Give some examples of everyday vibrating objects. Which exhibit SHM, at le/jqx e)gux ts c-l0i.3ast apprci.-/texx3)0 u gjsl qoximately?

Is the acceleration of a simple harmonic oscizpdt. jvg3ljl af4r pu3 so0w-.(k.u -llator ever zero? If so, where?

Explain why the motion of a piston in an automobile engi +v wu4-dc5el3ssmp e;ne is approximately simpl 3ecwvsl up-med+4s5; e harmonic.

Real springs have mass. Will the true period and frequency be larger or smal(ioaf, dpfb0l9ff0 /uwr ak;/ler than given by the equations for af0 f ka0(rabwf 9ip/;,f/lodu mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simpls)+1 wyqjy *dkam5ytm m0w*fis ;88h re harmonic oscillator (SHO)?

A 5.0-kg trout is attached to thenop. bo+ hi7rwe n(+1j hook of a vertical spring scale, and then is released. Dr e1.hn7wobjp o in++(escribe the scale reading as a function of time.

If a pendulum clock is accurate at if * .bek;e vot0d*8bksea level, will it gain or lose time when taken to high altio0tv ekebb*;8i*f.kdtude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–4;f-s,lvggw 2 w8). How could you estimate the hew- w,;vf2l sggight of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan ocrkdw5)iz )u 6tbra2n91l6kl nly if you shake the pan at ukda)ztb 662i )5lrr lcn9w1ka certain frequency?

Give several everyday examplesvffy:j,6h e,x sox(b + of resonance.

Is a rattle in a car ever a resonanceo;;0,ben sxi s phenomenon? Explain.

Is the frequency of a sif nf gcfq ;l0gu7q* 0y57esx1pmple periodic wave equal to the frequency of its source? Why 10qgsfn7g5 x p fq*7;uyfl0ceor why not?

Explain the difference between the speed of a transverse wave traveling dp zyynx-i /:,e02ax; :f zxvwmown a cord and the speed of a tin x: enzy20;x, -vampi/wyx :zfy piece of the cord.

Why do the strings used fx 7w498 x2raoykjqg6l3a jfsv2.*do o or the lowest-frequency notes on a piano normally have wire wrapped around them4j7a36x k .29sof*qoogdxjr a l82wvy?

What kind of waves do you/zk* (e uqpkc:muc h jx7.sjsm-kc. 2/ think will travel down a horizontal metal rod if you strike its end //e7k.scx(kz *u-jm q.sh m 2pk ccu:j(a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases wi1 / pmfc2s 03kofy+auath an increase in temperature, but the bulk modulus B is nearly independent of temperature, howoc 2yk31+s0/fam pfu a would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as they travel a.dsansym8 lw d1a33t /,:qs cmk 8xdo(wsakc( awx1 nmyod3s:ds lq38.8 t,m/day from the source.

Two linear waves have the samou4k5xx r-* jkgaj; 8pe amplitude and speed, and otherwise are identical, excorujg4x 8j x*k;5 ap-kept one has half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundaryc1khb v**j:l e between two sections of cord as in Fig. 11–j1b*kl h:* evc33, the frequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any t-2xh lsl;3g1hgh ):psu gn,nplaces you could touch it with a knife blade without distsg:tl 1n 32,h)h snl;xp- ghugurbing the motion?

When a standing wave eb7ukx2e. uik 8az8dw 5xists on a string, the vibrations of incident and reflected waves cancel at the nodes. Does this mean that energy was 5.k7 axz d8ub 8ewi2ukdestroyed? Explain.

If we knew that energy was being transmitted from one plac ci5 fqq7xia4mf7)*br v3rs)je to another, how might we determine whether the energy was being carried by particles (material bodies) or b a47x5fqi3im v jrqs rc7f))*by waves?

  If a particle undergoes SHgy. p.jh:wv+ ji:5fkkM with amplitude 0.18 m, what is the total distance it travels in one perio. w.5j+vyjikp h:g f:kd?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but 2:j:7ty y cl 9xefvct n.8(ruois 85 cm long when a weight 9v jor:ytf7uc.8:l tcye(2nx of 180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg cm l+5q6wunk*tqw /jf2 ar compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will tqm 2* +w/klqn6wj5fube the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm whe.yzx/ 6qren3, ro5o ahn a 2.7-kg fish hangs from it. (a) What is the spring sti3.x5ah6rq,ze n/ryo offness 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 ivghp c 73ih4(3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs frih(7c3 pv4ih gom it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11qb36 bcfa, g80jkj 6bj–2 at times t = 0,t = 68 j 6cbqbj,f a0jgkb3$\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 caughtgpa4ewd)-7hf in a spider’s web. The web vibrates predominately with a frequency 4-a fegphw7d )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 uvd5 buo:p6 *gfrequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency:bugp* o dv56u is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a springq)io+ax 5ftx4m 0zs +p vibrates 3.0 times per second with an amplit+ zqt m5+)xfopa0ixs4 ude 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 SHO half the maxk+ t(*poyx kr 8h* sw-nwabw9)imum valrn9 )ywhtaw8wkp*x k o+*-(b sue?$\approx$    A

A mass attached to the ecv8 - bvaf.mo*nd of a 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 vertical spring 0.315 m. If the sprieam)n1 /uyr3-qp9qe a (j jhw lc6;bp2ng is stretched an additional 0.130 m and releasaj39je ppnme;caqq/(- w1bu)6r yhl2 ed, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg s8ktca4nm64 v 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 a speed of 0.55 m/samcs v44tk n86
(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 )i8k/jk /qzhgg p2 d/kthe spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what spkpj/)h/ iz/k2g 8 qgkdeed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one end oq-b/xng a f18zf 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 q/1-zfnb8gax 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 equation xjc9vv b f tp2y6wyi:q; 2uw7)e = 0.45cos6.4t where x is in meters and t is in seconds. Dete :ty29iq vfjwe2v wu ;b67p)ycrmine
(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 nk1d m*y1/z ynSHO half KE and half PE?y *m1/nz ynk1d ±    A

  If one vibration has 7.c 1ekk9uo )ar10 times the energy of a second, but their frequencies and masses er9 ko)c1ua1kare the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light sp5k,b 3 g 01mcp1s kfp/vuai)c9elcem/ ring once every 0.65 1)cubkp/ m 1p m5vec9gflsc/0i,ke3 as.
(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, 7wtev ee 1 w*nr)4so6*a jh3;wpxd na)each we)sj1)a6;d 34xet*rnwop nhe* w7wv aith spring stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates a/bek t3dof+/b ccording to the equation x = 0.38sin6.5t where x is in meters and t is in seconds. Determine 3e/tk+ bodbf/
(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 ex+ w nn3pbw2lo:amples of SHM, 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 (k = 124bw (w50 0 ur2bwsstz4u N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Determine w05w 0uuz 4b twb(srs2
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305 N/m vibrates with an 4d /zugb9n ndg9nn p85amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes througdnnn gp 9ud/g84 z9bn5h 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 tdi8 ;:8r9: y kgvzgdsvwo 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 spring-cb0eup ij7m- whose spring stiffnesm7- iuepjb -0cs constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high bridge. After reaching hisr2c,dr.cenn) lowest point, he oscilla,r2 rnnce. c)dtes 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 vibrations in exactlynl yyxn;d0+r) 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 swing per sesb 0 x3 0fhz2u.*suuhdcond? (That is, one complete vibrdf0u2hu bsx z. *h3us0ation takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its pw:(l5gs:ky+c: k( b xwcj+r* yprt br+i4*r vceriod on Mars, where the acceleration of gravity is about 0.37 th(j (p4*r:rk ++w:tvr rcc:kixyb s *5wc+lgy bat on Earth?    s

  What is the period of a simple pzye9f;j1/j) h):r 3,rswb pdh uvlah 3 )xjvl)endulum 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 7lq*zwru+ts-o :lw2 v a mass of 365 grams, and it is release7lv*w :2lu-t qrzso+w d 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 hy qr8d h8t6pplby ycwt7;6 p3h9,rl)l as a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the len8t lw6cyr) 6blyd;hq98p3 lh,7yr pptgth of the pendulum? shortened by    mm.

Derive a formula for th,p6sv ur2nse 3e maximum speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At it is relea+*duczak,f9x sed from rest star*a cd,z9uxf k+ting 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 pass the bow of his g:dk2iy0 bk (xm3g 5flanchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast dx0 5k bigg(m fk2:l3yare the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and trttru. f4z 1 gsgrznyc*;- yt46avels with a speed of 343 m/sg1n;ty rcfz4g z-u.ry6s*4t t How far apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kiwu;0 s:-1tp/0 4 zukjmktry . buzw0bclohertz) and travelszyk zu;twk u/0jbpu0m tbw -41c0.:r with a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal waves bjh*0y3c0k9 k a1sb plx,nh w+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 denssj 7eb2hul8s*cb4 )d s1jx( bke as the other. In which rod will the speed of longitudinal14x j sbljk8 (us shbbc72*de) waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If mgs) zy)fpj ,(the tension in tpsz),(fjm ) gyhe cord is 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hiloe6p . 5 qxxoh:b*dta.l 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 anp6abo.he.xxo* tdq :5d 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 just below 2e4bi;f-wjinf zpn*0 the surface of the sea. He hears the echp;*4i0n z fe-jbinw2f o 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 speeds, and 5n8c ltzs2hb( this difference helps in locating the earthquake “epicenter” (where the disturbance took placetc h2n5z8lb s().
(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 apprgb;k 5 znd2n x,2sdz)qoximated by a sinusoidal transverse wave. 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 th2zsg)dndkb;2,zn5qx e ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intpldo+ 1s1l+sw8mkac s 3+kxb3ensities, and (b) the amplitudes, of an earthquake P s 1ls1m k ++bwc3skaopdx3+8l wave passing through the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave)fax/7 ohql0, l k0fhk passing through the Earth is measured to be /,kah0lkloqxf07 hf)$ 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 traveargcy:95l gf )l through the same portion of the Earth, but one is carrying twice the energy. What is the ratio c:5 gay)rfg9l of the amplitudes of the two waves?   

  Two waves traveling alon2yml7h.g7bouqh; . 7s*xm iwqg a stretched string have the same frequency, but one transports thre i*7.gh;wsux2m lqb q.ym 7oh7e times the power of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is obserw: y bff1b.j/sved to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave pas. b1bfs: /wyjfses. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fnaifvxmz*87rb (wm*: ig. 11–52 are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pun*i(fxm7 * r bvaz8:mwlses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 44+t n0hutyj96m a)2 wv0p4 tgws0 Hz as its fundamental frequency, what are the frequencies of the first four 2w00wtgst+ayt4 hmj9)nvup 6 harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what fr e1 dkzo8uz15kequency will it vibrate if it is fingered one-third of the way down from the end? (That is, ono ku z115dekz8ly two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 2ee)q /f)4q,t vn9ma*3 frz yeu80 Hz. Name at least three otaf*,zftvq)3eqe/9r u4m yne ) her frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of standing waly 0 oev5als.+ves is 475 Hz, how far apart are two adjacev0e+sl y.l5oant nodes?   m

