Give some examples of everyday vibrating objectspoy x.;te nq 41)7xcsh. Which exhibit SHM, at least approxiot ); x41c7.psyh qenxmately?

Is the acceleration of a simple harmonic oscillatv mw9b)px7b9/hah 5yior ever zero? If so, where?

Explain why the motion of *1w:ye .0z3lzdbdt kua piston in an automobile engine is approximately simple harmonic.klzd u 0 b*y.zed3w1t:

Real springs have mass. Wu+z jg t/z7-y +r2szgqill the true period and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealizey2 u7qs /-j+g rz+tgzzd massless spring? Explain.

How could you double the maximumqc(phgvh c m:kx d ncvb9d75+k/+ql)7 speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached t-eb3. cula do9o the hook of a vertical spring scale, and then is released. Describ- a9blo.dceu 3e the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose tht q)bf,/v/yarf./ pkime when taken to high altit,qa.tpr )/f /kh/bfyvude? Why?

A tire swing hanging from a branch reaches nearly to*m,gocs-m kq rv hy ,q2x)pq2, the ground (Fig. 11–48). How could you estimate the height of the branchpgq,cx,o qh-ks22 ,) qymmrv* using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shak;,aij70ba ro ie the pan at a certjorb,i07ia ;aain frequency?

Give several everyday examples of resonanwt ujb9jk)*dm 6chs )ir381 urce.

Is a rattle in a car ever a resonance phenomenon? E )iyg :bulv xn86og)2t2ymuu1mw:;lq xplain.

Is the frequency of a simple55tyhnmlmz s2bi a4 f)b5x;8j periodic wave equal to the frequency of its source? Why or why8y45faj ht2mln;5zsmxb i5)b not?

Explain the difference7ix :a. o6ia oqcn-ujq99dl6c between the speed of a transverse wave traveling down a cord and the speed of a t a9lox7icudqa6cq.jo9 6 :in- iny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano q6njh)/ (oo iznormally have wire wran/oioq)zj(6 hpped around them?

What kind of waves do you think will travel dow+ 4ouk jtei37( zbs +tk77vnukw.zz9zn a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally paralle eu4kj( k73i+nz 7.vtobwzs z z9tku+7l to its length?

Since the density of air decreases with an increase in temperature, but the 6rm:px 3dh*lcbulk modulus B is nearly independent of temperp 6hcx lm*r3d:ature, 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 asf:lqo0 h. h0wz they travel away fro wo.hq:zf 00hlm the source.

Two linear waves have the yg 1+gncj oym-3 3o: yal15uzssame amplitude and speed, and otherwise are identical, except one has half the wavelength of tn 1y:jauy+y3 glg-s5m3cz o o1he other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of cord aso4;ml z2o,,g oeo. gsyal5 ex: in Fig. 11–33, the frloaxolo 4:2syeeo gg ,z;m5, .equency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places you could toy cf+b/jl n-f pu5ij61uch it with a knife blade withofcj6+1fju in/-bl 5 pyut disturbing the motion?

When a standing wave exists on a string, the viba dtm,,ab xafu//z:9n rations of incident and reflected waves cancel at the nodes. Does this mean ,abnzu/: 9dat/ amfx, that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place toa*/dku8- m:pxd h1awf another, how might we determine whether the energy was being carried by particles (material bod*dw:u-1a pfk xm/a8hd ies) or by waves?

  If a particle undergoesi od/ ltw tgf.9t/p7 .l3iznu4 SHM with amplitude 0.18 m, what is the total distance it travels in . fw o4tl idl9p //znittu73g.one period?    m

  An elastic cord is 65 cm long when a weight ilabv j(p;73oof 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this ;vp(laib j37o elastic cord?    N/m

  The springs of a 1500-kg car compre iym thlu72qdy uq)76.ss 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequency oqu2qyh)t u7y.d 67limf vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg 23ia: ;rxrpd7dw2owkfish hangs from it. (a) What is th kd 7iw3o:22w;prdaxr e spring 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 with a frequency of 3.0 Hz when a mass of 0.60 kg iszjhq,yicypxffj6t009 d*xx-3.i z 7 o hunyzj.jf97 h 0fozyx3x6 cx0q-,d pti*ig from it. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x ofyds;+h6r h q5p the mass in Fig. 11–2 at times t = 0,t = + d6rp;sy5hq h$\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 wgjkfqjrle/(j7gj0(jd3 91s feb. The web vibrates predominately with a frequency of 4.0 Hqs gjfrje7(10/ jl j9jgd f(k3z.
(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 frs0:nu5b as7f/f az m)jequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz.50bus /m saf 7fan):zj What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times peroi 8h/ eq0h2jo,2xycb second with an amplitude of /,8bh 0heq x2c2o yoji0.13 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 equilibriu.5cxjmtep :ltx m(t ocv +x54o ke*it1k+-co,m is the speed of a SHO half the maximum value xv 45eot-lo .:jtcmctkp to5*,+xxike +cm(1?$\approx$    A

A mass attached to the end of a spring is stretched a distance *lhatq2 bnj 2*$x_0$ 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 verticc9)blvqe- 4fcal spring 0.315 m. If the spring is stretched an addibvc-fc )le 49qtional 0.130 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffj2 gp5jz*ez -uness 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 a speed of 0.55 m/jj *zpez u2-5gs
(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 ts2e ixxu /*p4p,1,tosxbzirvml78v (he spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. Wi 4, *bsxs/12vxxmlriziou(t ,8ep7v p th what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one end of;,z1 0.lzzbwk(gkxo5 b i:ujtu 9 y2zn 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 w9,wl0z ngybbk(x1;ot2i 5k:u z .zj uzith 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 acco8k00j h 4fdapwrding to the equation x = 0.45cos6.4t where x is in metehkf 8w04d0jap rs and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energynx/y+,fnyp6yp7xzk.w f / 3hc of a SHO half KE and half PE? ± yyxzn /+ph 7/ .xfnfpc6,w y3k   A

  If one vibration has 7.0 times the energy of a second, but their frequenz*6v d(qdp6l mcies and masses are the same, what is d q lm(*z6pv6dthe ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillm+o)*o 4 -rt,cdisqdiates from a vertically hanging light spring once every 0.65 s. i*i4)oo mq,ctrdd +s-
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical paral iyiuvlkl3s.+ );vbo1lel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibratio.+b) ovyv3 ;ulkil1 isn?

  A 300-g mass vibrates according to the equatiocrd-ru s1g/.nv;mx *87wwcj pn x = 0.38sin6.5t where x is in meters and t ism;g 78 dux-w .1vc/rspc*jrnw 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,ccrg8; vn+k ,x labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal spring j i(i za+io3gcsl5 ;qd:gpr89(k = 124 N/m) is struck9qigd+:gr;o c p l3iz(jas58i 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 constiq+e z6canr -*q;) 0luxei.psant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with pol)q-iispu*;aqr 6.ecx0 +e nzsitive 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 / o:c) g6)( poozrs7 mzxg;k qm,,e*ujmo8 coestiffness 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 fixeon1a.q qy;y:4 zrz:ajd horizontal spring whose spri:1;a zz:oyn 4qyraj.qng 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 jumps from a high bridghc4k v sl)2.+hdo*dp/sigi 3be. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. od dvh*lc ) /p3bgs4s2 +ikh.iHe finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 60 s. Whatbd ni(k 8- /j*tbei1fy is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly on +4alnt 10gm/:wnnqwqe swing per second? (That is,nwwqanlg4n :t 0q+/ 1m one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its peods,k ji9 9vttvool8x-6,k n3riod on Mars, where the acceleration of grad8oio o-xt36vvs 9k ,l9k, tjnvity is about 0.37 that on Earth?    s

  What is the period of a sim ;z/ks ct1mnt;ple 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-*od:2 ccc s+g m5f tcxd dx)74*cb12txehvge a mass of 365 grams, and it is released at an angle of 12:7sfc-dt 2egb) v2xchc54+o x1d e*tmcd g *xc.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 pendulm6etj dx h2qw1- 15nmp8 qxjo6um has a length of 0.9930 m. If the clock loses half a minute per day, how should yom1tqx8d nqj6x2 1h6 wpje-mo5u adjust the length of the pendulum? shortened by    mm.

Derive a formula for t-fsxv .m ) *d-k 4kl5a+hnzawahe 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. A3s goqck +5nez5nfyo340 i z,z*ak8xwt it is released from rest startin awc83kyo 0 5kne,g+3qoz*nz ix 5fzs4g at an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests y1e+o6al l+) prs5izepass the bow of his anchored boat every 3.0 s. yiel zr)5ap1 o+6ls e+He measures the distance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has ae.zmzw )eys7 ,xh(k t; frequency of 262 Hz and travels with a speed of 343 m/s How far aparty w ts;,ez k7e(.zx)hm are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilh;8n db2bi z5iohertz) and travel with a speed bdb28i 5niz;hof $ 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 ,8 u5xnc lmtt;vijd76 of longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic mao+djgm;2y r/odulus, but one is twice as dense as the other. In which rod will the speed of longitudinad/mojg+ 2r;a yl waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretvt 5 b:3dw7y+bnlr g1oched between two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a p5wrn+:b3bl 7 1ov gdtyulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of length4 yy.)n2ic ken 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminiy.)2ney4 kc nal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship juty6hrvg4ew t d/4* l86qma ;yrst below the surface of the sea. He hears the echo of the wave reflectedw*6 h;rvgrtyq mad4e68l4/t y 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 xaed+)ja, )65fh4tucbm -svxtravel at different speeds, and this difference helps in loca46ba fu)) jaxcsve5 tm+h,-xdting the earthquake “epicenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximatr6s( ix2uam,v3h1bfj ed by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what ampxb1a 3h, ju irf6sm(2vlitude 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) tw5bjwaoaw54 fxg :,g -he amplitudes, of an earthquake P wave passing tfww 5 5a,gax -4go:wjbhrough 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 is measured to.ce y3 9y8vcsa be 9.escyvay 38c$ 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 trazc*3 -ebd0jx. fjs5t vvel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitub5tzj 0fxv3e js .*d-cdes of the two waves?   

  Two waves traveling along a stretched string have the same frequ,intu ) y9a.7 wuyaeb0ency, but one transports three times the power of the othain,eb.0u9yy7atw u ) er. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed dy6w xf/z sz96to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. I/w xz9zys 6d6ff the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other.zzlw vd ;;y ytcqx:4:3 (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,tzxwyy; 3qz:cv; :4ld 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 fundamen;x(b(qn8klpsrc 9vx *sgy3r05g m1 k qtal frequency, what are the frequenv msx(gs q 0;pg(9*rq r3l1yb8xkknc5cies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when1 -oblq3 xjuzulij+ 50 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 t05u +3 iqo1zl-bju lxjhe string vibrates as a standing wave.)    Hz

  A particular string resonates inh zf2)y1 b7kxa four loops at a frequency of 280 Hz. Name at least three other frequencies at which it will resonate. bzak2x)fy 71 h$f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If therdvy5 *l1ct-/3yja sa frequency of standing waves is 475 Hz, how f - t/rjlsvyd1ay 5*3acar apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280xzf 7z/6n 7km2nipu(z Hz and 350 Hz, what is thz( 7 pn67i/kmz2u xzfne frequency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. Thouy ; yec9pko/.6m x-ue distance from the bridge to the support post is L = 62cm and the string ooeu; ymxckyp9.u6/- is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is)gvrqxe;lrrqa484 1 a supposed to vibrate at 200 Hz, but it is measured to vibrate at 20g 44rrrqa e8av;l1)xq5 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 n.zfzz ws.vv43n83b mis 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 tnbz3f w3nz.s8v4m z.v he frequency? decreased by    %

  One end of a horizontal string is attached to a smalz) z-tt:ysa q:l-amplitude mechanical 60-Hz v :qzsya: t-t)zibrator. The string’s 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 stri n:;fuw:ame,:z8g s 2r/n momung may be adjusted by moving the pulley. If the hanging mass m is fixmmguna :: /o:fm,uw zr8 s2;need 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 fowomd*z( cnkr( t*-bq-rth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. -o*(n- qwtmr(zd *bckWhat is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary within the Ekkegrq+* h/u-.ur vr:p5lko5q / sy a0arth between two kinds of material. Ifu:rshk 550+r/ey o/ .qu k ka*pg-vqrl it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velocity changes frt r j.8hur,) nvtskv+1om 2.8 m/s to 2.1 m/s If t)1v. un ktjh8,rst+v rhe incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air wh4f(ve uc)v1fc en it hits a layer of cold, dense air. If v c)euc 1fv4(fthe 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 y 01h:jxv *knirock at a 38hjy kx0:* vn1i $^{\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.kniys2 2-ec nrggx91+ According to the user’s manual, the dish has to be pointed in the direction of the satellite, but an error of aboutrins2c2n+- kexy1 g g9 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelenglkzpb *iv ;car4 .kf:*wh- f-mth 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 attracted to the shore to see : ai- z.pb-*frm;4 wk*chfvlk stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constang r 5z9-+in lzn/zn0aqt of 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 conservation of n- 9rznnq /a05zlzgi+energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which stretcn1+8 ipcsd 5abhes the 8d1pnc+ ibas5net 1.1 m. 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 the30 )h8x)j 3 qi8k c7sgju.sjpiij/ kee end of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is t)jp8i7ek.j3u /hii8 ) g 0kxj3secqjs he frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), ak) r;eyi2 f5ucompressing the spring 5;a2i5ey) rf uk.0 m. (a) What is the spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup ap6do0()y/uw gcl6f aof coffee (diameter 8 cm) at just the right pace of about 1 step per secon(a g p6fu0ad6 y)l/owcd, 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 gr+ oiizsn7aj* n0h+4 6i kzplh2oove 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sound lp ks 04ai62jziznho7 hi+ *n+emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x is inxz cvjxfsp-z t - y*m((jdcnx+5 /n3*r meters and t in seconds. Determin*-ztcnz x j(cd*vm( /+j3n5r-xpsy x fe
(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 frep lvx(s:f/ e1,7 +knk-hkjywtquency if it accelerates at 0.50g (a) upwar+:kxkn, el-/ tvj w(fpsk1y h7d,    f
(b) downward?    f

  A 220-kg wooden raft floats8*cqc2xct py6 vwu,g w qh,))c on a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps of),) ug,qc8*t2yqp cwhc x6wc vf, 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 fj af; x 7:/mnek7:siyare tuned to play at 392 Hz (G) and 440 Hz (a /xsejm:yf ;n7fk 7i: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-5 n8,ldc*x) ykoi6mfnpart cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greatex 5)clnm,6o*nf8iy kdr in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequenc2; mb;s7m38*b9 y mkvycrbe-t /mjlaly of 264 Hz, and the tip of each prong moves 1.8 mm to either side of center ;v lrmt 97-2yc mem3bs;jlbyk/a8b*m . Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motio/3 / 2gyhdga7nuoq+xln 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 (/+q/dg3x 7hyu g2lnao Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a riwktzm 57v;v6tn in0ox 9j71eqng that can slide without friction on a vertical pole (Fig. 11–57). Deiv7t;nt q9 v7o1w mkzn0exj56termine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a 5y nn (.udaag4i 0gund63m hcg)t mo-4period of exactly 2.000 s — each one-way swing takes 1m u4).d5 ggca(3-4 tdg aoh0u6mniyn n.000 s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertical direction or can s6tsh1jr ;uy 5lwing 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? [Hrtu5j s6 ;l1hyint: 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 stre ;qzr-g 41jjxhdmo.9 ctched under a tension of 255 N. A pulse is generated at onh9jro.z1 d;q c x4gmj-e end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with spring stiffneseath-k1ets m*00wq,x s constant k. A penny of mass m is placed on top of the *eth-sq w,a1 0kx0 metblock. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg ca g xt:ve4+ 1.uqymyg;kr 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 ot.u+v e4g :gk;xqm1yyf the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which also gives the fcbcuy 9v;x9.ctg+ i1dimensions of the block). You push xt1c 9fg9v c;icy+ b.uit sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz