Give some examples of everyday vibrat3j qddbz* 3tq+ing objects. Which exhibit SHM, at least approximadz b3j q*dq3+ttely?

Is the acceleration of a simple harmonic oscillator ever zero? I1cxpqq wk2 /j:w( u (8-cgpiwcf so, where?

Explain why the motioach)i 6y8/jytn of a piston in an automobile engine is approximately simpyc/)y8ihja6 t le harmonic.

Real springs have mass. Will the true period and frequency be largerp (ud4k pzp7:j or smaller than given by the equations for a mass oscip7pjz 4kpd(u :llating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillator (SHuv9eu. q,* yg8qsdif/v+ aj):qp/vi9d8koh rO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, lo9n qpcj98hfyr*77t and then is releasey7jq* coptl f9h7rn89 d. Describe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose time when ;(0d8ydh qf tmou;i 6lqt3a0u fzmv1+taken 6;umqfoldfq18(h+az3;0du0 mtyti v to high altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11– z ph(tmb nr-*9l+6wtl48). How could you estimate the height of tmz*p-brt t(n whl9 6+lhe branch using only a stopwatch?

Why can you make water slosh back and forth i0bajsv v7z k- 9afx8s;n a pan only if you shake the pan at a certain frequ709fav-8kzbajs s v ;xency?

Give several everyday 2vao(9-.nkd ljjwcv+ examples of resonance.

Is a rattle in a car ever a prw4j at l 0ix :zc pal5t.3w/4yh)7jwj;+yvn resonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequen .of 7xsv4dqqc02,zsvcy of its source? Whys 7s.xv o,2q0dc 4fqzv or why not?

Explain the difference between the spee t2;vu2cgcavqv/jrmk -w.b8 0d of a transverse wave traveling down a cord an/ct2 v;.vum cbjr2w08k-v a gqd the speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequxz *iz9q*()d6cvdb y3dl 6ockency notes on a piano normally have wird3 bq*z()c6 9*ov 6ilycxzkdde wrapped around them?

What kind of waves do you think will travel down a fz1+gm1dm9t ksb 3hu/horizontal metal rod if you strike its end (a) vertically from above and (bz+1/g s9bmt3f1 hdk mu) horizontally parallel to its length?

Since the density of air decreases wa:.0tabvso(3 z3 edj eith an increase in temperature, but the bulk modulus3 (:ebv dzaa3s.jt0o e B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease8od4zl / w4k7c4xl,zg.ulp7,kzqm qi in amplitude as they travel away from the/c .l,op iqzkld,m 7x4478lg4zwuz kq source.

Two linear waves have thv xwqg 8i9v;h7e same amplitude and speed, and otherwise are identical, except one has hal xg iq;8v7vh9wf the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave *4mq zprxk6rx)9 gh8 9xwf;m8bo.2fv( vu bs ocrosses the boundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity dorop ) ;xrvx(s 4m8 6zfwx8fko* q.92b guh9vmb change). Explain why.

If a string is vibrating in three segments, are there any places you could touc/,gc2.im3f,xbq rng jh it bg3x/cf j.n,q2irg, mwith a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incident a8ogfth /.bdidw0 u5c,nd reflected w.f 8iudh/dg,50botwcaves cancel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one placx zf ;ht50xh5le to another, how might we determine whether the energy wahhfz550;xlt x s being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total distas7.gip o5x2*tm i m8pjnce it travels m j7i5gxspo2*. ti 8mpin one period?    m

  An elastic cord is 65 cm long when a weight of 75 N h mh fmf* bni-8ln+frct( )/de9angs from it but is 85 cm long when a weight of 180 N hangs from it. What i +bn)ff8d(-rm ef*n9/m ihlcts 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 drivf )zz9qtij(/u er gets into the driver’s seat. If the car z/(9 ifqtujz) goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale 0lbpuv:d d; dlvp*48e6-irw bstretches 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the sprivd:bp4 8p*;-di l vreb lw0du6ng 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 is hv3 xy87zxfd mq*)z-4obh9s epzf5x7f qzhg 08 ung from it. What is its frequency if only 0.38 kg hangs from iedx7mxfz o7f xfy*9)-qzp8 g85 4zbvqhz0 3s ht?    Hz

Construct a Table indicating the pbw/y.g n3e:9 l2fvu6e1 28wvp -iva6hlao wthosition x of the mass in Fig. 11–2 at times t = 0,t - ga2/bly6wv e983utvwl2v6h.aofnpiw:1he = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web. The web vibrates predo ilwmjxog 29(c9fkqgt7n0 . zr9c r0-sminately with a frequency of 4.0 Hz0(79crks 0-j99 nfxz mi2l ogct. rwgq.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency of 0.88*2hydp ljv.9l1qaz8rs g 04zb Hz. When an additional 680-g mass is added t14r.l b*8j2 q0pdh zglsv yza9o m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end dgzcz ;b4f bg,uz4);*mqfc u)of a spring vibrates 3.0 times per second with an amplitude of 0.13 m. Dz4g;)bz*cgufu ; d 4f,mbzcq)etermine
(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 iug b407au (tbpd8 jw4eltg;3ws the speed of a SHO half the maximum val( dpgb 8wu0e4 ;374jgwuttbla ue?$\approx$    A

A mass attached to the end of a spring is stret /;hs- vyrxnar + /bng ibihwd0bdk0h62d2.4r ched 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 aetvf +,iguef/)pz(f - vertical spring 0.315 m. If the spring is stretched an additional 0.130 m and r i-vugp,e t+zfe/(f f)eleased, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3 4 zxjo1epik;5.0 kg 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 jekx4 1;o5 zpiposition, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a toy popgun 0.20h f/jd93wbz5baab c p b73ui6:ji oh;-0 m to “load” a 0.180-kg ball. With what speed will the ball leave the gu jfb bhh:35bo3/u a-ijap 9;6 c7izwbdn?    m/s

  A mass sitting on a horizontal, frictionlvp-3t)hlz)ado mb7e17 ywer+ ess 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 sprin)vhb)77empzr -1+l a tyw3doeg 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 x =;2kiv0kl 6ds3x. uolf 0.45cos6.4t where x is in meters and t is in secon306 o;fkl uld.2ixsv kds. 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 half PEhs,q)em n,9sqap :4d c? ±qp n49): sshd,m,qcea    A

  If one vibration has 7.0 times the energy of a second, but their fle:wh :k,y rlhrc0 1pr :bo)1irequencies and masses are the same, what is the ratio of their ye hop: w1bc:,rk0i rl1h l:)ramplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring once everna8cy 0 .r+7sfisht e) ,btn.8f +nkchy 0.65 s.h7.8t h,cafi08e cr sbsfyn+n nkt+).
(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 idenfgcp*ci u(1mg x.c+*qtical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). +g(mc* cgfxu.c i*1p qWhat will be the frequency of vibration?

  A 300-g mass vibrates according uxgm/(ygmj 4 o-l3gvu. nr9pth52 j8j to the equation x = 0.38sin6.5t where x is in meters an 5gl.hvnj-2 ggj3( rut8 jy poum/x9m4d t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows twu yb9mh.wbay0 s/4: vsjf+xk(hp e4(co examples 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 mv a3 fxxz,k;w gds,2xlp6+ 1wa horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s D6xa; glw3,,d12zpsmx wx+k f vetermine
(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 stif-gnp p)jrf1z7fness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. Tp)1r jfgp z-7nhe mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, witc45r/ ,ek giw6u ;g3gzm)fvhbh 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 6pbl5n(v*s tljtg7) nattached to a fixed horizontal spring whose spring stiffness j)bs(l pg v6ntln*t57 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 mas ym+2hdt,nrjs09 ks5k s 65.0 kg jumps from a high bridge. After reaching his lowest point, he oscillates 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. Calchrdkm2 9jt5n ,k0s+ys ulate 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 vibrati8tr4 + 4mmkahxeblm- 7ons in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactlyy+.l4s * eppp2n jw+bu one swing per second? (That is, onenlubjy.w +p2ep p*4+ s complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What isd/ xie saqa1,.:5nly h its period on Mars, where the acceleration of gravity is about 0.37 ty1 :d./nqeiaahls 5x, hat on Earth?    s

  What is the period ofmryr;1 /0-pckv( ihzp a simple 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 pendu -8lx c:2rxfb *mk0tedlum bob has a mass of 365 grams, and it is released at an angle of 12.0xr 8d-kbtfcx l:0e*2m $^{\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 clo8n*ri /pc b h-yb6e1o92 ik+zb 7z7v cjamv:ahck loses half a minute per day:ib b/voh2pz bc1 iaa c*-7kn+hv86ezyr j9m7 , how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum s3 qqschx:0mj5peed $v_{max}$ 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 released f.0 rzkf8q,ahurom rest starting at an angle of 1.0a r8uf zk,qh5 $^{\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 b unr4at8q :s5zf9: q7bgust:that wave crests pass the bow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast ar:4 7rnq g8utb:q9sb:u fs5 atze the waves traveling?    m/s

  A sound wave in air has a frequency o5ajbzi-+yji o1 r1r g)f 262 Hz and travels with a speed of 343 m/s How far apart a1zrijiy5r j) +bga1o- re the wave crests (compressions)?    m

  (a) AM radio signals have frequencie aegdi/ k*m nvf,x4ryy- mv604s between 550 kHz and 1600 kHz (kilohertz) and travel/kyvm04a 4giv*m r n-d,e fyx6 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 longijt r5t *1rq 4w+8 z0+z dy3whnedxj4dvtudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as o4sxfg; d7dlyzis bu5,5m2*)0axns w dense as the other. In which rod will the speed of longitudinal waves be greater, and by ,0*xmd yxsbso7)sld g5z4 wnafu i2 ;5what factor?   

  A cord of mass 0.65 kg is stretched betwe3itw 0v*9o)om -sequ wen two supports 28 m apart. If the tension in the cord is 150 N, how losoo- 3weuqti90)mv *w ng will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of lj5b./f fdsszh0u + zo:ength 620 m and diameter 1.5 cm bd.fs+ so 0/hf5jz:zu. 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 surfr ih9jn6) fuytpk :10jace of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How dee06kr 1 p fny:u9jhtj)ip is the ocean at this point?    m

  P and S waves from an earthquake bbe77dvtj c 8+travel at different speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbance took plac7 j7ecdtb +8vbe).
(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 e; 6q7 e9kq zb0hav.ijapproximated by a sinusoidal transverse wave. Assumi e.q6bah7 vki;9j 0zeqng a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplit rd4jz 18wgjf: vpbgm i7yf9-a,(t1k)w1ykigudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km m i:k1819)j,yi-rw k 4jv 7azgw(fd1gpgfb y tfrom the source?(a)    (b)   

  The intensity of an ea s. jip3,iheb *u-u3d9cz(efqrthquake wave passing through the Earth is measured to be ju3-pee, h i b3.qic(df sz9*u$ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency travel throu8d+ 8oh a5 1kampe3omsgh the same portion of the Earth, but one is carrying twice the energy.+aeha8o58so31 p kmm d What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along g1wn,lwn07u2afb /lg z a9sai+v9w :ga stretched string have the same frequency, but one transports three times the power of the other. What is the ratio of the amplitudes of t 2lnf9gwzs/w giv+a7waab 19 lu0:gn,he two waves?   

  A bug on the surface of a pond is observedu ,hcd9 ez3gt* 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 the bug’s maximued*h9gu zt3,cm KE change?   

The two pulses shown in Fig. 11vr3myo0, tpzgohfl7-j6+/ v m –52 are moving toward each other. (a) Sketch the shape of the strv + lzrmmytoo f-,h6g70pv/3jing 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 pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrq;; ip ,foi 80oc3hklbates at 440 Hz as its fundamental frequency, what are the frequencies of the first four harmo ifb ilho;q;p3o,80c knics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingeredkwb ;rr:0i . d*lho;rn. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrateswo 0rrhkl;n*. rib: ;d as a standing wave.)    Hz

  A particular string resonates in four loops at6:qtv8yiz.vb bu dm2 9 a frequency of 280 Hz. Name at leastz6.t b9vd8buvqm 2:yi three other 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 frequen 4pj4o* vico-dcy of standing waves is 475 Hp*4i -odjc o4vz, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrz; 0rb aav13z zzmeh ;*4qhma*ating string are 280 Hz and 350 Hz, what is the freq;mh *3zz;z a0*zq1 aeahb4vrm uency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance from the v4f p3ifjk(; rbridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first ;fri34jk pf(v two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is me*n c gd8h-nbd2vq:rf1snv8/i 5d z,gfasured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequencies gd/8f-b1dcz,2rd:i sv5 qnvn8 nhf*g are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is suppootaqb6he i .tu c204e 11m y+qzjn2f5ssed 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 corz qeym1utfjt bhesc0o6q24n 2a .15i+ rect the frequency? decreased by    %

  One end of a horizontal sh 2pr, aq rhymn(n7;b+tring is attached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass per unit length is;,+a (n7mn hy2qh brpr $3.9 \times10^{ -4}$ 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 adjk7j x3sst6ia5ey5z36 so se k-usted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many difk js 5s3-ie 6a76sxesotz3k5yferent 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 jusem.w u3+7sb6cyta0luwk a 534 cw )r8s,ekahht the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produyk0w s +3wa7a 5smuw archce 6tl3,.ubh4k)8ece 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 strikerix-*gkclu 53,ki v-u s a boundary within the Earth betweenuixv cg3 ir-u,kk-l5* two kinds 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 underwater “shelf” where the velocityrkc5p-(l+jqz r bod -2 changes from 2.8 m/s to 2.1 m/s If the incident wave crests make a -bd2o-5rlczrj p(k+q34$^{\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 layem5j2 vokr p60tr of cold, dense air. If the sound wave hit0trkv6o5m 2pj s 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 .zqsznbtv *5mo *s2m,rock at am nzsos*52 m,*z .tqvb 38 $^{\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 diametuhcgfi v;o3w q+k2 c(7er. According to the user’s manual, the dish has to bgk 27cvuh(fi;w co3q+e pointed in the direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocitys 4lkyh2fwo7 5yd .u rr.m1yk/ 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people osumoy/kyd .wf1kh 7y5r2l.r4bserve 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 stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffnk8x-e1gx yu7lp4tm92(ht . p2 nzjhy8flqrx3ess 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). [Hint: Use conservation of enp yluj7x9h 3 ty4nt 1exzqk 8-pmx g2rh(28fl.ergy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, wa50o b8(qj t*r/v qqpohich stretches the net 1.1 m. Assume that the net behaves like a simple sprin a5o(jtb rpq80vq *oq/g, 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 fre+i t,gll) )jihely hanging spring. The mass then falls 33 cm before itjtl hil)i), g+ stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huguyl)l xu6/) .i ufe)ree spring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) Whalyu)ie .lr)xfe)6u u /t 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 (diamete d-9d/b5ljso g7ae-pqr 8 cm) at just the right pace of about 1 step per second, t/ge9d bo57-qpa-sjld he coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-rpm phon.n ygt;ligz a -vlk*74ograph record have a wavelength of 1.70 mm. What will be the frequg-nvl*.a tiy;74klzgency of the sound emitted?    Hz

  A 2.00-kg mass vibrates accordhp1ms s;g*o ;qing to the equation x=0.650cos7.40t where x is in meters anhqm;ss *p;1g od 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 frequk/bt7 trukj:(ency if it accelerates at 0.50g (a) upwarurjk tt:k( /b7d,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the rqufk2 eg*,yz9rg;tq+ aft, it sinks 4.0 cm deeper int* ,fq ;9kggrz qeuy2+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 are tuned to play at 392 Hz (G) and 440eo ae4et u a3w3l0yofjal7 /5+ Hz (A)3 twalyj5ue7 f+3olae a /0oe4.
(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 travel.dxk+qrbant4e */3m aing down the stretched two-part 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 frequencbertda* . ma+xnq4/k3y 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 2bty nn:ma/+a7b 0xens;-s9 md xqee8-64 Hz, and the tip of each prong moves 1.8 mm to either side of center. Calculyexmsa/ -:qb 0aexn;9- 7dsb+mnn te8ate
(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 motion of frequency 1.5 cycles2alga oa mf9-). vb5at per second. What is the maximum amplitude with which the end of the boarao) gb5.9amlava -2tfd can 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” en 9 ayxsmu7hqatb2i9 uu ,g8gt1b.((hnd if that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of u( 9x.u myg2h(uh,7bna 9qtsi1a8gtbthe resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each ldr4+*2dds ( nuwn/qvet-9ulone-way swing takes 1.000 wd2uu-d4tdllr* senq+n / (v9 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 oscill k64 ftold-g *xekzhr/cd vpk.um065*ate in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the p/60x*kr kckzmd 54u6*.lhepdtgfo -v eriod 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 tr,k+ z8iug cf(ension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Whf r i8gc,+uk(zere will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with sprdc3 *os 5nq-fying stiffness constant k. A penny of mass m is pl- c *n3fsdy5qoaced on top of the block. 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 car at the junkyard. The steel crane cable is s9r83xbwf+ 1gubgg+ ika2 2ho22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the endf2g1krxu3 h 2sowbagi9g+8+ b 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 as shown in Fig. 11–58 (wh1 kooa rw,fkj2b;f ;utp7r t0v pd(*4bich also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate p1bv pj;tr, a2u04* (korf fdwtk;o7bthe 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