Give some examples of everyday vibrakxg ozrt t9xh s*7x,qiq;228t ting objects. Which exhibit SHM, at least apgqo;2hq7 , rt2 xxt*sk8tzx 9iproximately?

Is the acceleration of a simple harmonic oscillator ever (a ym1bzv1k00gfdpjz+n315)ifye c xzero? If so, where?

Explain why the motion of a piston in an automobin(2oagcc tdifkoonx .l61047 8kc x7f le engine is approximately simple halkkx(o f c c7igc o2o7a60x841f.ndtnrmonic.

Real springs have mass. Will the true period and frequency be lar 4)2+ aooxvp x1yknfz*ger or smaller than given by the equations for a mass oscillating on the end of 2ap)*o+oy1k znx f xv4an idealized massless spring? Explain.

How could you double the maximum speed of a simple h(.ww qhooxfhe+1ur,6y g( gr7 hw(h1garmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a verticallve7;lq ;3 fmk spring scale, and then is released. Describe the sc7ekl lfqm;3;v ale reading as a function of time.

If a pendulum clock i w;c c2p-b*gyt6yk0y ps accurate at sea level, will it gain or lose time when taken to high altitut ywb g06cpck;p*2-y yde? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–48). Hohwasm+hc**x 6 u, exi2,zs6bsw could you estimate the height of the branch using zw ,6xcubha*i+h *s62xem s,sonly a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake the pan av- eg 5efvlogsc*riy,p+jy 3 oh+5k7 1 mas1,zt a certain frequen mc ++zy* rjief l 5yepv-skgasv,3g,5oo 71h1cy?

Give several everyday ex pbk1 skty7 mx0k,5h:vamples of resonance.

Is a rattle in a car ever a resonance phenomenon? 2 be2ty+e:v4k+ jvwquExplain.

Is the frequency of a simple periodic wave equal to the frequency;z-4 q nn6ssdd64 l5v3origyc of its source? Why or why notdqr6;cgi5n4s 6 o3v- ylz4sdn?

Explain the difference between the speed of a transverse b5rt4mxetqk8 ( :2mnxwave traveling down a cord and the speed of a tinybneqk 42tr8( xx:mmt 5 piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano normallpbgetk-,:f r :xx t0e*y have witxrbe:gf ,: xt*ek 0p-re wrapped around them?

What kind of waves do you think wil0j;an h+c4s tnl travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally paracn s0tj;nh4+allel to its length?

Since the density of air decreases with an increase l2dvg)by8+ao:n y eqc /+knoar*c-+ f in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the lanac: d+ogqn8 k*/2- bf)+ yeoyvc +rspeed of sound waves in air to vary with temperature?

Give two reasons why circular watercp x.;z.hzi,b waves decrease in amplitude as they travel away from the szb;c.ihx ., pzource.

Two linear waves have the same amplitude and speed, and otg)x1+ox p7hxw-m ls y 5x5 z);m6owydm.a(cvsherwise are identical, except one has half the wavelength of the other. Which transmits more energy? By what factor? ylc)5hxx;gm. pway+ om-z()56somwsvx71d x

When a sinusoidal wave crosses the bounb ,m.b4 a0klr:bbdj g81q3nbx, 7y yfzdary between two sections of cord as in Fig. ydyba:x,. b,qgb1 lnb47bfr8jm z0k 311–33, the frequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are ther:m9e)xrou36 2mhw bpse any places you could touch it withx36h9bo sm)mrp wue2: a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incident an;cfzii5z/3)rp 9cswd.t zk t8d reflected waves cancel at the nodes. Does this meandf.csptii8 9c3zwt)k/5 r;zz that energy was destroyed? Explain.

If we knew that energy was be(7xy e bf*p,m,qcv4n eing transmitted from one place to another, how might we determine whether the energy was being carried by particles (material bodies) or by ,xfv4c m 7ee(y ,qnpb*waves?

  If a particle undergoes SHM with amplitude 0 *: volr4l,lwxqz)9av .18 m, what is the total distance it traverq,l:* xvao)l94v lzw ls in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs f8 90gdvnus;t oz,him6rom it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this elasticihu896on;vz tsmd g 0, cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver gets iw , y9(* f9mydihotvv 2z.cvi5nto the driver’s seat. If the car goes over a bump, what will be the frequency of*i y 9ovdhvfy (mz592icv.,wt vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (acq/; 9 7ixdqlm) What is the s qqm7 d;i/c9lxpring stiffness 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 5f7 owhpyw(i:u1a)7,prr boowith a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs from bwfhp)oirr71 :p uy 7,oao(w5it?    Hz

Construct a Table indicating the position x of the mtru,0 ri bdjru8 a+n.4ass in Fig. 11–2 at times t = 0,t u0run8 rri,da.4 tbj+= $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 c nzui6ho8nt1 x+s4i f;aught in a spider’s web. The web vibrates predominatel1nis+hf un;z 8o xt64iy 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. u 1wz-fq4d ev7When an additional 68uv-e1fw 47dzq 0-g mass is added to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of(lo,rv 0gc zq(aqk31c fj ,qy: a spring vibrates 3.0 times per second with an ampli 3(o,(k facgj:q0lyv rc,1zqq tude of 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 from equilibrium is the speed of a Sz3- zf fncflnbusg+3w;e;i 1u4yv 5 4zHO half the maximum valunf zff45u 3el+ w1 gbv4usc;-ni3yz;ze?$\approx$    A

A mass attached to the end of 86u es;g93uhgc/e cbpa spring is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a ver zmwt 6lpfmj c .qsgp(dkw+2,ri:y(q: h,8oa+tical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equz a,.pyf tj++m (2c,slr6dqi:(8owhpm :wkgqilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffnesgjh+ei7l0s b wrf(. 3us constant k = 280 N/m and is executing simple harmonis7wh eu+0l.j (bfigr3c 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 compres podsrd uu)zh)54h31us the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed zudp51r34u )dh)hu sowill the ball leave the gun?    m/s

  A mass sitting on a horizontbu-s hfmca.r i4nlqig99i)ng 1: v 7)fal, frictionless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15g f: 9aimvr)fcb-7ig uls.in q h9n4)1 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the.p0dk km+,cxd equation x = 0.45cos6.4t where x is in meters and t is in seconds. Deter + dk.mxp0,kcdmine
(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 , n)qps: fnz+aKE and half PE? )an znq :sf+,p±    A

  If one vibration has 7.0 times the energy of a second, but theezo4j4)ne5 ed utn0 2v/wkwa-ir frequencies and masses are the sa4w4ne2k5wu zjto0ve-d/e )name, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a verticax2x4yzu 2ddxa;y97 ty3 -wgoblly hanging light spring once every 0.65 -a x3y xy9b;oud t24 zg7wdx2ys.
(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 identv( g n6hbxz7rrlk ugb o)7+av919h0ptical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency thn6lpxv70+)1bb7ua okr zh g g(9vr9of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t whfba: )wma ))llere x is in meterabl))alm: wf) s 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, what ijuu-nvr9 tw*m)8 6 igq5 esuw,s
(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 hey7 go:lmsp6e8 i *z)aorizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Determypm a*: lz) e6go8s7eiine
(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 Nff ji9 7a-49tr1ouqvm ly(g +g/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 posita 9u f9ggvomr7ft-y i (4qlj+1ive 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 spri3ujdx8tr a t*n+p.(l buit;jsj/m0 *kngs, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed horizontal spring w2aeg6vq+b kq gu5tl .;hose spring stiffness coak+6e u5;ql2vgbgq .t nstant 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 of0i-uipwa:h3 v5ez )mass 65.0 kg jumps from a high bridge. After reaching his lowest point, he oscillpf :ih3oe 0-i5vaz uw)ates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness 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 vibra gd+:+6 ,hitc xd5nmnations in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one switl21a kqo0y-c6/ze rzng per second? (That is, one complete vibration takes exactly 2. z 1ck6az-/20qlortye0 s.)    m

  A pendulum has a period ofdp c0 x61*b )w4tuaeit 0.80 s on Earth. What is its period on Mars, where the acceleration of gravity is about 0.37 that onp1dw 6u)txtib0e ac *4 Earth?    s

  What is the period of a simpldg* i(r u:n30 qkf4lrxe 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 maz3ydur2u0qibm)) bngz03 vv9ss of 365 grams, and ibzvn z2 3m3)i090udryqb) gv ut is released at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 m. l87k 1jmtfmng)jo5 x9 If the clock loses half a minute per day, how should you adjust the lenmfj tkxm8975jlgo )n 1gth of the pendulum? shortened by    mm.

Derive a formula for te)t/ghrxg zm/ +4k4vnhe 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 2n5:fsbx7 / aec.5 Hz. At it is released from rest sts xb7/fa 5n:cearting 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 crestsk/xz2r2.w jq v pass the bow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the waves travel x/2.rvjwk2 qzing?    m/s

  A sound wave in air has0rfk)2en tr. z a frequency of 262 Hz and travels with a speed of 343 m/s How far apart are the kr20 trzn f.)ewave crests (compressions)?    m

  (a) AM radio signals have frequencies betwe/ i.ty3)/;h+fk ot/p8ni c/pu nmpaa uen 550 kHz and 1600 kHz (kilohertz) and travel with a speed n/8/ta pnut3k o p ma)ip./;f+yu /hicof $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal waves 3p v;u9.k1xetca(sc sin
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic m.ya 6gi,c(nhf odulus, but one is twice as dense as the other. In which rod will the speed of longinfc, .ah(6gy itudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretcg i-f+yj4p9i+dah bf,hed between two supports 28 m apart. If the tension in the cofi+gy9-p,hbfj+i a 4d rd is 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill oh+vf,) i a7fl459cgxzo fqq.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 vqaqh)oio 7fc x. f4zl5g,+f9 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 belo,gat8y9,t5qhtly t p;6vm x;y w the surface of the sea. He hears t;t 8yh; y pty5lgvtx,a,6qm9the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different spe( gbl6z 0 xo(b7vu8vnzeds, and this difference helps in locating the earthquake “epicenter” (where tun(v bvzb0z7x8lg (o 6he disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wb m76 o e8;0lvddrdui*ave can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typid i6 dulob;dm8e 0v7r*cal 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) the intensities, and (b) the a f1p hnz7 gs7:c98didamplitudes, of an earthquake P wave passing througha7p sh:f9cd7i8 1n zgd the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth i8d , lg)z6skkjs measured to be lzs) k,gdjk 86$ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency travel through thtr k65pu*r7 6gwzoawkk: dz:+e same portion of the Earth, but one is carrying twice the energy. W azpukr*+ dgw:75:kzt6 o6 rkwhat is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched strin2 )i ujt7. 6urfppwm;ag have the same frequency, but one transports three times the power of the other. Whut um.a);rf 2j76pipwat is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move 80 v3axzw cx 4(x y3s9m)iwonjup and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If timoj0wwanxz 8x9y 3sxvc(4) 3he 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 moiinst+3cqyo 2 :8ki,c6n p9 b3ofkom0ving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape 3i, nc p3oi8cnb 9ky+q2fkomts6 i0:oof 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 frequency,l8e7ysnnb u ;fwv6a;;um s 2v. what are the . au be vmw;2n7lf 8;svn6su;yfrequencies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 2k8i vqagn b5y5qqga4k8(0 zl 4jp7bx(94 Hz when 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 strib ja 5q75bv8g((nxzal8k4gyp k4q0qing vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 mf:kr tmv+l 0l+-tqd;s goap x5n35w *Hz. Name at least three other frequencies at nv rq0a3+5l -;lms tktdm gw o*5x+:fpwhich it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of wavesa6gl5d r5cu . wlr1gp)61vkxo on a string is 92m/s If the frequency of standing waves is 475 Hz, how far apart are aovk .)6 11rdgpcux6 ll5wgr5 two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hq1t1 -x:cplz uz and 350 Hz, what is the frequency of ttp1x1uczl :-qhe fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distancthv)9m8(ygtv je /7px e from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequenct yj7m9v) /e(p8vxhtg ies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 f8imvb004z:2arwt el pa; 5j sHz, but it is measured to vibrate at 200wfs8: a;aiv4502 jzrm bptle 5 Hz. By what percent should 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 vibrate at 200 Hz, but it is measured e9oj ef 7:pt.5s((iegk vdz l)to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency? dece)i e(pe s.l7 gd(jo9fz5kv:treased by    %

  One end of a horizontal string is attached to wgd lv.h0s*nu 3vu,wh/wq/; pa small-amplitude mechanical 60-Hz vibrator. The string’s mass per unit length isdw.nvu uphh / v*/ls0wq3g,w; $3.9 \times10^{ -4}$ 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 movin8gxsq* fi az79g the pulley. If the hanging mass m is fixed at 0.08q g8zfxi7a 9*s0 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 at just the right freque 3 ,f /efrgit;a/ ze3uekokvdn8.7q1 fncy, the water 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 t;i.q7ff1fu /oatz33e,kendvk 8re/g ub 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 boundar;6/gzsb57gc xs29pmx 4ztjvyy within the Earth between two kinds of material. If it approaches the boundary at an incident angle of 475;gxm/jgszb4zt7v s6x92yp c $^{\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 velocity changes from 2.1a(w.djgcqtmv+ufx) v z m76q47p) sb 8 m/s to 2.1 m/s If the incident wave cr)wjx4vvz1 7f)7.pac6 smqgt( um qd+b ests 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, de3vsv0 t6nu*c;ucyt 5bnse air. If the sound wave hits the cold air interface at an angle nu5ctsbv*6y utcv ;03of 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 z*bw1,hx 1dkg between two types of rock at a 38h1*wd bk1zg,x $^{\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 diameg e3xgzz rj2f:g3g2hz xa/(-vter. According to the user’s manual, the dish ha agzz regx: -(gz2j33v2h/gfxs 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 wavelengt)+zh)pfjaemz 1w*ag i f;vp. 3h 250 km and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attractedp+zfegw; )mv.p j*aih)faz 31 to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of j769q-eycesx 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use consy6e q79cse xj-ervation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18wvn :xk :sl+br lb9d,5 m below, which stretches the net 1.1 m5x+s9: d: l rvnb,kwlb. Assume that the net behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hanging spring. The mass thenrb,jn n8x jvtj 3v+,b: falls 33 cm before it stops and begins to rise. What is the frequency of the oscillat8vn,t :jbx3 j,brvjn+ ion?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), compressin nh*:pjjs4ge6p -7bkbg the spring 5.0 m. (a) What is the sp4:g khsb-b* 67epjp njring 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 3 3a3s6ewcnx1)epfnxcup of 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 sep36n)x 3af n ex31wcthe speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-rpm p0 bdqvo.wm/q. /2bfkfhonograph re f.qdb/qkov /w02fm.b cord have a wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equ1v.6a 5 5ov.iwf es1ugzm; kzaation x=0.650cos7.40t where x is in meters and t in seconds. De;z 5mosv.v1f6a1eakiz u w5g .termine
(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 frewh: 6qyh 9 ym6c+cym-squency if it acceleratemh9-wy 6+:sqchym6y cs at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on th4q1f;vo,l9jzgaj :jq2h(c2s pn df5p-z-qu o e raft, it sinks 4.0 cm deeper into the water. When he steps off, the:z ;vzqsaj(2 -qp 9f jp1u4oo5ld-n,2c jqhfg raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play at 392 Hz (G) and 440 iw+ h;y,vhj4 u7v*(d. hlu fctHz (ujh;vl cw u v+it4 ,h*y(f7dh.A).
(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 i *i1q3 fjo 7m;jp9gzuhe3 6ezFig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why m*9fziqe g h7ujzoep1;633ji ?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequencm52/ie imp:ai x ng 4y2o,ck9ky of 264 Hz, and the tip of each prong moves 1.:x,2o9ni mgm/i5 2y4iepk kac8 mm 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 oscillated/salhn n.wp - *dmvh(tme1*3 ruz+y(s with 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 pebble placed there (Fig. 11–56) will not lose contact with the board during the oscil1.he u(*n yp/*nrdhslv atdw-m3z(m + lation?

A string can have a “free” end if that end is attached to a ring that cazoz6;xp;d-pxv37xwdui +)s,vme -uun slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths ofu 6 di)o;xp-u3,v w+-uxesp7vx;dzmz the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum ham1lknb:kqsfwu 1h0f2s0bp l4ki.( p3(f1xtos a period of exactly 2.000 s — each one-way swing takes 1.0(123of plsh(w:p.b0b i kufx1q4lsmkkn tf0 100 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 tb j7 dg,0xw0qzwrr8ze51; uc nhe vertical direction or can swing as a pendulum of small amplitude, but not both at the samen8zg 0buwj ;zc 7err0qdx51 ,w 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 a77c;- gqr j y8hfnib0under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second 70- h8crqya7g;fjb inpulse 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 hds,yig:a.g ) with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations tha:hs)dg ,y.ia gt 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. th /dyk e8 eqkx5(v3,lip1, qaThe 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 perv,(1 /yak8idq5ktpxq,3 e lh eiod 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 also gives the xwlf1f pk,fnxyc(/r3:.(e z vdimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) 1klf/.z c(wevfxy :rpxn3 (f,of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz