Give some examples of everyday vibrating objects. Which exhibit n*fwl xbv1 1/lSHM, at least approxima/xbl* 1w 1flnvtely?

Is the acceleration of a simple harmonic oscillator ever zero?rwjh5r( (23iop,mc odyd1lc 3 If so, where?

Explain why the motion of a piston in an automobile engiwnzob,-f 3w e2ne is approximately simple har 3n, wezwf2b-omonic.

Real springs have mass. Will the true period and frequency be large/s9,6xfyvl vb5w rlm .r or smaller than given by the equations for a mass oscillating on the end ofv6f/ y5wsrxmllbv,9 . an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscil(m3;n +zs)lxtzy/ay b lator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring sc hl1wvcfxgk 24u90a :eale, and then is released. Describe the sckcf1gh0 a:vlx92uwe 4ale reading as a function of time.

If a pendulum clock is accurate at sea level, will jug1fgplb*mn:x+f 40it gain or lose time when taken to hi*um:0b f4xgnp+gf1 l jgh altitude? Why?

A tire swing hanging from a branch reaches nearly to the foqcts0*a,v6yo)tn)3pfcjqc :q ,lav* bq *) ground (Fig. 11–48). Hoo pq)ct*ovq6fan0ajc c, q) :v s* ,3yftq*)blw could you estimate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake thl q v3l7lsp5mdyv.u )+e pan at aply m53v +7uvdsq)l.l certain frequency?

Give several everyday example/ dr ug y4a+o/ aps6ir;+u7pnis of resonance.

Is a rattle in a car ever a resonance phenomenon? E9o9 d) puu)qdgxplain.

Is the frequency of a simple periodic wave0tkiw bcr;rz*wvx 1+n94,u xn equal to the frequency of its source? Whnc ; 9zvtw*wui +1n 0krx4rb,xy or why not?

Explain the differencemq(5)( iz72rgpi1p(yt eaxkh between the speed of a transverse wave traveling down a cord and the speed of a tiny pie ( 2iayp5 hq7irepmtz) (x1k(gce of the cord.

Why do the strings used for the lowest-frequency notes q5i y)au.yn j3on a piano normally have wire wrapp3y)ia n 5yqu.jed around them?

What kind of waves do you think will travel down a horizontal metal rod if you /,tbg 2blsb+tstrikt,sb+blg b2 t/e its end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase ob( ps :orq77pvoyle gts(-z2m/iq- :in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of stb(s7o ye gz :qp:v27-o-l /iromqsp(ound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as3cv fxrj)s4*y they travel away from tvjs )f4xcy3*r he source.

Two linear waves have t ftxmg.e ek37 efjg52/.;lhlqhe same amplitude and speed, and otherwise are identical, except one has half t/7tk;f.eh xf meg. gje5ql3l2he wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary betweenx78gy9px30t 8 .srs;hcl 9py;b tawbt two sections of cord as in Fig. 11–33, the78t l 9x8 w;t0hbybpyrsg s9x3c.;at p frequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in v:-ck8 eoi j+ylr l-c0three segments, are there any places you could touch it with a knife blade without disturbi8ljc:klo-i c-yev+0 rng the motion?

When a standing wave exists on a string, the vibrations of incident and ref 3 -4)syivueexyb twv0 i7w,;m*hxtg5lected waves cancel at the nodes. Does this mean that energy was destroyed?ybe5si txh3iv 7y0em ,x*u; gt-)v4ww Explain.

If we knew that energy was being transmitted from one place to anh57mj0cl cw wu 91oh,hqijo 69other, how might we detel6,h u j9 hw7jcocmw ohi159q0rmine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM wrvsem 6*r, 3)ypv0wnyith amplitude 0.18 m, what is the total distance it travels vr6n3 *y, yesrvmwp0 )in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from igxd4hc/g. wx a9mfmv9c- l r:g *u(b1gt but is 85 cm long when a weight of 180 N hangs from it. W1x(hg d4mmgbv9wa fc- x :/.9r ulggc*hat 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 driver gets into mn9 bric53 e 0c2,p1wq tnqvd-the driver’s seat. If the car goei, e 29 bd5p -nqrvcnwq3t1cm0s 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 +imkz2yc;kf q(1 k2vdvl55 lw hangs from it. (a) What is the spring stiffnz wl5v(lqi1mkk; k cd5y+v 22fess 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 w2ai qsk-o5q ; 4h;wpj5gvrky8ith a frequency of 3.0 Hz when a mass of 0.60 kg is hung fro5;-5saio2k8wyjrhg vp q ;4qkm it. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at iyczuf+a7.l )times t = 0,t = ufa)l +7.yicz$\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web. The web vibrates prr gwf 2,w4rk)gedominately with a frequency ofg2, k)rww4g fr 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 wicy(z5.j nfg e+th a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the vag+nejz5y .(fclue of m?    kg

  A 0.60-kg mass at thefie f0*gi2.h d end of a spring vibrates 3.0 times per second with an amplitude of 0.13 m. Determinehi.ie g*f0 d2f
(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 e til:h 61 tcw4i1v:yxnquilibrium is the speed of a SHO half the maximum value?6t cvy i:4w1hi:tnx1l$\approx$    A

A mass attached to the end of a spring is stretqn)s lan b 1:stk +1r;sqwd*lva+g +8oched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. If the:ctc 6bde(d: .tbr zb4 spring is stretched an additional 0.130 m and released, how long does it take to td bce:6 :rcdt z4b(.breach the (new) equilibrium position again?    s

  An object with mass 3.0 kg xlneyb83q b:6 is attached 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 is moving with y:3nq6xe b8lba 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 t,e: w4r9no:7b+tr csg/c fznh he spring of a toy popgun 0.200 m to “load” a 0.180-:hcr,/ogn 47c: snzr 9wbe+ftkg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one endal8vo gvhl0l 7uzg rw4j:.urmqxq-yu 1 )3d;1 of a spring; the other end is fixed to a walj ugr7xuodm.4l1uh)1vzl a-yr0:qwl ; 8 vq3gl. 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 according to the equationr v+*fyxuvy.7 x = 0.45cos6.4t where x is in meters and t is in seconds. D y +.vx7fuvry*etermine
(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 t61 mpb,zbvp7 equilibrium is the energy of a SHO half KE and half PEmp zb t71bp,6v? ±    A

  If one vibration has 7e/)c weqw4 ex+l1 r6suzoks 83.0 times the energy of a second, but their frequencies and masses are the same, what is the rx eweq/ 8wl ers1s6c43)z u+koatio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertzl3rw(3to/ gte ; did2gv31alically hanging light spring once every 0.65 s. dal/1 l2we3ti3gtd(rvz o;g3
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallel vertical springs, each/k;;yzyjgm9 z.rb/qtqes l .( with spring stiffness constant k (Fig. 11–s.qkq.t ;jy9b;/yr (ml/ zgez49). What will be the frequency of vibration?

  A 300-g mass vibrates accod 8ik25 uayf9krding to the equation x = 0.38sin6.5t where x is in meteru dfy95 ka8i2ks 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 isi:f-ne f,exe ie/ ;l3e
(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 spu9k gd,f. po6rring (k = 124 N/m) is struck by a hammer, whicdpouf.9 ,kg6r h 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 spri+,efh*y9 cs ring stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.26hs+ 9 crfe*,iy0 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 tyt7;d hu5zf( uwo springs, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed horizontal fvbq*/hkm5sp s08 /zs spring wh*8 /p/0sbs5 mv zkqsfhose spring stiffness 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 jumbxk j wm- aka-mi54fq/v ugcnv.;61pnjl3.7j ps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times cmj3kuwkmjqaf.vxjn vn7pb g1i6 / -4l5a -;. 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 vi3c(avxsp / vwn+;gq0jbrations 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- 20 bxs 2egz-;*llpzlw4xyof swing per second? (That is, one complete vibration -sxolex2l;4w g*02zlfzybp- takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its h4p4-th; zdghr :mpip6 uo,c7period on Mars, where the acceleration of gravity is about 0.376 chp:o;4 pg u td-p4ihhzmr,7 that on Earth?    s

  What is the period of a s(e* tf blo40ecimple 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, ap krfo+s o990the pendulum bob has a mass of 365 grams, and it is released at an angle of 1osf9p0k o9 r+a2.0 $^{\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. lh vioh)f21+5 *x5ukcwi:xji If the clock loses half a minute pei +xi )o5hi2 kfw5c1hlu*j :vxr day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum speepy 5rv) *jsp;cd $v_{max}$ 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.hr5ke( zs:4mg4xkd0 c5 Hz. At it is released from rest starting at an angle of g4k5s hdk0:(me crzx415 $^{\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 p+m ybki d 7p fyy5gy4r5.ay5r;ass the bow of his anchored boat every 3.0 s. He d b5ayk57y.mg i5ypry+ fy;r4measures 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 and:t;-tj3 y7sd. dj bgc +ec7jzt travels with a speed of 343 m/s Hot:s+7.tjbjd;dyt - z c73gjecw far apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kim5n6vu y/ fw(- ur(mv ulpl6*flohertz) and travel withy*l nl6r(mv5/vw - ffu(uup6m 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 longa7 gk, l s8-)drnip1afitudinal 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 dense as t mz g8j mcs2cj2q8.ox8he other. In which rod will the speed of longitudinal waves be greater, and by what facto8mo z2cgx2jcj8 qsm8.r?   

  A cord of mass 0.65 kg is stretched between two scd2 a ywn)g-g2i6pk2 tupports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one 2p6i t)gn y2gka2wc d-support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of len.8a ux9vqz u +h4 ljrx34dsqu,gth 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 it took 16 s for x9q+.z x v3ua,dulu8 r4sjh4qthe 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 bk5 ee3,us, ydjust below the surface of the sea. He hears the echo of the wave reflected from the ocea,sdk,3y5ee bun floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, s3 0y)1rmtdj48yk uj fs*6ecqand this difference helps in locating the earthquake “epicenter” (where the distr jc0s4jy fm8u3s *k e1)6yqdturbance 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 a.a)qor eww 4h*pproximated by a sinusoidal transverse wro4eh *w wq).aave. Assuming 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) the intensities, and (b) the amplitudes, of r+b/bf6(tj x 3b. 6s3tsibhj xan earthquake P wave passing through the Ear ss x6/tb3bftib.(hb6+jjrx 3th 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 isw( r9yv4ex s)m measured to be emy)94sw rv (x$ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency travel through the same portion of ax4j/wz4 bnfpdm++k oc ; nq.:the Earth, but one isomw4c+kj fpq/; nnx.dz + 4a:b carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretchedn4swg2+ h8tuonq/ 1gn m6d 2xr string have the same frequency, but one transports three times the power of the other. What is the ratio of the amplitu/xhnos2r81tnd6 nq+24 m uggw des of the two waves?   

  A bug on the surface of a pond is observeqk 7d8dyilf0. d to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factodq fdyk0 l7.i8r does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) Sketch thr+ qldluou6 few -k.m b,r*4a9e 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, ,u-odr lke.6aw lu+9m4bqr*fat the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrate ihg z-pu*1ob(s at 440 Hz as its fundamental frequency, what are the frequencies of the first four harmonics-o (*upzih 1gb?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what freq 7 zoe)nm5,bt3 45kqeiazuyz;uency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the s;3qi zkae z7u)b54ymznet ,o5 tring vibrates as a standing wave.)    Hz

  A particular string resonates in four loops atqr ln5d(-n wj.mo4q. d a frequency of 280 Hz. Name at least three othelmd5j.q(dq nn w 4.o-rr 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 9uq/lkt* .g4so2m/s If the frequency of standing waves is 475 lqt.o u/4g*k sHz, how far apart are two adjacent nodes?   m

  If two successive overtonev)b n ( vflm+8zjc:s/es of a vibrating string are 280 Hz and 350 Hz, what is the frequency of the fe: nj)bs/8m+ zfvcl( vundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The dni1qd* -(/fb wxd-rheistance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and firxi weq-n-(*1fr hbdd/st two overtones?    Hz

  A particular guitar ss;z crk(1sjtcy2f)0mb ( n)7xh9fw abtring is supposed to vibrate 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?So the)9; wb snfyr (c )t7jabcxz2f0(shm1k three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 2ej3 vq.25* s *g1dbabwhnuo9o00 Hz, but it is measured to vibrate at 205 Hz. By what percent should thsq*3bb vo1d.nujh 9og25 e*wae tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-ae;d .grq -p(qamplitude mechanical 60-Hz vibrator. The string’s mass per unit led-rea (g;qq p.ngth is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be adjusted byrurv3+ n3b )x2 app6wq moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave pppuaq x + 3rnrb)26v3watterns 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 rightr5 e;fc;i tkq( frequency, 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 tub is 0.85 Hz. What is the se(;crf ;t 5ikqpeed of the water wave?    m/s

  An earthquake P wave traveling at kzsaesanubpei f+s) zv)34 7 28.0 km/s strikes a boundary within the Earth between two kinds of material. If it approaches z 42zpuaa)isv8f b )es7+n3s ethe 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 velocity changes fr;)zm .qpe9l, v jmw9sv fx,/boom 2.8 m/s .v psxoq, zj;l)/f9 vmbme9 w,to 2.1 m/s If the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveli bnwa8h ijy3d1n8:+ 7/pzo2eqc7 tmf mng in warm air when it hits a layer of cold, dense air. If thbn2eqz87jft 31m wmn+8:poyi dah/7c e sound wave hits the cold air 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 wave strikes a boundary between two types of rockert-c(hk( 7, nq;ldx u at a 38 r-7duh;e (k nl(,qcxt$^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m in diameter. According toe-cq)ud es) w- the user’s manual, the dish has to be pointed in the direction -) )eu-ecwsdq 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 25z70j)bh,z ab,le) n.yvg. 1b5nm 2ri 0tb lvqy0 km and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in .z2 )n. l vg07nybez,am5i1b,yrjlhbqv b 0t)the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 550 jq6fep8fs ;7k 01pagn kN/m Find the maximum compression of the bumper if the car, with mass 1500afq6s 7e;f jpp 8n01gk kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which stretcheu sn ctbc tm-(eg6n1-.s the net 1.1 m. Assume that the net behaves like a simple spring,u .s-enct (b-gn t61mc 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 place-rm-fh, v y3bsd on the end of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of the osc-,h-rs b3vmfyillation?    Hz

  A 950-kg car strikes a huge sprivrrhlylxxlv0h 6+ 01 (wj 0nb9ng at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring st(hwyr1rvl h+l00nbv x 9jl6x0iffness 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 j w.j4a0ck5wc qisb0 p3ust the right pace of about 1 sa0 s5pjq.0 wkic3 4bcwtep per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the cent qvg2zg6 24hbwer of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sound emitted?vb4qw6 h2g 2zg    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650c.5hfqrfw(lm5+zrd3: x eoq k8os7.40t where x is in meters and t in seconds.fr xf5 hkq5:3 (loqr8.m+de wz 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 wu 0rc r;)g:l/d)sihl z60bi qkith frequency f. What is its frequency if it accelerates at 0.50g (a) u k00hd:s6zb;ilgi))qcr / ru lpward,    f
(b) downward?    f

  A 220-kg wooden raft floats 1 a4m s w8di3ifo4k:wnon a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for 4w 8 sda4ini1fo:k3mwa 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 are7hxez rg0o 99fc9gos + tuned to play at 392 Hz (G) and 440 Hz (A). 79 rs0 ogc oze+9hxgf9
(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. 11mo j1b r9:eya2–33. 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 wavelengt e92:abj 1romyhs 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 tip n).u(je1wkh h hkv -; /utbbgdqb/:5lof each prong moves 1.8 mm to either side of center. Calculaqehu 5b-(/;).kgb:1vt / kunh ljbdwh te
(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 8u.nhx;m,s-eh/z bee motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibmz- /8nhxhe, eebu.s;rate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” endejdq4lxt3 onmsmm tx 7,11b (, if that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the othere 1n ,b(s3t 1jlx,m omdx74qmt free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way ke1x*5g jyf4v swing takes 1.000 s. 5* xg1v4ye kjf
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertical direction or can(nqm:um/wl jg d z +5gg/o)ri2 swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hi/ 5nm/gqgj gwd ) o(mz2r+:ilunt: 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 tens8tx6 b2qx*w x)cyti0 tion of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated atc )yix8 w20txtbq x6t* the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spr kxx9z(pj 30 dl/bs(kying with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the /zks3xxyp lj0d(bk 9(maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkya)4boegpoj x/52szfyv*4 wcy1.b9 kgkrd. The steel crane cable is 22 m long and has a diameter of 6.4 jgzvpb4*oy b4 .s)g5c x/2kwyo9 f1ek 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.]    s

  A block of jello rests on a plajavpo49/ k (iote as shown in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the fra vok/ipo(j 94equency 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