Give some examples of everyday vibratqjwg (ly4z)pnn/yiz26 c(g 1ying objects. Which exhibit SHM, at least apprnqy) z42w(gzp/n1y lcg(6j iyoximately?

Is the acceleration of a simple harmonid rblx8t9+ag hqy *nu g7:lt6 k;9vjj4c oscillator ever zero? If so, where?

Explain why the motion of a p aqis6s, -:,+tkei lzeiston in an automobile engine is approximately simple hae, iitka:slz,6+ -seq rmonic.

Real springs have mass. Will the true period and frequency be ipmg 0(7hlc d3larger or smaller thmd(i gh0lcp 73an given by the equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the m 36xrjqx,ndd 9aximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and spkx*( .ovl u-szy50sthen is rel -0*op(ksys 5l uvszx.eased. Describe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lo+dc;)b 7bdbi/c) tfgese time when tak;/cbdbic ))tged f b7+en to high altitude? Why?

A tire swing hanging from a branch reaches nearly to the groun6p;x p jmdhvz85di0zo5; xb g1d (Fig. 11–48). How could you estimate the height of the branchz5jp xdh8;d0p g6;xo 51zimbv using only a stopwatch?

Why can you make water slosh back and forth in a pan only if youcb3v1( o ye2t:8+4 lahm wvfhg shake the pan av2tygwvh: o 4h1f+8bcal(me3t a certain frequency?

Give several everyday examples of resonance.+oer)ypf zis:8 e /*cqwt*osi0m* bo3

Is a rattle in a car ever a r2ihm( ssh9 5cwesonance phenomenon? Explain.

Is the frequency of a simple perioms s )swhjty)k /0cx+ sbd6.y-dic wave equal to the frequency of its source? Whh)bk/ sy sc) .m+jds60tys -wxy or why not?

Explain the difference between the speed of a transve:-jsgq jecc0x t;;lwa )) r)gkrse wave traveling down a cord and the s 0kwlea )j ccsr:;tqgg)-j;)x peed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes r5l lc97 /kugpw1ulq kk vp0h)t8+q z)on a piano normally have wire wrapped a8zvg qk)w9rlt )lk1hu 0 p +lpq7kuc/5round them?

What kind of waves do you think wxm 5pb(17:fl eicjfu :ill travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) hor7i(ecux p 1:l5fbj fm:izontally parallel to its length?

Since the density of air decreases with an increase in temp4: *ez z8zh6hl)dxnrqerature, but the bulk modulus B is nearly independent of temperature, how would you expect d:h *48zhezl6rxqn z) the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitudenkqg9pf5lp / cm)ypj0wp, f 7- as they travel away from the sourc0cy,-wf7g)j9qfpm p5 k p/plne.

Two linear waves have the same amplitude and9e iar+ e2a*)k2cvq 9-pdmjzp speed, and otherwise are identical, except one has half the wavelength ofi)* kqp ep2z-+r29e dmv9jaac the other. Which transmits more energy? By what factor?

When a sinusoidal wave crossep7 czz7o 1bd*3jwpv4js the boundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Exp*j 77zpdz 4j1bcvowp3lain why.

If a string is vibrating in three segments, ar1f;lyqxoj e-s.lof(quz: k *2e there any places you could touch it with a knif :quo;1j l.y *l2 f(eqkosxz-fe blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incident and rclqy2l:qj y0i arp9o b6q0o0 -0rhe4ceflected waves cancel at the nodes. Does this mean that energy was destroyed? Explain.r 0 92 0l horp0ejqbl0qcyi-cao:y6q4

If we knew that energy was g , *xgtx3r9nx0)(xtnhlg,f e being transmitted from one place to another, how might we determine whether the energy was beingg g*0)9t3,e gtnx ,xr( xflnhx carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total doi7gu,j6i4 8 :xgzcpk.p lt*tistance it trau67ic glp,*i8p zog.kt:4jx tvels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs f raj*v+ob z 3dg8fn0m/rom it but is 85 cm long when a weight of 180 N mgov ja+038/z*fbd nrhangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver getdw*9vwq g k-b4s into the driver’s seat. If the car goes over a bump gdbkv49qw w-*, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7- qqy6;gfmrv8*z k m8x4kg fish hangs from it. (a) What is the spring stiffne84kmmr8f g6q ;qyz v*xss 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 frequencyfw*r lbd)b,qe7m a4/u of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs from it? 4,7uqba rw)le /*mfbd    Hz

Construct a Table indicating the position x of t 1qud4tdjqy1 k+o o55jhe mass in Fig. 11–2 at times t = 0,t =d1 5 kq1jy5ojod 4q+ut $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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) ys)/ zm+g y/uevs:*gqs:g eu web vibrates predominately with a frequency of 4u g)e+ y ggu:*q)vy szs://sme.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 fre32(vs3ft xhq4 u3k4f ryas:r equency of 0.88 Hz. When an additionkx 3s4yu 2 (:4fr3heqav sft3ral 680-g mass is added to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 t(cddj(8 /( w xzm96tlpxwq zbqb ;fb v-1z(-odimes per second with an amplitude of 0.13 m. Determine(mtzj 8zbq 6xbwv;c 1- x o (fdp(-d(d9bl/qzw
(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 af-: wg 0uv ,sg.mnaw+t SHO half the maximum value v g,wgfanm0tu +w:s-.?$\approx$    A

A mass attached to the end of a spring r81 bggucvp, vmt40j1is 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. Ifug 1)(k e.yuwdl1khm5 the spring is stretched an additional 0.130 m and released, how long does kkuh)we5y11(. l dumgit take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with sb-wq94zibv se rey7 (:pring 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 movingzvs:qb e-7w(9ye4i b r with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the sp5)oz pyjq -zk8 u6y/kyring of a toy popgun 0.200 m to “loa8/p uqy6 z) 5kkjy-yozd” a 0.180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontaviu2ahoxcd+lm3xv. j 9 ,62djl, frictionless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mvi d2vhaj2.o9mx 6j cxl,ud+3ass 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 x =/3po84w )kwz 5zx dgky 0.45cos6.4t where x is in m /wok5kgpzx 34d)z8 wyeters 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 energy of a SHO half KE and ha5e + lr)ljelp6lf PE? 5+pl )rle6 ejl±    A

  If one vibration has 7.0 times the energy of a second, but thei-y a n+w)2 0wioliqzg(r frequencies and masses are the same, what is the ratio of their ampy)iaow l0w z2 g(inq+-litudes?   

  A 2.00-kg pumpkin oscillaps; yrg9 ;wg dl/f. n7zvx4u: 2hzyjq)tes from a vertically hanging light spring once every 0l.pg:znr v 27wjfz4g /s;y9qh ;x)duy.65 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 supportedyif 2rwmoxn/;5t n3m- by two identical parallel vertical springs, each with spring stiffness-f2nn t/ x;3w5iyo rmm constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t w40;. qxg5htu uovi.ib+gwa ( uhere x is in meters and t isuu;.+ov(h 0t axigw iu.bqg 54 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 exampleskue3ta*itwzlfo.n 3180ot exgmf; m(. :wd+ b 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 horco1ioro5k cws2 so/;1izontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Des1;c5/c2koo w s iroo1termine
(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 stiffnessxggo/i8)(k rk constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The m/k(kg 8ir)xg oass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring stiffness cu, hys5pj-ydpu,q+sbe f )1x,onstants $k_1$ 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 sp nr sm 2,4alh.a1,fbjfqn4lj7ring whose spring stiffness constan4 s qalbm7l4rj fh,2,1a nfjn.t 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. )d,krrrd neag 8qc)4 ( fps )9:wtjen-After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comesp r9wjs)n kr)(d4- anrdge,fcqt: 8e) 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 e/:8tumrczo*q xactly 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 oner.y qya9,w ,t uh iw)wzira/(1 swing per second? (That is, one c,qyyih1(9wu,wraazr/) w t.i omplete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is itrw rvsuti nx6v/2t3x mqr(1 4(s period on Mars, where the acceleration of gravity is about 0.37 that o/(x (rv6r1x4iu2vwm3q sntr tn Earth?    s

  What is the period of a simplevw,5 bssiv8xtz (le: 1 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 ha(+m+alw* uwlc s a mass of 365 grams, and it is released at an al(u+m clw*+wangle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 m. If the clock los(-. 3dne zbzws-xe j/n45trnn es half a minute per day, how should you adjust the length of the pendulum? shortn/n -z3 jr-e(xn sw5td.ne4bzened by    mm.

Derive a formula for the maxii2mqmzah,*j3 : . bl8gjm2tv ymum 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.z +)ke0ffepu:kqx eh; . 18,yf:mtrsn At it is released from rest stafhe8 fn;f0 k.p,: eem 1:tu+zky sq)rxrting 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 togi(cv y4m 34that wave crests pass the bow of his anchored boat every 3.0 s. He measures the distan o(mi3y4t4c vgce 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 travneu*)q yvrk22 els with a speed of 343 m/s How far apart are the wave crestsvqr)ueyn k *22 (compressions)?    m

  (a) AM radio signals have frequencies between 550 gnd86y6atr*0tg v-ho1yiu q2 kHz and 1600 kHz (kilohertz) and trny or 1gq2d- 8ut6avyh*6git0avel 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;06 vy2itab :s6(pwn1u mrpjo longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic qu z*1*i/v 5 xftop d/oc62q6ujfvw.gmodulus, but one is twice as dense as the other. In which rod will the speed of longitudinal.*2z1fovx c u itfp5q v/god*w6u q6/j waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supporr7iq.gg tqfw. pf; (r6ts 28 m apart. If the tension in the cord is 150 N, how long will it take a puq. 6r;ftqf.r(7i gpgw lse 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 length 62-w*(xd6ngx g-6dfuo x0 m awd6 nfx6--(g x*xgd uond 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 the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the surfacv)04 tben(a fze of the sea. He hears the echo of the vne4 )t0(azf bwave 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 this difcjzx4: 1elf2nyy06dtxji+ 6m nbnr ,)ference helps in locating the earnz+e )fn02yjy:n x4t1c6m ixdj6,rl bthquake “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 suyo k u)t(s.rqsak3l;7:-yifrrface wave can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0t.-q3 l)akk( ors7y ys;:iru f.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, ahy 5upc rce +unx:1a)7nd (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two poinu c1n5e)ap +xuc: 7hyrts 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave ktz )loy5iyo2*jx 81opassing through the Earth is measured to be 5t j2z)xy8i*o oyo 1lk$ 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)*di uq k htf(bl7x6q; the same frequency travel through the same portion of the Earth, but on7uf qqx(l*b6;thd k i)e is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the sama( 50m *yqrppzw1ux 2ue frequency, but one transports three times the power of the other. What is the ratio of the amplitudes ofmuu*z qrw( 0pypa2x51 the two waves?   

  A bug on the surface of a pond is observed4gon llnb9v8o+ i4 (fz 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 factor does th( 9i4o +f8nbznlg4v ole bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving t5 yk 1cwv669ynkdh-m wn: to*toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pa 6ktk m-:nvt1c*59yhywdnwo 6ss each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, wha (vks7sssv)9/ l m+pcwt are the freque7wmsps/9 lkc+(sv vs)ncies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequw / p11 0e2efldwkdnx0ency will it vibrate if it is fip dl / wn2x1e1d0ew0fkngered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four lojmmcvp5 , xt2;ops at a frequency of 280 Hz. Name at least three other frequencies at which it will resonate. mv ;5tc2pj m,x$f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If)6mrmgum+cdc w7, e3x the frequency of standing waves is 475 Hz, hrgc ) u,7dmcxmw6+em3ow far apart are two adjacent nodes?   m

  If two successive overtones g8 x f+1oa8,8xb.fd7n (ii:xvzbhlh) fj p(ioof a vibrating string are 280 Hz and 350 Hz, what is the frequency of n8 (izfia:x 8o)d v.+ji b8,bhxog(f7xhpl1 f the fundamental?    Hz

  A guitar string is 90 cm long and hfxbaas 1o9 w6)as a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencie6f91b x ao)wass of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is ulq, o/lvy8/z measured to vibrate at 205 Hz. By what percent should the tension in the string be cqoll 8/u/ ,yvzhanged to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz8j9wue)ktea/y*p cq01 bpp1 y, but it is measured to vibrate at 205 Hz. By what percent should the tension in they8pwyu0 j9 etcp/ap eqb)*11 k string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amw-w.2b 0udfi*g c 3ecwplitude mechanical 60-Hz vibrator. The strfwc. w-*0cw 2biuged3ing’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 string may be adjusted by moving t2gfhpjxd9v x ofo;h2 .5,8lrifh8-k o he pulley. If the hanging mass m is fixed at 0.080 kg, how many diffo 5l8i-h vf2jxo;fok8xhg,.9 rphdf 2erent standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the rightbs/g:oj 9v0 ij zz k:lr)k8f)a frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. i) jjob:zrs/k:ka8zgl 0 f9) vSuppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s vy8vgo5(os 7b0h2nh 3,*lah v ilio5 hstrikes a boundary within the Earth between two kinds of material. If it approaches the boundary ,8ohal*vv s7 i52ohh03b(vhg5y lnoi 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 t 0+x1 a;nh-yro bu32pr +)yais k4gulwhe velocity changes from 2.8 m/s to 2.1 m/sbx4l;ag1rhyu++nk0si3y2 ) uwp o- ar 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 layer2(x kk) 5ghlwr of cold, dense air. If kg2 l)khr 5xw(the 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 l+ +j0uhzfo22 u izv8awave strikes a boundary between two types of rock at a 382+iuo +ja z8zlh2vf0u $^{\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 to the user’sy/,hvht:an 2r manual, the dish has to be pointed in the direction of the satellite, but an error of abouttryvhh,a:2n / 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and 2 adfky 4vnd.(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 knowledgydd42kan (f v.e 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 kN/m Find.;wegm: qht3 132:gv+bxr n dewfwa0v the maximum compression of the bumper if the car, with masegah b.3 +e0n; wq2:v vgt:dfww1 m3xrs 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m ben:d xt+(nf*dw cl 6)9d6b ;y1jdlc ptrlow, which stretches the net 1.1 m. Assume that the net behaves like a simpl6*+tf(9 d6l dtdc1)c rnbjdw;ylpnx :e spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hanging spr,.q/ nt(idmu; jc*v nzing. The mass then falls 33 cm before it stops andtijqc,;n vu/nd*(z m. begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge springizu (ascdn---hm.5st at a speed of 22 m/s (Fig. 11–54), compressinhsum5-( t-zn dca .s-ig the spring 5.0 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 of coffee (diameter 8 cm) at just the rigf:bh0q4sra n9j :1xbght pace of about 1 step per second, the coffee sloshes more and more until eventually it st:41:n hj9rab 0xbfq sgarts 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 thkt keb7wd5l0us1u)6. ,mmqes m2w / gle center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be thed2uwsgk/m6btwl m.0k 1 me75l )e ,squ frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates accordzenro w 02,3bming to the equation x=0.650cos7.40t where x is in men03o b ,rwzme2ters and t in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. What is its fr .uf e. .npw9izj-m7tf:agkk7 equency if it accelerk-k 7.enput. 9w f7.amji:fgzates at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 7po.edah xu- 9h.e7 u;4vcy9br5-kg man stands on the raft, it sinks 4.0 cm deeper inxp9;- .9vueyd a.oh47rubch e to the water. When he steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument ar-tq -gu6-eoahe tuned to play at 392 Hz (G) and 440 Hz (A). 6huea tq---go
(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 tra pja vy04bphk1z:q.s1veling down the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of ts1: kbyj.1p pa4zh v0qhe 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 fr l( o)jxsz4bk4equency of 264 Hz, and the tip of each prong moves 1.8 mm to eithek4jo (bsxl4)zr side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simjx 5q irihtpn b/0c81-c5 yb)gple harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) wiln/ctr8 -1)qc0bgpyb5 5 jihi xl not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a ring that can slidf(m+ 6osvj /gn n-x+0ig a7qvqr1gm6pe without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a st-qpja(gs0o/ vgiv n6mfrgx1+q +m67n ring with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — -m9vq5jtyih9/f 3dhceach one-way swing takes 9j/3hy tv5-hid9 qfmc1.000 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 vcuc v 1-vtxu rd3es-:3zm v:v,ertical direction or can swing as a pendulum of small amplitude, but not both at the same tx:-u1v 3 d :mrc-scvu,v3ezvtime. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched under a tension of-1 giqv2awx4-fe-ers 255 N. A pulse is genfxi 2wr4e1g ev q--a-serated at one 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 sw v9it jiw)ngj(x 3kj (s*h7.xtiffness 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(i jxjs*. g7(w3thi9kj vwx) n block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cable e c o0gz2kgpql7(*/utis 22 m long and has a diameter of 6.4 mm. A breeze starts the k7/ oe*c pg t0l2gzuq(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 plate m sfi: 6xe.tr pgw5yvfxq 4,oog*v:90as 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 txf9oyegv :,ps wr*ovfgit4xq.m 0 5:6o 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