/ r(tbwg/icq )ere6 i.0 km/s strikes a boundary within the Earth between two kinds ogv )e j/crbqieq/6qn e: rs9w/;t(d/ if 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 )hehsgb, tc d7w1ny bzd2o:+)“shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wavo) gtwy +b c7d he:z)hd2b1n,se crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer of cold, dense air. 3xtv juh,yc kfpl4,0 4ph,)ojhhxz6d.m0hg / If the sound wave hits the cold ailhy6,ocj k4d zh0 0, thg4)pxjupxv,fm h3h./r interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wa c)i2ud vv33micg,/a,.qypd cve strikes a boundary between two types of rock at a 38iiu3vdpcgc qma/y )3 dv .c,2, $^{\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 inrn;eu9h) f 2lx04jel q diameter. According to the user’s manual, the dish he; h r4)njfle lx02q9uas 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 vew 26iocrha:6r locity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much o6 r2wc6a:r ihtime do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper haslmhfh,z h0z,jhjw0: t;9wcxia 2.y+q a spring stiffness constant of 550 kN/m Find the maximthjc2z i0 h,a :wq,0j wz+fh;h.9 lxymum 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 au)8qll xv1,r4v 7gu mg window to a fire net 18 m below, which stretches the net 1.1 m. qu1m7r xv8lg,)4vug l 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 ohl 9zh1ga3wdenn39:-(g .w vnjkcn a :n the end of a freely hanging spring. The mass then falls 33 n :.waa:(3h ghezldw919gnnj-k3vnc cm before 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.nys dt sg1-d09 11–54), compressing the spring 5.0 m. (a) What is the 19t0snsy-gd dspring 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 8 cm) at jnx8-uxi .-qj 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. 1j. xx-ju -8inq1–55). 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-r)rmubs 1 xc s)a0q ne u0;b4k6dpv6u:tpm phonograph record have a wavuu))1 c adp 0vsr;q: setkbm6nb6u04 xelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x is in 5 z;pbqp: uabcg*.qcwltrt3-6mt c19 meters and t in seconds. t pl ;*c prabq cb9w5cq3 g1mut6t:z.-Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency ehpk c4l-)sk79g t swm1kq6+lf. What is its frequency if it accelec 1l+m ht-pklkkq )6ses9 4g7wrates at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on /h ;,xyf.g tcaa;i 0n xt5e3cma lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the wath g.x;a3 c atfet5 ;iym,c/0nxer. 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) anda::-yc*hdh 1q fbjn; m 440 Hz (A:hac;-j m*b:dy fh1qn ).
(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 stretc -tfj lg7/sm.zpkd /9tcfx2 k1, ibf;ched 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 thel z. ,cd2s1cfpkk;gf//t7i9 jmfxtb- wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tipn4w 5iuwb:h9 /gzdnf : of each prong moves 1.8 mm to either side of center. Calculateu/gbhzd i 9n:n :w5f4w
(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 fr t3cmnips+z mu(*y q))equency 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 cosm)m+ utzp3 *qc( ni)yntact with the board during the oscillation?

A string can have a “free” end if that end is attachedhb0) egqn j(h+ m1iqp1 to a ring that can slide without friction on a vertical pole (Fig. 11–57). hqq)(j g imhe1 nb0+p1Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has ark gfas9m02g0an8 n0bv1sc .e period of exactly 2.000 s — each one-way swing takes 1.00fav.cma gknse2nr9g 1s00b 08 0 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 oscmiuqm )-d za1 n*r//bh2o zpda6w;w)yillate in the vertical direction or can swing as a pendulum)apm wu1z- q*d/ ad6 r;/ h2z)iownmby 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 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 tension of 255 N. A puls4go- pn9 7mjhce is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two ph4cjg-nm 97op ulses first meet?    m

A block of mass M is suspended from a ceinm2i9vxcv v(wf3lvvq, 7.qy(ling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the blocvq3f, vyiqv9l x.vv7w2n(( mck. 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-kgg v xn-w7i 7:0ygd8ldw car at the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bog i7ddn78w-y:w0g xv luncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which also giv(a(dp:wqu9 i2t9v /ftn+g niqes the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to /tw(u9(p ia +td2ninfq gv: q9vibrate. 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