  If two successive overtones of a vibrating string ak9yozh /gsgf 9rd 1c38re 280 Hz and 350 Hz, what is the frequency of the fundamentalg9k1/83ory zhd9 fcg s?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distanb9x8 zm+ y5jzyce from the bridge to the support po8z ybjy9m+zx5st is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrat3do.zom(6l n pu3j3m de 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 frequencyn(3jdol3dm ou6p 3zm.?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supigyk(di ko:x v052p/lrve f4+posed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent shode5kx r(4 pi vgolv:+0i/2fyk uld the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is atmga/*v lp),c62op fed tached to a small-amplitude mechanical 60-Hz vibrator. The e2,6 *)gfdmvo /clppastring’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 leng(d5 4gabs-jbr0r8 8rqt8 eroeth of the string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be abretgso08e8r-j( r d5qb 4a8r chieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water w/n ) a4n,w vxkr 1+:/zw wri;exw3nmjback and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the cenrw;1z/vkm ) j4,3xwxrww +/ n:iannw eter. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at knxtt /yn/ *a/)o*h1qwjc7up b.0 km/s strikes a boundary within the Earth between two kind ja/7cpntqhyb1x)*ot un w/* /s of material. If it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an hw)c:t 7y 6nglunderwater “shelf” where the velocity changes from 2.8 m/:htc ygw 7n6)ls 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 traveling in warm air when it hits a layer of cold, dense aoyzore +yg5e*t1za9. bt3fvs wi;+o1 ir. If the sound woeo+.s1r1oe a9vgwz zt5 ti+b3 *yy;fave 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 trd d mz.nt ko rg8jx)c4msi35 nf,9c-8wo types of rock at a 3trk 8jnxz3rn89 c ifd4s,.)5mmg -odc8 $^{\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 x0z 0 vwfb4w8fm in diameter. According to the user’s manual, the dish has to be pointed in the direction of the satellite, but an w00wzfb4vx8 f 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 wavelengx7v u2dws40* heb3il ath 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 safetyb3*e0dalu iv4h2sxw 7? (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 aznuxjdp 2i ete0 d10dy(t l(*/ spring stiffness constant 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). [tdy1(jp(00xdt d e/ui2 ez*l nHint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, whichr6mfepn 1vix17r or4 d-py21x stretches the net m- ne x1p1rrox vf72r4dy1 pi61.1 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 the end of a freely hang/y91e quchc7gnz (p*cing spring. The mass then falls 33 cm before it stops and begins tu1hnc qc yeg p(c9*/z7o rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge sp wh1js cxrf+l*l w07dzcu,v76 ring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m.7 wzluhdrvj 1*c67sw+x l fc0, (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 of coffee (diameter 8 cm) at just the right pace of ab:n hf8ts/;z i4sme)reout 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of wave hzmre8 n4/ts)f;se: is in the coffee.    cm/s

  The ripples in a certain gr0a t: rwk*g+ya3bdh. poove 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the3h akyw * r+.ag0bptd: frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation xp3( 0tc-gwjr6i,bv jd* f o+g/ 3fwwfn7dinj*=0.650cos7.40t where x is in meters and t in secondg t o6/br3-fi dwpn(0nj+v,g c3w*djf*f7 wjis. 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 witw* kgl58g x9qymicu.0h frequency f. What is its frequency if it accelerates at 0.50g (a) upwarwi .g9my*cklq 8x50gud,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man suwcc73p;o 5o 3v *7*el2a axrlohzr)rtands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft 57ovcz a73 l2aruecoxo;lh3 )p rw*r*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 instrupl pw;vwoqn82 ix(o10ment are tuned to play at 392 Hz (G) and 440 Hz (A). 8iw 2plw0no o1 qvpx;(
(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 strehth fgf5.e,t8tched two-part cord of Fig. 11–33. Determine hfg5 eft8. ,tha 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 greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 +lq83gyw3is tnq ezifl011 : hHz, and the tip of each prong moves 1.8 mm to either side of center. Calct 1lz wlf33gq i:q+sy01einh8ulate
(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 harbfh0xv6h:)0tc6(e pu2 sud nzes5g7 o monic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board cavf0g6hzopudn5 s:c (2xbsh6 )70eue tn vibrate 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” end if that end is attached to a lee2va 2u,r0s*vlfd( ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavdeslu , 2v l20ear*f(velengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum haka7 q ht*2xy0 mzm6dd3s a period of exactly 2.000 s — each one-way swing takes 1.000 skadxt23 dmm0z 67 hy*q.
(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 schd,2 s igkwbq)k03n9wing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the verdqb c9nk)hs0k 23gwi ,tical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

  A block with mass $M=5.0\mathrm{kg}$ rests on a frictionless table and is attached by a horizontal spring $\begin{pmatrix}k=130\mathrm{N/m}\end{pmatrix}$ to a wall. A second block, of mass $m=1.25\mathrm{kg}$ rests on top of M. The coefficient of static friction between the two blocks is 0.30. What is the maximum possible amplitude of oscillation such that m will not slip off M?    m

  A 10.0-m-long wire of mass 123 g is stretched under a-iys*k jwa+l5rvls x40 6kl*t(9u kfj tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated jyki96uv- *k0f5jl k+wsxs(ta*ll4r at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspendkfu sl.-(x3wrg)c,d w ed from a ceiling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the blod.(l-ruc wk,)3fxw sgck? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. Tmz(u1jx0x 3zk )hs1g4l lj:mihe steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the zj kls xx3m gm)0izuh( l4j:11end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate au/(4qm (obxx ajszu:/ s 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 begix(/m jz 4/uu(b:axso qns 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